QR ‘EHE FEQBLEMfi G? NGNRES?O§~E§E
ANS EMFfiQPER REEFONSE Y6
CONFERMATIOfi REQUESTS

“Waste {'05. fin Degme 0‘? Ms. D.
fiflCiiEGiaR SHTE UNEE‘ERSETY

h r *-

Endgame £1. 5&943

1%?

This is to certify that the

thesis entitled

ON THE PROBLEMS OF NONRESPONSE AND IMPROPER
RESPONSE TO CONFIRMATION REQUESTS

presented by

Eugene H. Sauls

has been accepted towards fulfillment
of the requirements for

Ph.D degree in Business Administration

”Kw/M .5 M5:

Major professor

/’
Date Mfiw’fiky le /<7é/
/ I

0-169

 

-—r “’*‘--—u

v ~_.~. aya.‘ -..

 

m-v-J—o—nvuM

ABSTRACT

ON THE PROBLEMS OF NONRESPONSE AND IMPROPER
RESPONSE TO CONFIRMATION REQUESTS

by Eugene H. Sauls

The circularization of accounts has been a standard
auditing procedure for many years. There has, however,
always been some who have felt that the inadequacies of
this procedure have not been fully recognised.

The two major shortcomings of the circularization
of accounts are: (1) some of those to whom a confirmation
request is sent do not reSpond and (2) the auditor cannot
be sure that those who do reSpond checked their records.

These two shortcomings lead to errors in estimation
which are reSpectively called nonreSponse and improper
reSponse errors. NonreSponse and improper resPonse errors
are members of a larger class called nonsampling errors.
Nonsampling errors are those errors which would exist if
each account were circularized.

The effect that nonreSponse and improper reSponse
errors have upon the estimates of the accounts has not
heretofore been determined. It is principally to this
end that this thesis is directed.

Hypotheses were formulated concerning the behavior

of confirmation request recipients. These hypotheses

Eugene H. Sauls
concerned reactions to confirmation requests which reflected
correct amounts and requests which reflected incorrect
amounts. Hypotheses concerning reaction to various forms
were also formulated.

These hypotheses were tested by means of statistical
tests based on results of experiments conducted on deposit
accounts of the MSU Employees Credit Union and loan accounts
of the Continental Illinois National Bank and Trust Company
of Chicago. The eXperiments were conducted by sending out
confirmation requests which reflected incorrect amounts as
well as confirmation requests which reflected correct amounts.

These tests revealed that improper response is an
important variable which must be dealt with by the auditor.
They also indicated that«nonresponse, though prevalent, may
not adversely affect the auditors' estimations concerning
the accounts.

Recommendations are made, based on the results of
this study, of means by which the auditor may avoid improper
reSponse and circumvent nonreSponse errors. These recom-
mendations can be incorporated into the statistical samp-
ling techniques currently employed in the auditing profes—

sion.

ON THE PROBLEMS OF NONRESPONSE AND IMPROPER

RESPONSE TO CONFIRMATION REQUESTS

BY

Eugene H. Sauls

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Accounting and Financial Administration

1969

Copyright
by
Eugene Howell Sauls

1969

ACKNOWLEDGMENTS

This dissertation could never have been completed
without the assistance, counsel, and guidance of my fel-
low graduate students, friends, and faculty members at
Michigan State University. To these peOple I am eternally
grateful.

William Morris and Jim.Parker conceived with me the
need for and possibility of this study. They graciously
. allowed me to make it Operational because I was then at
the dissertation stage. George Murphy and Elaine Ritts
assisted me in the conduct of the field work. Charles
Conley aided me in certain statistical aSpects but even
more importantly, in obtaining participation. To Mrs.
Frances Lesnieski, General Manager, MSU Employees Credit
Union, Mr. Thomas Foster, Chairman, Supervisory Committee,
MSU Employees Credit Union, and_Mr. G. Gardner Davenport,
Vice President, Continental Illinois National Bank and
Trust Company of Chicago, I am esPecially indebted; with-
out their help, this study could not possibly have been
done. Professor Robert Jensen, of the University of Maine,
encouraged me, counseled me, and reviewed the first draft
even though he was in the process of moving to Maine. He
gave me more than his time, however; he instilled in me

an interest in research and knowledge. To my dissertation

ii

(xxmnittee I eXpress my sincere appreciation. Professor
Herbert Miller (Chairman) , Professor Richard Lewis, and
'Professor Geraldine Dominiak not-only directed and en-
<couraged me but conscientiously eXpedited the completion
of the dissertation. The many criticisms of my committee
members immeasurably improved the quality of the final
product.

To Professor James Don Edwards, Chairman, Department
of Accounting and Financial Administration, I wish to ex-
press a special note of thanks. I, as do other doctoral
students at MSU, owe him a debt which cannot be repaid.

He has made us proud of our association with the Depart-
xnent of Accounting and Financial Administration of MSU,
both within and without the university.

The American Accounting Association, the Department
of Health, Education, and Welfare, and the many contribu-
tors to the fellowship fund of the Department of Accounting
and Financial Administration, through their generosity, have
allowed me to work full time towards the completion of my
degree.

To my wife, Frances, I pay tribute. Through crisis
after crisis she remained steadfast. She never complained
and she was always sympathetic. She made these trying
times very pleasant and happy times for me. The comple-
tion of this dissertation is due in large measure to her

efforts.

iii

TABLE OF CONTENTS

Acm OWLEDGmmT S O O O O O O O O O O O 0 O O O O 0

LIST OF TABLES O O I O O O O O O O O 0 O O O O 0

LIST OF ILLUSTBM IONS O I 0 O O O O O O O O O O 0

Chapter

I.

II.

III.

IV.

PRELIMINARY CONSIDERATIONS . . . . . . . .

IntrOdUCtion o o o o o o o 0
Limitations of Confirmation
Procedures 0 o o o o o o 0
Prior StUdieS o o o o o o 0
Statistical Sampling . . .
Liabilities vs. Receivables
Purpose of Study . . . . .

HHHH HH
0 O O O
ountflp RNA
0 O O O O

O O O O O

O O O O O

O O O O O

THEORETICAL CONSIDERATIONS . . . . . . . .

2.1 Behavioral Reaction to Confirmation
RequeStS o o o o o o o o o o o o o
2.2 HypOtheSeS o o o o o o o o o o o 0

DESCRIPTION OF EXPERIMENTS . . . . . . . .

3.1 Description of Credit Union
Experiment . . . . .
3. 2 Description of Bank EXperiment. . .

RESULTS OF EXPERIMENTS AND ANALYSES OF
RESULT S O O O O O O O O O O O O O O O O O

4.1 Results of EXperiments . . .J

b. 2 Analysis of Results of EXperiments
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

Summary Of Results 0 o o o o o c o
COHCluSIOnS o o o o o o o o o o o 0
.Recommendations . . . . . . . . . .
Recommendations for Further
ResearCh o o o o o o o o o o o o o

uuntnUx
cwnnnd

iv

Page
11
vi

vii

1o
11
21
22
28‘
28
33

51

110

APPENDICES . .
Appendix A
Appendix B
Appendix C

BIBLIOGRAPHY .

Page
112
112
115
118

121

LIST OF TABLES

Table Page
1. Summary of Responses to Deposit Account
confirmation RGQueStS o o o o o o o o o o 67
2. Summary of Telephone Calls and Visits to
CredltUnlon.............. 69
3. Summary of ReSponses to Loan Account
Confirmation Requests . . . . . . . . . . 71
A. Summary of Telephone Calls to Bank . . . . . 72

vi

LIST OF ILLUSTRATIONS

Figure Page
1. Behavioral Reaction to Confirmation Requests . 29

2. Dichotomization of Behavioral Reaction to
Confirmation Requests . . . . . . . . . . . 29

vii

CHAPTER I
PRELIMINARY CONSIDERATIONS

1.1 Introduction

In regard to the question of confirming

receivables by direct communication with
the debtor, the following recommendation
is made:

That hereafter, whenever practicable and
reasonable, and where the aggregate amount
of notes and accounts receivable repre-
sents a significant portion of the current
assets or of the total assets of a concern,
confirmation of notes and accounts receiv-
able by direct communication with the
debtors shall be regarded as generally
accepted auditing procedure in the examina-
tion of the accounts of a concern whose
financial statements are accompanied by an
independent certified public accountant's
report, and that the method, extent, and
time of confirming receivables or a part
thereof, be determined by the independent
certified public accountant as in other
phases of procedpre requiring the exercise
of his judgment.

This statement of position, issued by the Committee
on Auditing Procedure of the American Institute of Accoun-
tants, was the first in a series of similar statements on
the position of the Committee concerning the procedure of

confirming accounts receivable.

 

1Committee on Auditing Procedures, Statements on
Auditin Procedure, No. 1 Extensions of AudIti Proce-
dure, (New York: *ImerIcan Institu e of Accountants;
October 1939), pp. 7-8.

 

2

The Committee on Practice Review of the American
Institute of Certified Public Accountants stated in 1966

that generally accepted auditing procedures

require that in all cases in which receiv-

ables or inventories are material factors,

the omission of confirmation of the receiv-

ables . . . with reSpect to the latest 1

balance sheet should be disclosed . . .

This thesis is an examination into the problems
connected with the confirmation procedure. More Speci-
fically, it is addressed to the problems caused by those
recipients who fail to reSpond and by those who reSpond
that the confirmation request is correct when in fact it
is wrong.

There are four questions which must be resolved
by the auditor in confirming accounts. (1) Are confirma-
tions necessary or even desirable under the particular
circumstances? (2) What type of confirmation should be
used? (3) How many accounts should be circularized? (4)
Which accounts should be circularized?

In determining the need to circularize the accounts
receivable the auditor must decide whether they are a sig-
nificant portion of the current assets or of the total
assets. If he concludes that they are significant he

must decide if the confirmation procedure is reasonable

and practicable. "In auditing, practicable means 'capable

 

. 1Committee on Practice Review, De artures From
Generall Accepted Auditing_Standards ang Accountin
PrInprIes, (New York: *American Institute of Certified

u 1 c ccountants; 1966), p. 3“.

3
loff'being done with the available means' or 'with reason
or prudence': reasonable means 'sensible in the light of
‘the surrounding circumstances'."

The type of confirmation that can be used is
either positive or negative. A positive type confirmation
is one which requests the recipient to reSpond whether or
:not.the amount reported on the confirmation request is in
agreement with his records. A negative type confirmation
is one which asks the recipient to reSpond only if the
amount reported on the confirmation request is not in
agreement with his records. In general, a positive type
confirmation should be used if the amounts of individual
accounts are large, if there are indications that the
account is in dispute, or if there is reason to believe
that a negative type confirmation will not receive the
proper attention.2 A negative type confirmation may be
used if there are a large number of accounts none of which
has a large balance.

The number of accounts that the auditor should
confirm ranges from all of the accounts down to a sample

of a relatively small percent of the accounts. If.therei

—_.__

1Committee on Auditing Procedure, Auditin Stand-
ards and Procedures, (New York: American Institute of

CerEIerd PuEIIc Accountants, 1963), p. 38.

2See for example Norman J. Lenhart, Philip L.
JDefliese, Montgomery's.Auditin , 8th ed., (New York:
{Phe Ronald-Press Company, 19 , p. 175 or Howard F.

Stettler, Auditin Princi les 2nd ed., (Englewood Cliffs,
N} .J.: PrentIce-RaII, Inc., I961), pp. 158-9.

L;

are only a small number of accounts, all of the accounts
Should. be confirmed. In the usual circumstance (where
'there are a large number of accounts) a sample of the
accounts may be confirmed, under the assumption that the
sample represents the population of the accounts. There
.are two forms of sampling: judgment sampling and statis-
tical sampling. Judgment sampling is a subjective
determination of the number of accounts to be confirmed.
Statistical sampling requires the auditor to establish
certain boundaries of acceptable results which in turn
determines the size of the sample. As pointed out by
the Committee on Statistical Sampling of the American
Institute of Certified Public Accountants, "Only after
the auditor has Specified in quantitative terms, the
levels of precision and reliability which are acceptable
to him may statistical sampling be used to determine the
size and other characteristics of the sample to be drawn
for the audit test.“1

The selection of the Specific accounts to be con-
firmed can be accomplished by a selective sample or by a
random sample. A selective sample is one in which the
auditor selects those accounts which appear to him to be
the ones most likely to be misstated or the ones whose

misstatement would have the greatest impact upon the .

 

1Committee on Statistical Sampling, StatiStical

Sam 11 and the Inde endent Auditor, (New YorE: American
InsEIEuée o? CerEIerg PuEIic Accountants, i961).

5

statements. A random sample is one taken without regard
to the condition of any of the accounts so that each
account has a known probability of being selected. A
random sample is required for the use of statistical
sampling techniques. The use of random sampling does
:not preclude the weighting of accounts with large
‘balances. If some form of weighting is desired, it can
be accomplished by stratifying the accounts and confirm-
ing a larger percent of accounts in one strata than in

another strata.

1.2 Limitations of Confirmation Procedures

There are two types of errors that may occur in
any sampling technique which tend to reduce the effec-
tiveness of the confirmation procedure; sampling errors
and nonsampling errors. Sampling errors are those errors
which occur because all of the items in the population
are not examined. Statistical sampling has the desirable
attribute of quantifying the probability of and the extent
of sampling errors. Judgment sampling, on the other hand,
simply assumes that the probability of and the extent of
Sampling errors are within a range which is acceptable to
the auditor. Nonsampling errors are those errors which
would occur even if a complete census of the population
were taken. Professors Vance and Neter suggest that non-

sampling errors may be more important than sampling

1
errors.

There are two major sources of the nonsampling
errors which arise from the circularization of accounts:
:nonISSponse and improper response. Nonresponse errors
arise when the recipient of the confirmation fails to
reSpond to the request. Improper resppnse errors arise
when the recipient confirms the amount (i.e., states that
the amount is correct) when in fact the confirmation is
not in agreement with his records or when the recipient
states that the amount is incorrect when in fact the
amount is in agreement with his records.

NoanSponse is obvious whenever positive-type
confirmations are used but when negative-type confirma-
tions are used it is not possible to determine the extent
of nonresponse. The problem of nonreSponse can be resolved
in a number of ways. (1) The auditor can assume that the
recipient would have reSponded if there had been a dis-
crepancy. Such an assumption was advocated by an unnamed
practitioner in answer to a question posed in The Journal
of Accountancy. This practitioner contended "that any
debtor who disagrees with the amounts shown by the
accountants' confirmation form will be sure to reply" and
that the accountant"is reasonably safe in assuming that such

debtors as do not reply accept the amounts stated in the

 

1L. Vance and J. Neter, Statistical Sam lin for
Auditors and Accountants, (New York: 3055 Wiley E Sons,
n00: a PP. 0

7
confirmation forms as being correct."1 This position was
opposed by Norman Lenhart and Philip Defliese who stated
that "the auditor may not assume that failure to reply to
the request indicates that the debtor agrees with the

reported balance."2

This latter viewpoint seems to pre-
'vail in the auditing profession today. (2) The auditor
can assume that the proportion of incorrect accounts
among nonrespondents is the same as that among reSpon-
dents. This assumption is implicit in those instances
where the auditor accepts the responses and draws conclu-
sion therefrom. Since the auditor does not test this
assumption it is untenable. In Spite of the lack of evi-
dence to support this position, it is often implicit in
statistical sampling models currently in use in the
auditing profession. (3) The auditor can perform alter-
native steps. There are many accountants who advocate
the use of alternative procedures as a substitute for
confirmations which are not returned. Norman Lenhart

and Philip Defliese state that if the auditor "fails to
receive positive confirmation of a substantial number of
accounts or material dollar amount of receivables, the
auditor should employ supplementary auditing procedures .

.-.”3 Professors Vance and Neter concur that the solution

 

1Accounting Questions, Answer from an unnamed
practitioner Vol. 58, No. 5. (The Journal of Accountangy,
November 1935), p. 391.

26g.‘.1t., p. 174.
31b1d.. p. 175.

8

is "to obtain sufficient evidence from other sources to
settle the point if the confirmation cannot be had."1
lRobert E. Healy, in discussing an actual small company
case, detailed a procedure followed by the auditor to
satisfy himself as to the reasonableness of the accounts.
Healy reports that in a case when 30 or 108 accounts did
not reSpond the auditor

employed the usual alternative auditing

techniques and examined shipping documents

for the invoices in question, as well as

original remittance advices of the cus-

tomers. These procedures provided him

with the evidence that the balances were

bona fide and served as a su stitute for

the customer's confirmation.
One might ask, how satisfactory these alternative proce-
dures are as a substitute for the confirmation? W. H.
Broadhurst contends that "alternative auditing steps are
less conclusive and more time-consuming than confirmation
replies."3 Richard C. Lytle takes an even stronger
position regarding the possible inadequacy of alternative
procedures as a substitute for confirmations. Lytle
states that

iri most cases, omission of the confirma—

tion procedure, or inability to obtain a

reply where the amount is material, can

pose serious problems for the independent
auditor in obtaining sufficient competent

 

102. cit., p. 141.

2Robert E. Healy, "Sampling in Auditing is for All

Auditors," The New York Certified Public Accountant, Vol.
XXXVI, No. , May 19 . p. .

3W. H. Broadhurst, "Follow-up of Accounts Receivable
Circularization," Canadian Chartered Accountant, Vol. 86,
No; 2, (February 1965), p. 1H5.

 

9

evidence to support an unqualified opinion,

and may require qualification of an

Opinion or a disclaimer.
(b).A sample of the nonreSpondents can be taken and these
can be contacted in order to get an answer to the request.
The results of this sample are combined with the results
of the first sample and projected to the population. This
method will be discussed at greater length later in this
thGSiBo

Improper reSponses pose an even greater challenge
to the auditor than do nonresponses because the auditor
is not able to measure their effect. Historically the
auditor has accepted a confirmation at its face value
without questioning the respondent further. This is
probably more a matter of necessity than of choice.
Carman G. Blough quoted the following comments by Manfred
E. Philip regarding confirmations of small loan companies.

Many accountants feel that many of these

debtors do not know the exact amount of

their balance and, therefore, are in no

position to confirm a figure of which

they have only a hazy notion. To accept

any confirmation received under these

circumstances at face value would give2
the auditor a false sense of security.

 

1Richard C. Lytle, ed. "Accounting and Auditing
Problems," The Journal of Accountancy, Vol. 118, No. 3,
(September 1965), p. 75.

2Carmen G. Blough, ed., "Confirmation Procedure
Must Be Adapted to the Circumstances,".Accounting and
Auditing Problems, The Journal of Accountaggy,‘Vol. 97,
No. 3, (March 1954), p. 345;

10
1.3 Prior Studies

An experiment was conducted by Gordan Davis, John
Neter, and Roger Palmer which directly concerned audit
confirmations.1 This study was conducted by placing a
code number directly below the account balance on the
bank statements of a sample of customers. Confirmation
requests were then sent to these customers asking them
to confirm.both the balance in the account and the code
numbers. Three hundred and fifty positive-type confirma-
tion requests were mailed of which 200 reflected inac-
curate code numbers. One hundred and eighty-three of
the inaccurate confirmations were returned; however,
about 36% of these failed to note the discrepancy. This
quality of reSponse must certainly raise some doubts
about the confidence the auditor can place in an indi-
vidual confirmation request.

A.related study was conducted by E. Scott Maynes
in 1963.2 Prof. Maynes circularized a sample of members
of the Census Federal Credit Union. The questionnaire
Which was employed requested the recipient to provide the
data concerning his savings and loan accounts. The

recipient was informed, by means of a cover letter, that

k

1Gordon B. Davis, John Neter, and Roger R. Palmer,
"An Experimental Study of Audit Confirmations," The

Journal of Accountancy, Vol. 123. No. 6. (June 1957).
PP. ' "’ o

2E. Scott Maynes, "Minimizing ReSponse Errors in
Financial Data: .The Possibilities," Journal of the
American Statistical Association, Vol. 65, No. lzl,
Marc , pp. 1 - .

11
the questionnaire was in conjunction with a study which
had the approval of the Credit Union and The Bureau of
the Census. Some of the recipients were asked to check
their records and some were asked to furnish the informa-
tion without checking their records. Of those who were
asked to check their records and responded to the ques-
tionnaire, 85% were within 1% of the credit union's
balance; 91% were within 5% of the credit union's balance.
This leaves 9% of the reSpondents reporting errors in
excess of 5% of their balances. These studies certainly
cast doubt upon the reliance that can be placed on the

accuracy of confirmation requests.

1.4 Statistical Sampling
1.4.1 History of Use in Auditing:

As is typical for innovation it is not possible to
exactly set the time of the beginning of the auditors!
interest in statistical sampling. Alden Smith proposes
that,

Perhaps the first article advocating the
application of statistical sampling tech-
niques to test checking by auditors was
'The Efficacy of Tests' by Lewis A.
Carman,.which was published in The American
Accountant in December 1933.

It was not until the 19508, however, that the certified

public accounting firms began.to.take.a serious interest in

k

1Alden C. Smith, "The Accounting Profession's
Growing Interest in Statistical Sampling," The New York
Certified Public Accountant, Vol. XXVII. No. 7, (July
1957 l , p. [+529

12

statistical sampling and began conducting research into
its application to auditing. After its introduction it
enjoyed rather Spectacular growth, as exhibited by the
results of reviews of working papers of Price Waterhouse
& Co. These reviews revealed that in 1960, 32% of the
engagements reviewed used statistical sampling, in 1963
this percentage had increased to 55%.1 These reviews
encompassed large, medium, and small engagements, there-
fore one would eXpect that 100% application would not be
appropriate because the small engagements would be less

amenable to the use of statistical sampling.

1.4.2 Advantages:

Hill, Roth, and Arkin rank the advantages of sta-
tistical sampling as first, Measurement; second, Objec-
tivity: then, Effectiveness and Efficiency.2 Their con-
tention is that measurement aids the auditor in forming
a sound opinion regarding the account under consideration.
{The auditor is able to SXpress the parameters with which
lne is concerned in such a manner that he can determine

WTiether they are within an acceptable range. For example,
if? a given percentage of the accounts receivable confirma-

tions reveal errors in the accounts, the auditor will.

y

1RobertE. Healy, "Sampling in Auditing: The
Whole Story," Price Waterhouse Review, Vol. 9, No. it,

(Winter 1964), p. 55.
ZHenry P. Hill, Joseph L. Roth, and Herbert

Arkin, Sampling in Auditing, (New York: The Ronald Press
Company, 9 a PP. ”9o

13
have a measure of the probable range of error. The auditor
will, therefore, be able to base his judgment as to the
reasonableness of the accounts on a defined estimate and
not some vague notion. One of the desirable traits of
an audit tool is that it be objective. Since statistical
sampling is objective it is of great advantage to the
auditor. One of the advantages of statistical sampling
is that it is more likely to assure a cross section of
the accounts. Another advantage of statistical sampling
is that the auditor establishes beforehand the criteria
on which he will make his decision. Once these criteria
have been established, the extent of verification required
is determined by the statistical sampling model used. The
criteria which the auditor establishes are the confidence
interval and the confidence level (both to be discussed
later).

The effectiveness of statistical sampling is derived
.in part from the fact that it requires the establishment

(if the criteria for acceptability prior to the actual

txast and in part because it focuses attention on the objec-
tjnves of the test. The objectives of the test and the
criterion for an error must be clearly defined and under-
Stood.

Statistical sampling is never less efficient than
judgmental sampling. A tool is more efficient if it
requires less effort to obtain the same result. The
reason statistical sampling is never less efficient can

in easily shown. Once the criteria for the test have

14

been established, the auditor utilizes the statistical
sampling model to determine the sample size, the sample
size thus determined is the minimum which will satisfy
the criteria established: any less would be insuffi-
cient. If judgmental sampling results in less verifi-
cation, then the auditor has not gathered a sufficient
amount of evidence. If, on the other hand, judgmental
sampling results in more verification, then the auditor

has performed more work than was necessary under the

circumstances.

1.4.3 Terminology:

There are two technical terms used in statistical
sampling which must be defined for any discussion in the
area. The two terms are confidence interval and confi-
dence level. Confidence interval is defined here as the
range of values on either side of the eXpected value of
the parameter being estimated. The result, then, is a
Irange of eXpected values for the parameter being esti-
nuated. The term precision is sometimes used to refer to
'tllis range. Confidence level is defined as the prob-
alaility that the confidence interval encompasses the true
'Vsilue of the parameter being estimated. For example, if
tile eXpected value of the parameter being estimated is
(3.35 (as a result of the sample) and the auditor estab-

lishes a confidence level of 95% and a confidence inter-
val of £0.05, then the auditor is 95% sure that for any

random.sample of the same size from the population, the

15
confidence interval computed from the sample would
include the true value of the parameter. The implica-

tion drawn from this is that the true value of the

parameter is between 0.30 and 0.40.

1.4.4 Sampling Plans1

The sampling plan which the auditor employs must
be attuned to the purpose of the Specific test. The
sampling plans which are normally used are acceptance
sampling, attribute sampling, variable sampling, and
discovery sampling.

Acceptance sapplipg is based on the notion of
accept or reject. The auditor establishes a maximum
error level as a criterion for acceptance of the popu-
lation from which the sample is drawn. For example,
the auditor may establish the maximum error rate for
accounts receivable confirmations as 10%, that is, if
the estimated proportion of errors, based on the sample,
Iaxceeds 10%, the auditor will not accept the accounts as
t"Bing reasonably stated. A sampling plan which is
Classely related to acceptance sampling is double or mul-
tilple sampling. Multiple sampling is characterized by
establishing two critical levels. In the case of
fleczounts receivable confirmations the procedure would be

1K) set an error rate for acceptance and another error

—._¥

1The order of discussion in sections 1.4.4 and
1.4.5 closely follows the order in Sampling in Auditing
by Henry P. Hill, Joseph L. Roth, and Herbert Arkin.

16
rate for rejection. An acceptance level of 2% and a
rejection level of 5% would mean that if the percentage
of errors in the sample were less than 2%, the auditor
would accept the balance of the account as being rea-
sonably correct; if the percentage of errors in the
sample were more than 5%, the auditor would reject the
balance of the account as not being reasonably stated;
if the percentage of errors in the sample were between
2% and 5% the auditor would eXpand his sample, either
with new acceptance-rejection levels or maintaining the
same levels.

Attribute sampling is a natural extension of
acceptance sampling: it not only indicates whether the
error rate in the population exceeds some acceptable
limit but it also estimates the rate of occurrence of
the error. Attribute sampling is useful in estimating
Some qualitative feature of the population. This is
‘eSpecially useful for an evaluation of internal control.
lune degree of internal control is not dichotomous, (i.e.,
it: cannot be evaluated as totally effective or nonexis-
tent), it Spans a wide range which, for reasons of con-
venience, is expressed in discrete terms. Attribute
Saunpling is useful in estimating the proportion of
errors in the population and from this the auditor may
'be able to evaluate the internal control as being at a

certain level.

Variable sampling is designed to estimate some

17

quantitative feature of the population and for this reason
is extremely useful to the auditor in rendering an opinion
as to the reasonableness of the account. Variable sampling
essentially estimates the dollar value of the account.

In the case of accounts receivable confirmations the
auditor would estimate the dollar value of errors in the
accounts based on the dollar value of errors uncovered

by the sample.

Discovery samplipg is a plan whereby the auditor

is concerned with any error disclosed. This plan is
generally employed when the auditor is primarily concerned
with the possibility of a defalcation. It has been gen-
erally established that the independent certified public
accountant does not bear the reSponsibility for uncover-
7 ing a defalcation in the ordinary course of an audit

when the purpose of the audit is the rendering of an
opinion as to the reasonableness of the accounts and the
fairness of their presentation by means of financial
=3tatements. Although independent certified public account-
Euats may not find discovery sampling useful for uncover-
irlg irregularities, they may find it useful in testing for
afilherence to stated procedures. Internal auditors may,
011 the other hand, find discovery sampling has many desir—
8flole qualifications. In those cases where the internal
auditor wishes to satisfy himself that there are no irregr
ularities or that the employees are following the pre-

scribed procedures as established by management, an

18
appropriate tool would be discovery sampling because one
incident may be enough to require attention for correc-

tive action.

1.4.5 Random Number - Systematic Sampling:

There are two major methods of applying the statis-
tical sampling plan selected: Random number sampling and
systematic sampling. Random number sampling is the
process of selecting the items for examination on the
basis of a table of random numbers. These tables are
plentiful and are often provided in books on statistical
sampling. The tables are generated in such a manner that
human biases do not affect the selection process. The
use of the tables poses no problem to the auditor; he has
only to determine a starting point and proceed from there.
If the items in the population are prenumbered, the audi-
tor would use the reSpective identifying digits, i.e., if
the numbers in the population were in the thousands, the
aiuditor might use the last four digits of the numbers in
tflle random number table. If the items in the population
sure not prenumbered, the auditor might number the items
811d proceed as he would if they were prenumbered. This
1£Llustrates one of the problems associated with the use
of? random.number tables. It may often be inconvenient
tn: number the items if they are not prenumbered. In this
case the auditor may find it more convenient to conduct a
Systematic sampling process. Systematic sampling is the

process of selecting every ngg item in a population.

19

Systematic sampling has the advantage of not requiring
the numbering of the accounts; however, it has the disa
advantage that the sequence of items in the population
may be in such a manner as to introduce a bias in the
sample. For example, the accounts receivable subsidiary
ledger may be prepared by entering a particular type of
account at equal intervals. The auditor Should be aware
of these potential dangers and make certain that they

do not exist. It should be pointed out that the use of
systematic sampling is not restricted to those instances
where the accounts are not prenumbered, it is simply
that its relative advantage is increased under these
circumstances. 1

Either random number sampling or systematic

sampling can be applied in different ways. The sampling
can be done on the basis of a Simple random sample, a
Stratified sample, or a cluster sample. A simple ran~
<iom sample is one in which each item in the population
:13 treated as an independent item and as each item is
Ctrawn from the population each remaining item has an
GQual probability of being selected. A simple random
Sexmple has the advantage that generally a smaller sample
Bern be used to provide the same confidence interval and
confidence level than either a stratified or a cluster
sample. .A stratified sample is one in which the items
in the population are segregated, on some basis, into

groups and then random samples are taken of the items

20
within these groups. A stratified sample has the advan-
tage that weights can be given to those accounts which
are considered the most critical or important. For
instance, the accounts receivable may be segregated on
the basis of size, the larger accounts in one group and
the smaller accounts in another group. A larger pro-
portion of the larger accounts could be sampled, thus
providing more information on the upper range of the
estimated value of the accounts. Stratified sampling
would require a larger sample if one were testing for
attributes whereas it might require a smaller sample if
one were testing for dollar amounts, under the assump—
tion that the accounts would more likely be overstated
than understated. A third way to sample is by cluster
Sampling. Cluster sampling is grouping the items in
some contiguous fashion and taking a sample of these
groups. Each item in the groups selected would consti-
tute a part of the sample. Cluster sampling has the
advantage of convenience, it is generally much more
convenient to examine each item in an array of items
than to examine the same number of items on an unrea
Stricted random basis. If the groups are naturally of
eclual size, the use of cluster sampling is even more
£51ttractive because the auditor would have no need to
‘3Ount the items in the group. If the groups are not
Of equal size then they should not have an equal probe

ability of being selected. The probability of selection

21
of a group should be proportional to its size. The dis-
advantage of cluster sampling is that a larger sample is
required to obtain a particular goal than would be

required if unrestricted random sampling were used.

1.5 Liabilities vs. Receivables

The discussion so far has centered around accounts
receivable; the same is generally true of the literature
on confirmations. However, the confirmation procedure is
equally applicable to liabilities. One of the reasons
that attention is focused on receivables is that one
normally assumes that a client will attempt to present
his position in the most favorable light possible. This
being the case, the client is more likely to overstate
than to understate assets; the reverse is true for lia-
bilities. It follows therefore that the auditor must be
on guard against fictitious assets and omitted liabil-
ities. If the liability is omitted, the auditor may not
have an opportunity to include this in his sample for
Circularization. There are, of course, ways by which
the auditor may avoid this problem with liabilities to
Suppliers. The auditor can examine invoices or cancelled
Checks for the names of past suppliers who are not
Included in the list of accounts payable. The names of
tnaese past suppliers could be added to the list of
accounts payable to form the population from which the

auditor draws his sample.

This attention to accounts receivable should not

22
be interpreted to mean that accounts receivable confirmau
tions are more important than liability confirmations,
eSpecially in the case of a financial institution which
holds deposits for its customers. The Committee on Bank
Accounting and Auditing of the American Institute of
Certified Public Accountants suggests that confirmations

should be sent to a sample of active deposit accounts and

1

to a sample of nonactive deposit accounts. The Committee

recognized the possibility that the recipient of a confir-
mation of a loan account may not know the amount of his
unpaid balance. The committee recommends that "it is
frequently preferable to request the borrower to confirm
the amount of each monthly payment and the number of pay-

ments remaining."2

1.6 Purpose of Study

The purpose of this thesis was to inquire into, to
analyze, and to answer some of the questions concerning
the auditing procedure of circularizing accounts receiv-
able and deposit accounts. This was accomplished by con-
<hlcting eXperimentS confirming loan accounts and deposit
Euzoounts under normal auditing conditions. The remainder
Cfi‘ this section is devoted to discussions of the Specific

areas ,of inquiry which received attention and the means of

L

, 1Committee on Bank.Accounting and Auditing, Audits
of Banks, (New York: American Institute of Certified
PuBIIciIccountants, 1968), pp. 134~5.

21bid., p. 120.

23
resolving these Questions.
An examination was made of the effects of none

reSponse upon the conclusions which the auditor may draw

 

concerning the reasonableness of the balance of the
account and upon the reliance that can be placed on the
internal control of the firm being audited. To determine
‘bhese effects, confirmation requests reporting incorrect
amounts were sent in addition to confirmation requests
wflnich report correct amounts. Correct is defined as that
aunount reported on the books of the company. .A compari-
son of the extent of nonreSponse for each of these
Samples was made to determine whether there is a statis-
1aically significant difference in the amount of non-
reSponses.

The relative effects of nonreSponse upon loan
succounts and deposit accounts was analyzed to determine
if?‘there is a difference between the two. This analysis
was made only on the basis of first requests because
Se(Bond requests were not used in conjunction with the
learn.account confirmation requests which reflected incor-
recrt amounts. It is felt, however, that the results of
the: first requests were sufficient for the comparison to
be made.

The effect of the direction of the error was ana-

lyzed.for deposit accounts to determine whether the con-
firmation recipient is more inclined or less inclined to

respond to an error in his favor than to one in the

24

company's favor. This was tested by sending confirmation

requests with comparable errors in either direction; i.e.,
the amounts on some of the confirmations were understated
and the amounts on others were overstated. The results
of these two samples were compared to determine if there

is a statistically significant difference in the amount of

nonreSponseS to each.

The effect of the size of the account was analyzed,
1J1 the case of the deposit accounts, to determine if there
:is a relationship between the size of the account and the
1xr0portion of reSponses. One would normally eXpect that
the larger the account the more likely the recipient would
13erto reSpond to the confirmation request. It would seem
natural to assume that a person would be more concerned
about his account if the account represents a large amount
tflnan he would if the account represents a small amount.
Ihawever, the size of the account relative to the wealth
Of' the recipient may be the factor which influences
response rather than the absolute amount of the account.
Data concerning the wealth of the recipients were not
avaiilable and therefore this latter idea could not be
tesrted. The results of the experiment were subjected to
Statistical analysis to determine whether there is any

difference in the reSponse due to the size of the account.
The influence that the ages of the confirmation
recipients have upon the amount of reSponses was tested

by subjecting the results of the deposit account confirma-

25
tions to statistical tests.

The effect that the form and content (wording) of
the confirmation has upon the amount of nonreSponses was
tested by preparing confirmations in several forms where
the only difference was the form itself. This test was
(conducted for both the loan accounts and the deposit
accounts.

An.analysis was made of the effects of improper
:reSponse upon the conclusions which the auditor may draw
concerning the reasonableness of the balance of the
account and the reliance that can be placed on the inter-
rual control of the firm being audited. This was accom-
Lilished by sending confirmation requests which reflected
irlcorrect amounts to a sample of customers. The esti-
nuated proportion of improper reSponses was computed for
'bcrth the deposit accounts and the loan accounts so as to
luave some idea of the probable extent of improper
response.

The proportion of improper reSponses on the loan
accounts was compared with that of the deposit accounts
t0 cistermine whether there is a statistically significant
difference between the two. Second requests were not
Sent on the loan account confirmations which reflected
incorrect amounts so the comparison was made on the basis

of the first requests.

The effect of the direction of the error was anam

ly2ed for the deposit accounts to determine whether the

26

confirmation recipient is more inclined or less inclined
to respond improperly to an error in his favor than to
one in the company's favor. This was tested by sending
confirmation requests with comparable errors in either
ciirection. The results of these two samples were com-
;paaed to determine if there is a statistically signifi-
caun:difference in the proportion of imprOper reSponses
to each.

A possible solution to the problem of improper
reSSponse is to utilize a confirmation form which does
n<3t provide the account data for the recipient to com-
psare with his records but instead asks him to furnish
tine data which can then be compared to the company's
rwecords. The use of such a form was tested both for
ijzs reliability (i.e., obtaining the correct amount)
anti for the probability of obtaining a reSponse. This
tyjpe of form was sent to a sample of both deposit
accrounts and loan accounts. Statistical tests were
peleormed to determine whether the reSponse to this
type of form differs from that of the form which pro-
vides the recipient with the data concerning his
account and asks him to compare these data with his
records and reSpond, either confirming the data or
noting an exception.

The final purpose of this thesis is to propose
means whereby the problems of nonreSponse and improper

response could be minimized or eliminated. To achieve

27
this purpose sampling models which have been developed
to counteract the problem of nonreSponse were studied to
determine their applicability to auditing and to provide,

if necessary, a statistical sampling model which includes

‘variables for nonreSponse. NonreSponse is a problem

trhich has been confronted by the professional statistic
ciian and some work has been conducted in developing a
seampling model which overcomes the nonreSponse error. A
rwsduction in the problem of improper reSponse will hope-

flllly be achieved through the results of this study.

CHAPTER II

THEORETICAL CONSIDERATIONS

2.1 Behavioral Reaction to Confirmation Reqpests

Each recipient of a confirmation request reacts in

such a way that he becomes a member of one (and only one)

of the following reaction groups:

G1 -

G6-

Flsure 1 is

Those who compare the confirmation requests
with their records and reSpond that the amount
iS correct.

Those who do not compare the confirmation
requests with their records and respond that
the amount is correct.

Those who compare the confirmation requests
with their records and reply that the amount
is not correct (i.e.,take exception to the
amount). _

Those who do not compare the confirmation
requests with their records and reply that the
amount is not correct.

Those who compare the confirmation requests
with their records and do not reply.

Those who do not compare the confirmation
requests with their records and do not reply.
a matrix representation of this division.

28

29
Figure l
Behavioral Reaction to Confirmation Requests

respond reSpond do not
correct exception reSpond

 

 

Compare confirmation with
records G1 G3 G5

Do not compare confirmation
with records G2 G4 G6
Each of these groups (G1. . . . G6) can be dichoto-
mized by those confirmations which reflect correct balances
euui those confirmations which reflect incorrect balances

(Figure 2).

Figure 2

Dichotomization of Behavioral Reaction
to Confirmation Requests

Confirmation amount

correct Gla G2a G33 G48 C'5a G6a
Confirmation amount
incorrect Glb sz G3b GLVD 65b GOb

It is not possible for the auditor to determine the
Preper group into which confirmation requests should be
Placed because (1) it is not feasible (and probably not
possible) for the auditor to determine whether the reci-
Plents did compare the confirmation requests with their
records and (2) the correctness of the amount is the pur-
pose in the confirmation procedure; if the auditor knew
this, there would be no need to send confirmations. The

andltor must summarize the groups into categories about

30
which he has knowledge. These categories are:

C1 - Those who reSpond that the amount is correct.

C1 = Gia + Gib + G2a + G2b
C2 - Those who reSpond that the amount is incorrect.

C - Those who do not reSpond.

3
C3 = G58 + GSb 4‘ G68. "I' Géb
Category one is accepted by the auditor at its face

value. This acceptance may influence the auditor to erron-

eously accept the account balance as being reasonable.

This erroneous acceptance would occur when reSponses are

in group (lb) or group (2b). Although those who are in

group (2a) did not perform as requested by the auditor, the

auditor will still be influenced toward making a correct

decision as to the reasonableness of the account balance.
Category two requires additional work on the part

of the auditor. The auditor must extend his examination

on these accounts until he has satisfied himself either

that the reSpondent or that the client is right. Those

Confirmations from reSpondents in group (3a) can often be

reconciled by an examination of transactions around the

Confirmation date. For example, an accounts receivable

confirmation which is returned with the customer claim-

ing a smaller balance may be reconciled by a payment

recorded within a reasonable length of time subsequent to

the confirmation date: because the payment was in transit

the account on the creditor's records will not reflect

31
it whereas the debtor has recorded the payment on his
records. Those confirmations from reSpondents in group
(4a) are the most aggravating to the auditor. In these
cases the respondent would probably make a general state-
ment to the effect that the amount was wrong. The auditor
would prefer not to risk alienating the reSpondent by
requesting additional information, so he will make a
search of the records in an attempt to determine the
validity of the reSpondent's claim. This search will
continue until the auditor decides to (1) consider the
exception as being an error by the customer, (2) accept
the exception, but with reservations, or (3) request
additional information from the reSpondent. Often the
auditor will choose not to contact the reSpondent and he
is usually unwilling to disregard the exception, So he
ends up accepting the exception with reservations.

Those confirmations from reSpondents in group (3b)
luust be followed up by the auditor; but, they generally
irequire less time than those from respondents in groups
04a) or (4b) and are of great assistance in judging the
ireasonableness of the account balances and the effective-
ruess of the internal control. Those confirmations from
INSspondents in group (4b), though properly an exception,
may waste a great deal of the auditor's time. As with
those in group (4a) the reSpondent will often make a
general statement about the incorrectness of the account.

The auditor will make a search of the records in an

32
attempt to determine the validity of the claim. If the
auditor is fortunate, he will quickly locate a discrep-
ancy in the client's records which would verify the
reSpondent's claim, if not, he may spend a great deal of
time following up the exception and he may never find
evidence to support the reSpondent's claim.

Category three requires the auditor to employ
alternative procedures to satisfy himself as to the
reasonableness of the account balances. AS was the case
with confirmations from reSpondents in category one, the
auditor's decision as to the reasonableness of the account
is not affected by the recipients' failure to compare the
data on the confirmation requests with their records.

One cannot say without qualification what the effect upon
the judgment of the auditor will be as a result of non-
reSponses; but, it would seem reasonable to conclude
that the auditor would be influenced toward erroneously
Judging the account balances as being correct. The
rationale behind this is that for groups (5a & 6a) the
auditor will.not make an incorrect judgment because he
WilJ.not find an.error (since there are no errors)
Whereas with groups (5b 8. 6b) he may not discover the
(Error and therefore he will reach an incorrect conclu-
sion. If one accepts the assumption that the confirmation
'Procedure is more efficient and more effective than
alternative procedures, then it follows that the auditor

is more likely to discover an error through the confirmau

33
tions than through alternative procedures.

There are, then, three variables working upon the
confirmation procedure; the reSponse variable (reSpond
correct, reSpond exception, do not reSpond), the
inSpect variable (compare confirmation with records, do
not compare confirmation with records), and the correct_
ness variable (amount correct, amount not correct). The
reSponse variable can be evaluated presently by the auditor.
The inSpect variable does not affect the auditor's decision
regarding the reasonableness of the account, only the
amount of work required to reach that decision. An evala
uation of the correctness variable would improve the
auditor's judgment as to the reasonableness of the account
balance. This study is a step toward providing the auditor
with the means whereby he can evaluate the correctness

variable.

2.2 Hypotheses

The remainder of this chapter is devoted to the form
Imllation of hypotheses which were tested by the eXperiments
<iescribed in chapter three. The eXperiment on the deposit
Eiccounts was more comprehensive and was, therefore, analyzed
111 greater depth. It is for this reason that some hypothe-
Ehas were formulated for deposit accounts but not for loan
aCcounts. The hypotheses are divided into three classifia
Cations: those concerning deposit accounts, those concerns
ing loan accounts, and those which concern the relationship

between deposit and loan accounts.

34

To aid the reader in understanding the hypotheses
some definitions will be reviewed. A proper reSponse is
one which acknowledges that the amount reported on the
confirmation request is correct when the amount is in
fact correct or which states that the amount is incor-
rect when it is incorrect. Correct here means that the
records being audited are in agreement with the recipi-
ents' records. Incorrect here means that the records
being audited are not in agreement with the recipients'
records. PrOper reSponses, then are the sum of groups
(1a), (2a), (3b), and (4b). An improper response is one
which acknowledges that the amount reported on the con-
firmation request is correct when in fact the amount is
incorrect or which states that the amount is incorrect
When the amount is in fact correct. Improper reSponses,
then, are the sum of groups (1b), (2b), (3a), and (4a).
INonresponses arise from those confirmation requests which

Tare not returned, these are the sum of groups (5a), (5b),
(6a), and (6b).
13.2.1 Hypotheses Concerning Deposit Account

Confirmation Requests:

Fifteen hypotheses concerning deposit account con-
firmation requests were formulated. These are presented
131 the following groupings:

DiaD7 Hypotheses on the effect of incorrect amounts

on the proportion of proper reSponses, on

the proportion of improper reSponses, and

35

on the proportion of nonreSponses.
D8-D9 Hypotheses on the effect of the confirma~
tion form on the proportion of reSponses.
D10 Hypothesis on the relationship between
first and second requests.

D11-D12 Hypotheses on the effects of age of recipi-
ents and size of the accounts upon the prom
portion of responses.

D13-D15 Hypotheses concerning telephone calls and
visits to the office being audited and
their relationship to proper reSponses.

Hypothesis D1 - The proportion of proper reSponses
tn) confirmation requests which reflect amounts that are
Snceater than the amounts shown on the recipients' records
153 0.90. The alternative hypothesis against which the
Ullll hypothesis is tested is that the proportion of proper
IWSSponses to confirmation requests which reflect amounts
tliat are greater than the amounts shown on the recipients'
records is less than 0.90.

As discussed in chapter one, the auditor implicitly
assumes either that the proportion of proper reSponses to
COrifirmation requests which reflect incorrect amounts is
1.()O, i.e., each confirmation request which reflects an
1l’l-correct amount will elicit a proper reSponse, or that it
533 equal to the proportion of reSponses to confirmation
reQuests which reflect correct amounts. The 1.00 is con»
Sixlered too stringent a criterion for testing and the
'latter, i.e., that the proportion of proper responses to

confirmation requests reflecting incorrect amounts is

CQual to the proportion of proper reSponses to confirma-

tion requests reflecting correct amounts, would cause the

36
test criterion to be dependent upon the results of the
eXperiment.

The 0.90, though arbitrary, is considered the mini-
mum proportion with which the auditor can be satisfied.

Hypothesis D2 - The proportion of proper reSponses
to confirmation requests which reflect amounts that are
less than the amounts shown on the recipients' records
is 0.90. The alternative hypothesis against which the
null hypothesis is tested is that the proportion of proper
responses to confirmation requests which reflect amounts
that are less than the amounts shown on the recipients'
records is less than 0.90.

The discussion concerning hypothesis D1 applies
equally to this hypothesis. It is conceivable that the
auditor would not view these two errors as equals. It is
probably true that most auditors would be more concerned
about the accounts which are understated, because this
would lead to an understatement of the liabilities, and
would want a greater proportion of proper reSponses from
these accounts. These differences are not taken into
account because it is difficult to establish some defena
sible criterion on whichtxitest and even more difficult
to establish some defensible relative criterion on which
to test related parameters. In addition to the practical
problem of establishing criteria there are the theoretical
aSpects which raise doubts about the contention that the
auditor should be more concerned about errors in one direc-
tion than errors in the opposite direction. Concern for
the direction of error would probably be justified only
if the auditor knew that any error which might exist would

be in a given direction.

37

Hypothesis D3 - The proportion of improper responses
to confirmation requests which reflect amounts that are
greater than the amounts shown on the recipients' records
is 0.05. The alternative hypothesis against which the
null hypothesis is tested is that the proportion of
improper responses to confirmation requests which reflect
amounts that are greater than the amounts shown on the
recipients' records is more than 0.05.

The selection of the five percent was arbitrary.
It would be naive of the auditor to believe that the per-
centage was zero; because, one must recognize that, for
various reasons, there are always going to be some cases
of people reSponding improperly.

Hypothesis D4 - The proportion of improper responses
to confirmation requests which reflect amounts that are
less than the amounts shown on the recipients' records is
0.05. The alternative hypothesis against which the null
hypothesis is tested is that the proportion of improper
reSponses to confirmation requests which reflect amounts

that are less than the amounts shown on the recipients'
records is more than 0.05.

The discussion concerning hypotheses D2 and D3
apply to this hypothesis as well. For the sake of brevity
these discussions will not be repeated.

Hypothesis D5 - The prOportion of nonreSponses to
confirmation requests which reflect incorrect amounts is
equal to the prOportion of nonreSponses to confirmation x
requests which reflect correct amounts. The alternative
hypothesis against which the null hypothesis is tested is
that the proportion of nonreSponses to confirmation
requests which reflect incorrect amounts is not equal to
the prOportion of nonreSponses to confirmation requests
which reflect correct amounts.

Whenever population estimates are made without an
adjustment being made to compensate for the nonreSponse,
from samples which were subject to some nonreSponse, there
is an implicit assumption that this null hypothesis is

true. It has been a common practice to accept this

38
assumption if alternative procedures did not reveal evi-
dence to the contrary.

Hypothesis D6 - The proportion of improper reSponses
to confirmation requests which reflect amounts that are
greater than the amounts shown on the recipients' records
is equal to the proportion of improper responses to con-
firmation requests which reflect amounts that are less
than the amounts Shown on the recipients' records. The
alternative hypothesis against which the null hypothesis
is tested is that the proportion of improper reSponses to
confirmation requests which reflect amounts that are
greater than the amounts shown on the recipients' records
is not equal to the proportion of improper responses to
coanrmatIon requests which reflect amounts that are less
than the amounts Shown on the recipients' records.

The proposition of this hypothesis is that a reci-
pient's reaction to incorrect amounts is independent of
the possible benefit to the recipient. There is an obvi-
ous implication that if people are basically honest then
this hypothesis will be supported. It is not the inten-
tion of this study to attempt to pass judgment on the
integrity of mankind, nor is it felt that such a judgment
would be justified on the basis of the acceptance or
rejection of this hypothesis. There are many reasons why
a difference might exist; but, no effort will be made to
determine the reason, or reasons. If the auditor knew
that one direction of error is more likely to elicit an
improper reSponse, he might use this information in esti-
mating the account balances. For example, if the auditor
knew that recipients are more likely to reSpond improperly
to errors in their favor, then he could assume that his

estimate of the account balance was more apt to be over

the true amount than under the true amount.

39

Hypothesis D7 - The proportion of nonreSponses to
confirmation requests which reflect amounts that are
greater than the amounts shown on the recipients' records
is equal to the proportion of nonresponses to confirmation
requests which reflect amounts that are less than the
amounts shown on the recipients' records. The alternative
hypothesis against which the null hypothesis is tested is
that the proportion of nonresponses to confirmation
requests which reflect amounts that are greater than the
amounts shown on the recipients' records is not eqpal to
the proportion of nonresponses to confirmation requests
which reflect amounts that are less than the amounts shown
on the recipients' records.

The discussion concerning hypothesis D5 applies
equally to this hypothesis. The assumption that is gen-
erally made, though implicitly, is that these proportions
are equal. Any inequality that might in fact exist should
certainly raise some serious questions concerning the
present evaluations of internal control and estimations
of account balances. If errors in accounts were consis-
tently in the same direction as the direction associated
with the greater proportion of nonreSponses, then the
auditor would be more influenced towards overestimating
the effectiveness of the internal control and the estimate
of the account balance would be further from the true value
than would be the case if the proportions of nonreSponses
were equal.

Hypothesis D8 - The proportion of reSponses to con-
firmation requests is independent of the form or content
(wording) of the confirmation requests. The alternative
hypothesis against which the null hypothesis is tested is
that the proportion of responses to confirmation requests

is de endent u on the form or content (wording) of the
confirmation requests.

There are many confirmation forms in general use.

It would seem reasonable to assume that in this age of

40

great interest in packaging, the form of the confirmation
request would influence the proportion of reSponses. If
this is true, the auditor should seek to discover the
"best" confirmation request form, thus deriving the
greatest possible benefit from the effort eXpended. If,
on the other hand, the form and content of the confirma—
tion request has no effect upon the amount of reSponses,
the auditor might just as well use that form which mini-
mizes the cost of the circularization procedure. The only
justification for additional costs is that the results
will be better. Norman Lenhart and Philip Defliese con-
tend that "EXperience has shown that a form of positive
request which requires of the recipient a minimum of
effort will produce the greatest percentage of replies."1

Hypothesis D9 — The proportion of responses to con—
firmation requests which ask the recipients to confirm the
account information provided on the requests is equal to
the proportion of reSponses to confirmation requests which
ask the recipients to provide the information concerning
their accounts. The alternative hypothesis against which
the null hypothesis is tested is that the proportion of
reSponses to confirmation requests which ask the recipi-
ents to confirm the account information provided on the
requests is not equal to the proportion of reSponses to
confirmation requeSts which ask the recipients to provide
the information concerning their accounts.

Assuming that the major cause of improper reSponses
is the unwillingness of recipients to compare the data on
the confirmation requests with their records, or viewed

another way, the willingness of the recipients to

acknowledge the amount as correct (or incorrect) without

 

lop. cit., p. 176.

41
comparing the data on confirmation requests with their
records, the use of a form which required the recipients
to examine their records in order to complete the requests
would tend to reduce (and perhaps even eliminate) the
amount of improper reSponses. One must, however, be aware
that the recipients may seek the required information
from the very source being audited.

Hypothesis D10 - The proportion of proper responses
to the first requests of confirmation requests which
reflect amounts that are not correct is equal to the pro-
portion of proper reSponses to the second requests of
confirmation requests which reflect amounts that are not
correct. The alternative hypothesis against which the
null hypothesis is tested is that the preportion of
proper reSponses to the first requests of confirmation
requests which reflect amounts that are not correct pp
gpeater than the proportion of proper reSponses to the
second requests of confirmation requests which reflect
amounts that are not correct.

It seems reasonable to eXpect that if recipients
react differently to first and second requests, the pro-
portion of proper reSponses might be greater on the first.
requests. If the recipient is the type of individual who
would reSpond to the circularization as he was asked, it
would seem that he would generally reSpond to the first
request. It would follow, also, that there would be a
smaller proportion of improper reSponses to the first
requests. To moderate this greater improper response to
second requests are those reSpondents who on the first
requests deliberately reSpond improperly in the hopes that
there is an error in the company's records but that this

error will go undetected if they acknowledge that the

amount is correct. This latter reaction would apply only

42
if the error were in the reSpondent'S favor.

Hypothesis D11 - The proportion of proper reSponses
to confirmation requests is independent of the age of the
recipient. The alternative hypothesis against which the
null hypothesis is tested is that the prOportion of proper
reSponses to confirmation requests is dependent ppon the
age of the recipient.

The Spectacular growth of the auditing profession
in recent years and the growing awareness of the business
environment might lead one to suppose that a particular
age group would be more knowledgeable or more concerned
about business related occurrences. Or, one might con-
tend that with increased age and maturity one becomes more
aware of the purposes behind the many items with which he
is called upon to deal. The various reasons why one age
group might reSpond better is of little importance to the
auditor, he is more concerned with the resulting facts
(i.e., which age group, if any, respond better).

Hypothesis D12 - The proportion of preper reSponses
to confirmation requests is independent of the size of the
account balances. The alternative hypothesis against
which the null hypothesis is tested is that the proportion
of proper reSponses is dppendent upon the Size of the
account balances.

If the size of the account balance influences the
recipient's reSponse. the auditor should stratify his pop~
ulation and sample accordingly. If, on the other hand,
the proportion of proper reSponses is independent of the
size of the account balances, then any scheme of stratim
fying must be less efficient for attribute sampling.
Stratified samples may still be more efficient for varin

able sampling.

43

Hypothesis D13 - The proportion of telephone calls
or visits (to the office being audited) from recipients
of confirmation requests which reflect correct amounts is
equal to the proportion of telephone calls or visits (to
the office being audited) from recipients of confirmation
requests which reflect amounts that are greater than the
amounts shown on the recipients' records. The alternative
hypothesis against which the null hypothesis is tested is
that the proportion of telephone calls or visits (to the
office being audited) from recipients of confirmation
requests which reflect correct amounts is less than the
proportion of telephone calls or visits—(to the office
being audited) from recipients of confirmation requests
which reflect amounts that are greater than the amounts
Shown on the recipients' records.

If the number of telephone calls or visits from
recipients is independent of the correctness (or incor-
rectness) of the confirmation requests, the auditor would
have no reason to become suSpicious if such calls or
visits occur. On the other hand, if incorrect confirma-
tion requests generate significantly more calls or visits,
the auditor should become suSpicious if he learns of such
calls or visits.

Hypothesis D14 - The proportion of telephone calls
or visits (to the office being audited) from recipients
of confirmation requests which reflect correct amounts is
equal to the proportion of telephone calls or visits (to
the office being audited) from recipients of confirmation
requests which reflect amounts that are less than the
amounts shown on the recipients' records. The alternative
hypothesis against which the null hypothesis is tested is
that the proportion of telephone calls or visits (to the
office being audited) from recipients of confirmation
requests which reflect correct amounts is less than the
proportion of telephone calls or visits (to the office
being audited) from recipients of confirmation requests
which reflect amounts that are less than the amounts shown
on the recipients' records.

This hypothesis is the same as hypothesis D13
except that the direction of error is reversed. The dis-
cussion concerning hypothesis D13 is equally applicable

here.

44

Hypothesis D15 - The proportion of proper reSponses
among confirmation request recipients who call or visit
(the office being audited) concerning their accounts is
equal to the proportion of proper reSponses among confirm
mation request recipients who do not call or visit (the
office being audited) concerning their accounts. The
alternative hypothesis aginst which the null hypothesis
is tested is that the proportion of proper reSponses among
confirmation request recipients who call or visit (the
office being audited) concerning their accounts is not
egual to the proportion of prOper reSponses among confir-
ma on request recipients who do not call or visit (the
office being audited) concerning their accounts.

If recipients who call or visit subsequently
reSpond properly, auditors would not have to be concerned
about these calls or visits. However, if the recipients
substitute the calls or visits for proper reSponses,
auditors would need some means of controlling these calls
or visits.

2.2.2 Hypotheses Concerning Loan Account

Confirmation Requests:

Seven hypotheses concerning loan account confirma-
tion requests were formulated. These are presented in the
same order as the comparable deposit account hypotheses.

Hypothesis L1 - The proportion of proper responses
to the first requests of confirmation requests which
reflect amounts that are greater than the amounts shown on
the recipients' records is 0.70. The alternative hypothe-
sis against which the null hypothesis is tested is that the
proportion of prOper reSponses to the first requests of
confirmation requests which reflect amounts that are
greater than the amounts shown on the recipients' records
is less than 0.70.

The 0.70 criterion was established under the assump-
tion that if incorrect confirmations elicited proper

reSponses of seventy percent on both the first and second

requests, the proportion of proper reSponses for the two

45
would be slightly over ninety percent, (1x70%) + [1-(1x70%fl
70% = 91%.1 Ninety percent was the criterion established
for the deposit account hypothesis D1. The assumption
that the proportion of proper reSponses to second reQuests
is the same as the proportion of proper reSponses to first
requests was tested via deposit account hypothesis D10.
The discussions concerning deposit account hypotheses D1
and D2 are applicable to this hypothesis and will not be
repeated here.

Hypothesis L2 - The proportion of improper responses
to the first requests of confirmation requests which reflect
amounts that are greater than the amounts Shown on the
recipients' records is 0.05. The alternative hypothesis
against which the null hypothesis is tested is that the
proportion of improper reSponses to the first requests of
confirmation requests which reflect amounts that are
greater than the amounts shown on the recipients' records
is more than 0.05.

Unlike hypothesis L1 there was no attempt to adjust
the criterion established for the comparable deposit
account hypotheses to allow for the fact that second
requests were not employed. The reason for this is that
it is felt that the five percent criterion is the lowest'
that can be meaningfully tested and also that there is no
reason to adjust the criterion for one percent. The dis-
cussion concerning deposit account hypotheses D3 and D4
are applicable here.

Hypothesis L3 - The proportion of nonreSponses to

confirmation requests which reflect incorrect amounts is
equal to the proportion of nonreSponses to confirmation

 

1It should be noted that this computation is made
under the assumption that there is no improper reSponse.

46

requests which reflect correct amounts. The alternative
hypothesis against which the null hypothesis is tested is
that the proportion of nonreSponses to confirmation
requests which reflect incorrect amounts is not equal to
the proportion of nonreSponses to confirmation requests
which reflect correct amounts.

This hypothesis is comparable to deposit account
hypothesis D5. The discussion concerning hypothesis D5
is applicable here and will not be repeated.

Hypothesis L4 - The proportion of nonresponses to
confirmation requests is independent of the form or con-
tent (wording) of the confirmation requests. The alterm
native hypothesis against which the null hypothesis is
tested is that the proportion of nonreSponses to confirm
mation requests is deppndent upon the form or content
(wording) of the confirmation requests.

This hypothesis is comparable to deposit account
hypothesis D8. The discussion concerning deposit account
hypothesis D8 is applicable here and will not be repeated.

Hypothesis L5 - The proportion of nonreSponses to
confirmation requests which ask the recipients to confirm
the account information provided on the confirmation
requests is equal to the proportion of nonreSponses to
confirmation requests which ask the recipients to provide
the information concerning their accounts. The alterna-
tive hypothesis against which the null hypothesis is
tested is that the proportion of nonresponses to confirma-
tion requests which ask the recipients to confirm the
account information provided on the confirmation requests
is not equal to the proportion of nonresponses to confir-
matIon requests which ask the recipients to provide the
information concerning their accounts.

This hypothesis is comparable to deposit account
hypothesis D9. The discussion concerning hypothesis D9
is applicable here and will not be repeated.

Hypothesis L6 - The proportion of telephone calls
(to the office being audited) from recipients of confirma-
tion requests which reflect correct amounts is equal to
the proportion of telephone calls (to the office being
audited) from recipients of confirmation requests which
reflect incorrect amounts. The alternative hypothesis
against which the null hypothesis is tested is that the

 

Ml.

a ~C D. T.

cap-ltvic

47
proportion of telephone calls (to the office being audited)
from recipients of confirmation requests which reflect
correct amounts is less than the proportion of telephone
calls (to the office being audited) from recipients of
confirmation requests which reflect incorrect amounts.

This hypothesis is comparable to hypothesis D13.
The discussion concerning hypothesis D13 is applicable
here and will not be repeated.

Hypothesis L7 - The proportion of proper reSponses
among confirmation request recipients who call (the office
being audited) concerning their accounts is equal to the
proportion of proper reSponses among confirmation request
recipients who do not call (the office being audited) con-
cerning their accounts. The alternative hypothesis
against which the null hypothesis is tested is that the
proportion of proper responses among confirmation request
recipients who call (the office being audited) concerning
their accounts is not equal to the proportion of proper
reSponses among confirmation request recipients who do not
call (the office being audited) concerning their accounts.

This hypothesis is comparable to hypothesis D15.
The discussion concerning hypothesis D15 is applicable
here and will not be repeated.

2.2.3 Hypotheses Relating Loan Account Confirmation

Requests to Deposit Account Confirmation Requests:

Five hypotheses were formulated relating loan
account confirmation requests to deposit account confirma-
tion requests. These hypotheses are meaningful for two
reasons. First, if there is no significant difference
between the results of the loan account experiment and the
deposit account experiment, the inferences drawn from the
more comprehensive experiment (on the deposit accounts)
may be applicable to the other. Second, if there is no
significant difference, the auditor may apply the same

techniques to the confirmation procedure, without regard

48
to the type of accounts being circularized; if there is a
difference, the auditor must apply different techniques
to the confirmation procedure, depending on the type of
account.

Hypothesis DLl - The proportion of proper responses
to loan account confirmation requests is equal to the
proportion of proper reSponses to deposit account confir-
mation requests. The alternative hypothesis against
which the null hypothesis is tested is that the proportion
of proper reSponses to loan account confirmation requests
is not equal to the proportion of proper reSponses to
deposIt account confirmation requests.

There are three reasons why the proportion of proper
reSponses to loan account confirmation requests may be dif-
ferent from that of deposit account confirmation requests.
First, the confirmation procedure may not be equally suit-
able for loan accounts and for deposit accounts. Second,
the population of reSpondentS may be different in the way
in which they reSpond to confirmation requests. And third,
the attitude of the recipients towards the firm may influa
ence the amount of reSponse. It is not within the scope of
this research project to attempt to determine the reason for
any differences that might exist. It Should be kept in mind
that these causes may result in reactions which negate each
other in total so that the null hypothesis is not rejected
because of differences between the populations or because
of the influences of the companies concerned.

Hypothesis DL2 _ The proportion of nonresponses to
loan account confirmation requests which reflect incorrect
amounts is equal to the proportion of nonreSponses to
deposit account confirmation requests which reflect incora

rect amounts. The alternative hypothesis against which
the null hypothesis is tested is that the proportion of

31'

is

CV

. NIH. AU \P.“

c

winkh... (a If“ m. A:
LIV h A.» A... t DPT

QM
Ala

49

nonresponses to loan account confirmation requests which
reflect incorrect amounts is not equal to the proportion
of nonreSponses to deposit account confirmation requests
which reflect incorrect amounts.

The auditor needs to know the effectiveness of the
confirmation procedure to disclose errors regardless of
the type of account. If the proportions of nonreSponses
differ, the auditor may not be able to place equal relim
ance upon each. The discussion concerning hypothesis DL1
is also applicable here.

Hypothesis DL3 - The proportion of improper reSponses
to loan account confirmation requests which reflect incor-
rect amounts is equal to the proportion of improper
reSponses to deposit account confirmation requests which
reflect incorrect amounts. The alternative hypothesis
against which the null hypothesis is tested is that the
proportion of improper reSponses to loan account confirma-
tion requests which reflect incorrect amounts is not eral
to the proportion of improper reSponses to depositiaccoufit
confirmation requests which reflect incorrect amounts.

The discussions concerning hypotheses DL1 and DL2
are equally applicable here.

Hypothesis DL4 - The proportion of nonreSponses to
loan account confirmation requests which ask the recipi-
ents to provide the data concerning their accounts is
equal to the proportion of nonreSponses to deposit account
confirmation requests which ask the recipients to provide
the data concerning their accounts. The alternative
hypothesis against which the null hypothesis is tested is
that the proportion of nonreSponses to loan account conu
.firmation requests which ask the recipients to provide
the data concerning their accounts is not pqual to the
proportion of nonreSponses to deposit account confirmation
requests which ask the recipients to provide the data con-
cerning their accounts.

This hypothesis relates hypothesis D9 with hypothe-

813 L50

50
2.2.4 Corollary to Hypotheses:

In addition to knowing whether one rejects or
accepts a hypothesis one may also want to have some
notion about the true value of the parameter being
examined. This can be satisfied by making a point
estimate or an interval estimate of the parameter.

In this particular case, point estimates would have
little meaning: however, interval estimates may be
very meaningful.

For this reason, confidence intervals were
estimated for the percentages of: proper reSponses,
improper reSponses, and nonresponses on loan account
confirmation requests which reflected amounts that
were greater than the correct amounts, on deposit
account confirmation requests which reflected amounts
that were less than the correct amounts, and on
deposit account confirmation requests which reflected
amounts that were greater than the correct amounts.

The estimated confidence intervals are pre-

sented along with the tests of hypotheses in chapter #.

CHAPTER III
DESCRIPTION OF EXPERIMENTS

3.1 Description of Credit Union Experiment
This section is a discussion of the eXperiment con-
ducted on the time deposit accounts of the MSU Employees

Credit Union.

3.1.1 Participants

The management of the MSU Employees Credit Union
recognized the usefulness of a study of this type and felt
a certain reSponsibility to participate in research con-
ducted at Michigan State University. It was felt that the
Supervisory Committee should be consulted since it is the
Committee's responsibility to act in the capacity of
auditors for the members. The Supervisory Committee is
charged with the responsibility of engaging external
auditors for the annual audit and periodically performing
such examinations as they deem advisable. The Supervisory
Committee gave its approval and the study was conducted
under its auspicies.

The MSU Employees Credit Union, founded in 1936,
had approximately 10,000 members with assets totaling
$10,715,887 as of December 31, 1967. It is the thirteenth

largest credit union in the state of Michigan and the

51

52
largest university affiliated credit union in the United
States. An indication of the relationship between the
members and the credit union can probably best be shown
by the fact that approximately 3,500 members attend the

annual meetings.

3.1.2 Accounts Used:

The eXperiment was conducted on time deposit
accounts as of February 29, 1968. Certificates are
issued to the members, thus providing the members with
some tangible evidence of their account. The balance of
the account represents principal only. Interest is
accrued monthly; but, it is not credited to the account
until the end of the quarter. Quarterly or annually,
whichever the member chooses, the accrued interest is
paid to the depositor. All depositors had received their
accrued interest as of December 31, 1967, at which time
the balance of these accounts totaled $1,669,473, and
also a statement reporting the balance in the account as
of that date. It was this same balance which was used in
the experiment plus any additional deposits and minus any
withdrawals. A report is prepared monthly by a data
processing service in Lansing, which reports the beginning
balance, additions, deletions, accrued interest, and the
ending balance for each account.

The monthly report was obtained for February 29,
1968. A review of the accounts was made with the chair-

man of the Supervisory Committee to delete those members

53

to whom the committee preferred that a confirmation not be
sent. There were 478 members listed on the report. Twenty-
two of these members were deleted, leaving a total of 456
in the population to be sampled. Of the 456 accounts in
the population some were members of the same family. It
is recognized that this might tend to bias the results but
no consideration was given to this condition, each account
was treated individually and independently. Any bias that
might result is considered so small as to be negligible.
The accounts were numbered sequentially because the
numbering system used by the credit union is coded to indi-
cate the location of the member (i.e., whether at East
Lansing or the Oakland extension of M.S.U.) and also for
children's accounts and because the numbers are so large
as to increase the amount of work involved in drawing a

sample.

3.1.3 Confirmation Forms:

There were three different confirmation forms used
in the eXperiment; a copy of each is presented in Appen-
dix A. The standard confirmation form and the short form
are modifications of confirmation forms used by one of the
national CPA firms for credit unions and banks. The third
form was prepared specifically for the purpose of this
eXperiment without reference to any source.

The standard confirmation form provided the recipi-
ent with information concerning his account number (this

is the individual member's number, not the number of the

54

certificate), the date of the certificate (in some cases
the members had two or more certificates, this problem
was overcome by using the oldest and latest dates separ-
ated by a hyphen), and the amount of the certificate
account (if the account represented two or more certifi-
cates, the total was entered). The standard form was
prepared on MSU Employees Credit Union letterhead sta-
tionery. The form was prepared so as to inform the
recipient under whose auspices the audit was being con-
ducted and the purpose of the audit. The member was
asked to compare the information provided with his records
and to reSpond directly to the Supervisory Committee. A
return envelope was enclosed as is typically done in the
confirmation procedure. Proper authorization for the
request was affixed. The recipient was provided with
Space to indicate his exceptions (if any) and for his
signature. The recipient was put on notice that this
was not a statement, this was done to reduce the chance
that the recipient of one of the adjusted accounts would
use the confirmation in a claim that the balance of his
account was more than was actually the case. These con-
firmations were mailed in MSU Employees Credit Union
envelopes.

The short form provided the recipient with the
same information concerning the account as the standard
form. The size of the short form confirmation was con-

siderably less than that of the standard form, requiring

55

only one-third of a sheet of 8% x 11 bond paper. The
description was brief and did not indicate the purpose of
the confirmation nor did it eXplicitly state that the con-
firmations were sent under the auspices of the Supervisory
Committee. There was no authorization indicated on the
form. Rather than providing the recipient with room for
exceptions he was asked to use the back of the confirma-
tion. A return envelope was provided and the confirma-
tions were mailed in MSU Employees Credit Union envelopes.

The third form employed in the eXperiment did not
provide the member with any information concerning his
account. This form will be called the "blank" form for
the purpose of identification. The recipient was asked
to disclose his account number, the amount of the balance
of his account, and to sign the form. He was told the
purpose of the request and that it was being conducted
under the auSpices of the Supervisory Committee. Proper
authorization was indicated. The style was similar to
the standard form and MSU Employees Credit Union letter-
head stationery was used. A return envelope was provided
and the confirmations were mailed in MSU Employees Credit

Union envelopes.

3.1.4 Description of Samples:
A random number table was used to select the
accounts which would be circularized. The accounts were

divided into five samples as follows:

k1 —

56
a sample of fifty accounts which were circu-
larized without adjusting the balances of the
accounts. This sample represented the control
group and the accounts therein were confirmed
using the standard confirmation form.
a sample of thirty accounts, the balances of
which were adjusted by a positive adjustment
in the amount of ten percent of the balances
of the accounts (rounded to the nearest fifty
dollars) with a maximum adjustment of $500.
The standard confirmation form was used to
circularize the accounts in this sample. The
purpose of this sample was to test the effect
of an error in the member's favor upon the
amount of nonreSponses and improper responses.
One of the recipients of these confirmations
was informed that the confirmation request was
part of a study, therefore, that account had
to be deleted from the sample, leaving twenty-
nine accounts in the sample.
a sample of thirty accounts, the balances of
which were adjusted by a negative adjustment
in the amount of ten percent of the balances
of the accounts (rounded to the nearest fifty
dollars) with a maximum adjustment of $500.
The standard confirmation form was used to-

circularize the accounts in this sample. The

57
purpose of this sample was to test the effect

of an error in the credit union's favor upon
the amount of nonreSponse and improper
reSponses.

4 - a sample of fifty accounts which were circu-
larized without adjusting the balances of the
accounts. The short form confirmation was
used to circularize the accounts in this sample.
The purpose of this sample was to test the
effects of the use of a simpler and shorter
form upon the amount of nonresponses.

k - a sample of fifty accounts which were circu-

larized using the blank confirmation form.
The purpose of this sample was to test the
effects on nonreSponses of a form which required
the recipients to consult their records in

order to answer the reQuests.

3.1.5 Confirmation Procedure:

Having selected the sample, the confirmations were
prepared and mailed. The addressing was done by means of
the addressograph. The information concerning the accounts
was typed for samples k1, k2, k3, and k4.

It was recognized that some recipients might con-
tact the office of the credit union either by telephone or
in person. The employee who maintained the time deposit
account records was instructed (1) to attempt to talk the

callers into confirming the adjusted accounts without

58
taking exception to the amount and (2) to keep a record of
those who contacted the office. The rationale behind
these instructions was that if the recipient of a confir-
mation request of a misstated account contacted the employee
reSponsible for the misstatement, that employee would
attempt to persuade the recipient that the account was in
order and that he should either disregard the confirmation
or return it without taking exception. Unfortunately, the
employee to whom these instructions were given was absent
from work during the period of time that the contacts were
made by the recipients. As things actually worked out,
the employees who handled the complaints instructed the
recipients to follow the instructions provided on the con-
firmation form. One would eXpect, then, that the propor-
tions of nonresponses and improper responses would be less
than they would be in an audit where the accounts were
misstated. The employees were asked to prepare a list of
the calls which they handled. In order to make certain
that the list was reasonably complete the employees were
asked to scrutinize a schedule of the confirmation recipi-
ents for any names which they might recognize.

Fourteen days after the first requests were mailed,
second requests were mailed. The second requests were
clearly marked as such. After a reasonable time all con-
firmations received were treated as second requests even
if they were physically the first requests. The reason

for treating all returns as second requests was that it

59

was assumed that the second request was the stimulus which
brought about the completion and return of the first
request.

Upon the mailing of the second requests the employ-
ees were again instructed to tell all callers to disregard
the confirmation. They were to tell the caller that the
matter would be brought to the auditor's attention and
therefore it was not necessary for him to trouble himself
further. Fortunately, these instructions were not needed
because no one called or visited the office in reSponse to

the second requests.

3.1.6 Additional Data:

Personal data were obtained on the age of each of
the recipients. Where possible the data were extracted
from the addressograph plates maintained in the mail room.
Those individuals for whom the data were not available on
the addressograph plates were listed and the list was
given to the manager of the credit union who obtained thev
missing data. The purpose in obtaining these data was so
that analyses could be made to determine whether age had
any effect upon the amount of nonreSponses or improper

reSponses.

3.1.7 Follow Up:
Letters were sent to those members who noted excep-
tions. This letter acknowledged the error and thanked

the reSpondent for his cooperation. The reSpondent was

60
not informed that he had participated in a study. The
letter was worded as if there had simply been an error on

the part of the auditor.

3.2 Description of Bank EXperiment
This section is a discussion of the eXperiment con-
ducted on loan accounts of the Continental Illinois

National Bank and Trust Company of Chicago.

3.2.1 Participant:

The management of the Continental Illinois National
Bank and Trust Company of Chicago agreed to participate in
the study as a means of assisting academic research. The
Continental Illinois National Bank and Trust Company of
Chicago is one of the largest banks inifluaUnited States.
As of December 31, 1967 it ranked seventh in amount of
permanent capital funds ($459,864,000) and eighth in
amount of deposits ($5,419,388,122). On December 31, 1967

the balance in the loans and discounts accounts was

83 .54u9078 .5700

3.2.2 Accounts Used:

The accounts which were used in the study were
direct personal loan accounts and direct automobile loan
accounts. The samples were drawn from approximately

fifteen hundred of these accounts.

3.2.3 Confirmation Forms:

There were three different confirmation forms used

61
in the eXperiment. A copy of each of these forms is
included in Appendix B. The characteristics which were
common to each of these forms were: (1) Continental
Illinois National Bank and Trust Company of Chicago
letterhead stationery was used, (2) the requests were
made under the auspices of "auditor", (3) proper author-
ization, via signature, was affixed, and (4) the recipia
ent was asked to sign the request and provision was made
for his signature.

The standard confirmation form was a modification
of a form used by a national CPA firm and of forms illus-
trated in auditing texts. In addition to the common
characteristics already mentioned, the standard form
informed the recipient of the purpose of the request and
noted that it was not a request for payment. The recipi-
ent was provided with the following data concerning his
account: the unpaid balance, the date of the note, the
amount of the note, the date of the last payment, and the
amount of the last payment. The recipient was asked to
compare the given data with his records, note any discrep-
ancies on the reverse side, and return the request.

The blank confirmation form was developed for the
specific purpose at hand. In addition to the common char-
acteristics the blank form informed the recipient of the
purpose of the request and noted that it was not a
request for payment. The recipient was asked to provide

the following data concerning his account: date of note,

62

amount of note, date of last payment, amount of last pay-
ment, and the unpaid balance.

The short confirmation form was a modification of
a confirmation form used by a national CPA firm. Unlike
the standard form and the blank form the short form did
not inform the recipient of the purpose of the request
but simply asked him to compare the given data with his
records, note any exceptions, and return the request.
The recipient was provided the following data concerning
his account: the amount of the note, the date of last
payment, and the present balance.

The confirmation requests were mailed in Continen-
tal Illinois National Bank and Trust Company of Chicago
envelopes and return envelOpes were enclosed with each

request as is customary.

3.2.4 Description of Samples:

Four random samples were drawn from the available
accounts. The average balance of personal loans in the
samples was $1,200 and the average balance of the automo-
bile loans in the samples was $1,800. The accounts were
divided into four samples as follows:

b1 - a sample of one hundred accounts which were

circularized without adjusting the balances
of the accounts. This sample represented the
control group and the accounts therein were
confirmed using the standard confirmation

form.

63

b2 - a sample of thirty accounts, the balances of
which were adjusted by a positive adjustment
in the amount of approximately ten percent
of the balances of the accounts. The
standard confirmation form was used to circu-
larize the accounts in this sample. The pur-
pose of this sample was to test the effect of
an error upon the amount of nonreSponses and
improper reSponses.

b3 - a sample of one hundred accounts which were
circularized using the blank confirmation
form. The purpose of this sample was to test
the effects on nonreSponses of a form which
required the recipients to consult their
records in order to answer the requests.

b4 - a sample of one hundred accounts which were
circularized without adjusting the balances
of the accounts. The short form confirmation
form was used to circularize the accounts in
this sample. The purpose of this sample was
to test the effects of the use of a simpler
and shorter form upon the amount of nonrea

sponses.

3 ~ 2 . 5 Procedure:
Instructions were submitted to the consumer credit
manager who executed the experiment. The eXperiment was

cOnducted during March and April 1968, with second requests

64
being mailed about two weeks after the first requests were

mailed. However, because of the adverse reaction by some

of the recipients to the first requests, second requests

were not sent on those accounts which were adjusted.

The results of the eXperiment were summarized by

the bank's personnel and transmitted for analysis and

inclusion in the thesis.

CHAPTER IV
RESULTS OF EXPERIMENTS AND ANALYSES OF RESULTS

4.1 Results of EXperiments
The first part of this chapter presents the results
of the eXperiments. Some of the data presented is for the
general information of the reader and is not used in the sta-
tistical analysis which follows. The data which are not
used in the statistical analysis are considered important
and relevant for a thorough understanding of the results
of the experiments; but, they are of a general nature and

not amenable to analysis.

4.1.1 Results of Credit Union Experiment:

The eXperiment of the deposit account confirmation
requests yielded a great deal of data. Actual results of
each of the samples will be presented first, then the
additional information will be presented.

Sample k1 - A sample of fifty unadjusted accounts
using the standard confirmation form,
generated forty proper reSponses to the
first requests and eight to the second
requests.

Sample k - A sample of twentyunine accounts which

2
were positively adjusted by an amount

65

66

of ten percent of the account balance
(rounded to the nearest $50), subject .
to a maximum adjustment of $500, gen-
erated thirteen proper responses and
four improper reSponses to the first
requests. The second requests gener-
ated seven proper responses and two

improper reSponses.

Sample k3 - A sample of thirty accounts which were

negatively adjusted by an amount of
ten percent of the account balance
(rounded to the nearest $50), subject
to a maximum adjustment of $500, gen-
erated twenty-three proper reSponses
and three improper reSponses to the
first requests. The second requests
yielded two proper reSponses but no

improper responses.

Sample k4 - A sample of fifty unadjusted accounts,

Sample k

5

using the short confirmation request
form, generated thirty-six proper
reSponses to the first requests. The
second requests generated ten proper
reSponses and one response stating an

inability to comply with the request.

- A sample of fifty accounts, for which

the data concerning the accounts were

67

not furnished to the recipients, gener-
ated thirty-one proper reSponses to the
first requests and eight proper reSponses
to the second requests. Two respondents
stated that they were unable to provide
the requested data and two failed to
provide the amount of their accounts.

The results of the credit union eXperiment are sum—

marized in Table 1.

TABLE 1

SUMMARY OF RESPONSES TO DEPOSIT
ACCOUNT CONFIRMATION REQUESTS

 

 

 

 

 

 

Sample
kl k2 k3 k4 k5

Sample Size 50 29 30 50 50
Proper ReSponses

ist requests 40 i3 23 36 31

2nd requests 8 7 2 10 8
Total 48 20 25 .46 39
Improper ReSponses

lst requests 4 3

2nd requests 2 0
Total 6 3
Nonresponses 2 3 2 3 7
Data not Supplied 2
Unable to Comply 1 2

 

50 29 30 50 50

68

Three people in sample k2 went to the office to
check on their accounts; one of these also called the
office. Two people from sample k3 went to the office;
one of these, with an account balance of $5,000, stated
that he did not know he had an account. One person from
sample k“ and one from sample k5 also went to the office.
The person from sample k5, with an account balance of
$600, stated that he did not know he had an account
balance.

There is a possible eXplanation for those who did
not know they had an account. They may have been con-
fused about the account being a time deposit account,
thinking that it was a regular account.

Telephone calls were received from one person in

sample k1, four people in sample k , and the one person

3
already mentioned in k2.

Confirmation requests were mailed or delivered to
the credit union by one person in sample k1, and two
people in sample k3.

All of those who visited or called the credit
union pr0perly confirmed with one exception, the person
in sample k5 who visited the credit union.

Table 2 is a summary of the calls and visits to

the credit union.

69
TABLE 2

SUMMARY OF TELEPHONE CALLS
AND VISITS TO CREDIT UNION

 

 

 

Sample
kl k2 k3 k4 k5
Visited credit union 3 1 1
Called credit union 1 1* 4

Mailed or delivered confirmau
tion to credit union 1 2

Properly reSponded

 

 

* Also included in

visited credit union.

The amount of the adjustments to the accounts of

those who reSponded improperly ranged from $150 to $500.

The average amount

reSponses was $423.

of the adjustments of the nine improper

75.

4.1.2 Results of Bank Experiment:

The results

of the eXperiments concerning the loan

account confirmation requests will be presented in sample

order.

Sample b1 -

A sample of one hundred unadjusted
accounts, using the standard form,
generated forty-nine proper reSponses
to the first requests and twenty-three

proper reSponses to the second requests.

70

Sample b2 - A sample of thirty accounts, whose
amounts were positively adjusted by an
amount of approximately ten percent of
the account balances with an average
adjustment of $120, generated thirteen
prOper reSponses. Five of those classi-
fied as prOper reSponses stated that
they didn't know the correct amount but
felt that the figure was too high.
There were six "antagonistic" phone
calls of which four knew the correct
amount. Those who called did not sub-
sequently return the confirmation
requests. There were no improper
reSponses.

Sample b3 - A sample of one hundred accounts, for
which the data concerning the accounts
were not furnished, generated fortyasix
replies. Forty-three of the forty-six
replies furnished the correct balance
(four reported only the number of pay-
ments made) and three omitted the
balance. Approximately sixty percent
of the responses were incomplete in some
reSpect. The first requests generated
twentymeight replies and the second

requests generated eighteen replies.

71

Sample b4 - A sample of one hundred unadjusted
accounts, which used the short form
confirmation requests, generated
forty-five proper responses to the
first requests and twenty-four
proper reSponses to the second
requests.

The results of the bank eXperiment are summarized

in Tables 3 and 4.

TABLE 3

SUMMARY OF RESPONSES TO LOAN ACCOUNT
CONFIRMATION REQUESTS

 

 

 

 

 

Sample
b1 b2 b3 b4
Sample Size 100 30 100 100
Proper ReSponses
lst requests 49 13 45
2nd requests 23 24
Total ‘ 72 13 43 69
Improper ReSponses mmmmmmmm none .........
Incomplete Responses 3
Nonresponses 28 17 54 31

 

100 30 100 100

 

72

 

 

 

 

TABLE 4
SUMMARY OF TELEPHONE CALLS
TO BANK
Sample
b1 b2 b3 b4
Called bank 0 6 0 0
Properly responded 0 0 0 0

 

4.2 Analysis of Results of Experiments
The analysis of the results of the eXperiments will
be presented in the order of the credit union, the bank,
and then the relationship between the two.
The following notation will be used throughout this
section.
Ho = null hypothesis
Ha = alternative hypothesis
p = proportion of sample which reSponded properly,
reSponded improperly, or did not reSpond
P = proportion of the population that would
reSpond properly, reSpond improperly, or not
reSpond

P-ll’

eXpected value of the proportion of the popula-
tion which would reSpond properly, reSpond
improperly, or not reSpond

An asterisk suprascript to a statistic symbolizes
that the statistic is the observed value of the statistic.

73
For example, t* means the observed value of the t statis—
tic.

y = number of successes in the sample.

4.2.1 Analysis of Results of Credit Union EXperiment:

The analysis of the results of the credit union
eXperiment will be presented first as it relates to the
testing of hypotheses and second as it relates to the
computing of confidence intervals.

A major problem was encountered in analyzing the
results of the credit union eXperiment. The distribu-
tions of the sample parameters obeyed the hypergeometric
probability law. The ratio of population to sample was
so small as to invalidate estimates (such as the binomial
estimate) of the probability distribution. The size of
the population was 456 and the smallest sample size was
twenty-nine. It was necessary to compute tables for the
hypergeometric distribution against which tests were con=
ducted. The confidence intervals were computed in a
similar fashion. For some tests a binomial test was
employed, but not until it had been tested against the
confidence intervals to determine that it was reasonable.
Several transformations were employed, these are disc
cussed as they are first employed.

1

Tests of significance were conducted at the 0.05

 

1Significance level is the probability of rejecta
ing ‘the null hypothesis when it is in fact true.

74
level and confidence intervals were computed at the 0.95

confidence level.

4.2.1a Test of hypothesis D1
Ho: P = 0.90 Ha: P (0.90
Where P = the proportion of proper reSponses to
confirmation requests which reflect
amounts that are greater than the
amounts shown on the recipients' records
(sample k2).
y = 20
p = 0.67
The hypothesis was tested by using a table developed
for a sample of twenty-nine, a population of 456, and a

probability of 0.90. The table revealed that:

20
Zpu) = 0.00106
X=0

Therefore, the null hypothesis is rejected at the

0.05 significance level.

4.2.1b Test of hypothesis D2
Ho: P = 0.90 Ha: P (0.90
Where P = the proportion of proper responses to
confirmation requests which reflect
amounts that are less than the amounts

shown on the recipients' records (sample

k3).

75
p = 0.83
The hypothesis was tested by using a table developed
for a sample of thirty, a population of 456, and a prob~
ability of 0.90. The table revealed that:

25
:p(X) = 0017361
X=0

Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.10 Test of hypothesis D3
Ho: P = 0.05 5 Ha: P>0.05
Where P = the proportion of imprOper responses to
confirmation requests which reflect
amounts that are greater than the amounts
shown on the recipients' records (sample
k2).
y = 6
p = 0.21
The hypothesis was tested by using a table developed
for a sample of twenty-nine, a population of 456, and a

probability of 0.05. The table revealed that:

29
P(x) = 00001.8“F
X:

Therefore, the null hypothesis is rejected at the

0.05 significance level.

4.2.10 T... of hypothesis 04

Ho: P = 0.05 Ha P>0.05

O.

76

Where P = the proportion of improper reSponses to
confirmation requests which reflect
amounts that are less than the amounts
shown on the recipients' records (sample
k3).

3

p = 0.10

‘4
II

The hypothesis was tested by using a table developed
for a sample of thirty, a population of 456, and a probaa
bility of 0.05. The table revealed that:

0
p(x) = 0.18630
x:

Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.1e Test of hypothesis D5

Ho: ‘P1 = P2 Ha: P ¢ P

1
the proportion of nonreSponses to con—

2
Where P
1

firmation requests which reflect incor~
rect amounts (samples k2 and k3) and

P2 = the proportion of nonreSponses to con-
firmation requests which reflect correct

amounts (sample kl).

vi = 5
y2 = 2

" 0.0”

’d
N
i

77

The hypothesis was tested by using the t test for

1 The test

count data proposed by Bennett and Franklin.
transforms the data so that the difference between the
statistics (tZ-tl) "is approximately distributed as the
range of 2 normally distributed variables for which the
upper 5% and 1% points are 2.77 and 3.64 reSpectively."2
This statistic was suggested for counts from a binomial
probability distribution: however, a comparison of the
results from using this statistic to compute the confia
dence intervals for some parameters in this study yielded
no difference from the confidence intervals computed in

the exact manner.

The test statistic is tz-tl where:

131 = 2 («[(Xl-i-l) (iii—5.) ‘Nfln'xl) P )

 

 

 

t2=2(W-./Tn-x2+1)fs)
where x1 = the number of successes in the sample
with the smaller proportion of successes,
x2 = the number of successes in the other
sample, and
5 = the proportion of successes of the com-

bined samples.

For this test: x = 2

 

. 10ar1.A. Bennett and Norman L. Franklin, Statistical
Analysis in Chemistry and the Chemical Industry, (New York:
0 ey & 0nS, 110.. 9 . ppo 11"]. 0

2Ibid., p. 612.

78

5 = 7/109 = 0.06
t1 = ~0.04
t2 = 0070

The value of the statistic is less than the 2.77
criterion noted by Bennett & Franklin at the 0.05 signifi-
cance level. Therefore, the null hypothesis is not

rejected at the 0.05 significance level.

4.2.1f Test of hypothesis D6

Ho: P1 = P2 Ha: P1 # P2

Where P1 = the proportion of improper responses to
confirmation requests which reflect
amounts that are greater than the amounts
shown on the recipients' records (sample
k2) and

P2 = the proportion of improper reSponses to

confirmation requests which reflect
amounts that are less than the amounts
shown on the recipients' records (sample
k3).

vi = 6

y2=3

p1 = 0.21

P2 = 0.10

The t test described in section 4.2.1e was used to

test this hypothesis. For this test: x1 = 3

79

X = 6
2
5 = 9/59 '-" 0015
t1 = ““093”
t2 = 0.72

tz-t1 = 1.06

Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.1g Test of hypothesis D7

Ho:

Where P

P2 =

P = P

1
1

3
2

"" 0.10

0.07

2 Ha: P1 % P2

the proportion of nonreSponses to confir-

mation requests which reflect amounts that
are greater than the amounts shown on the

recipients' records (sample k2) and

the pr0portion of nonreSponses to confir-

mation requests which reflect amounts that
are less than the amounts shown on the

recipients? records (sample k3).

The t test described in section 4.2.1e was used to

test this hypothesis. For this test: x = 2

1
x

2 3
5/59 = 0.08

t1 = 0.33

ll

80

tz-tl = 00 05

Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.1h Test of hypothesis D8

HO: P1 = P2

Where P1 _ the proportion of responses to confirma-

Ha: P1 i P2

tion requests using the standard form

(sample k1) and

P2 = the proportion of responses to confirma-
tion requests using the short form
(sample k4).
y1 = 48
y2 = 46
P1 = 0.96
P2 = 0.92

The t test described in section 4.2.1e was used to
test this hypothesis. For this test: x = 46

1

X = [+8

2

f3 = 94/100 = 0092‘"
t1 = -0.62

t2 = -0.62.

t2-t1 = o. 00
Therefore, the null hypothesis is not rejected at
‘the 0.05 significance level.

81
4.2.11 Test of hypothesis D9
Ho: P1 = P2 Ha: P1 ¢ P2
Where P1 = the proportion of reSponses to confirmae
tion requests which provide the recipients
with the data concerning their accounts
(sample k1) and
P = the proportion of reSponses to confirma—
tion requests which ask the recipients
to provide the data concerning their
accounts (sample k5).
y1 = 48
y2=39
p1 = 0.96
p2 = 0.78
The t test described in section 4.2.1e was used to

test this hypothesis. For this test: x1 = 39
X2 = [+8
5 = 87/100 = 0.87
t2 = 1.76

tzet1 = 3.39
Therefore, the null hypothesis is rejected at the
0.05 significance level.

4.2.1j Test of_hypothesis D10

Ho: P1 = P2 Ha: P1 g P2

Where P1 = the proportion of preper reSponses to

the first requests of confirmation

P

2

y1=36
9

‘4
N
II

82
requests which reflect incorrect amounts
(samples k2 and k3) and
the proportion of proper responses to
the second requests of confirmation
requests which reflect incorrect amounts

(samples k and k3).

2

p1 = 36/59 = 0.61
p2 = 9/16 = 0.56
The t test described in section 4.2.1e was used to

test this hypothesis. For this test: x = 9

1
X2 = 36
5 = u5/75 = 0.60
t1 :3 «0.10

2 = 0.00

tzetl = 0.10

Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.1k Test of hypothesis D11

Ho: P1

Where P1

= P2 = P3 Ha: P1 e P2 ¢ P3

the proportion of proper responses by
age group 1 (20-39) to confirmation
requests (samples k1, k2, k3, k4, and
k5), and

the proportion of proper reSponses by

age group 2 (40-59) to confirmation

83
requests (samples k1, k2, k3, k“, and

k5), and
P3 = the proportion of proper reSponses by

age group 3 (60 and over) to confirma-
tion requests (samples k1, k2, k3, k4’
and k5).

y1 = 48

y2 = 83

y3 = 44

p1 = 48/57 = 0.84

p2 = 83/95 = 0.87

p3 = 44/53 = 0.83

Those recipients who were less than twenty years
old were omitted from the analysis because a parent may
have completed the form. Variance analysis was used to
test this hypothesis. In order to use variance analysis
the data were transformed via Bartlett's transformation
for a binomial distribution.1 The particular transforma-
tion employed was g(x) = arcsinnfii The "two variables
of classification" scheme presented by Dixon and Massey2
was employed in the analysis. The analysis of variance
yielded an observed value for the F statistic of:

F* = 0.20

F.05(2.8) = 4.46

1M. S. Bartlett, "The Use of Transformations,"

ggpmetrics, Vol. 3, No. 1, (March 1947), pp. 39-52.

 

2Wilfrid J. Dixon and Frank J. Massey, Jr..
Introduction to Statistical.Analysis, Second Edition,
(New York: McGraw-Hill Book Company, Inc. , 1957) , pp. 157-8.

84
Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.11 Test of hypothesis 012

Ho: P1=P2=P3 Ha: P1¢P2¢P3

Where P1 = the proportion of pr0per reSponses to
confirmation requests from recipients
with account balances of $2,000 or less
(samples k1, k2, k3, k4, and k5), and

P2 = the proportion of pr0per reSponses to
confirmation requests from recipients
with account balances of $2,001 to
$5,000 (samples k1, k2, k3, k4, and
k5), and
P3 = the proportion of proper reSponses to

confirmation requests from recipients
with account balances of over $5,000
(samples k1, k2, k3, kg, and k5).

vi = 69

Y2 = 57

y3 = 52

p1 = 69/78 = 0.88

p2 = 57/64 = 0.89

p3 = 52/67 = 0.78

The transformation and variance analysis described
in section 4.2.1k was used to test this hypothesis. The

observed value of the F statistic was: F* = 1.06

3305”,,” = 4.46

85

Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.1m Test of pypothesis Di;

Ho: P1

Where P1

Y1 = 1

= P

2 Ha: P1<'P2
the proportion of telephone calls or
visits (to the office being audited)
from recipients of confirmation requests
which reflect correct amounts (sample
k1) and

the proportion of telephone calls or
visits (to the office being audited)
from recipients of confirmation requests
which reflect amounts that are greater

than the amounts shown on the recipients'

records (sample kg).

The t test described in section 4.2.13 was used to

test this hypothesis. For this test: x = 1

1
X2=3
3 = 4/79 = 0.05
t1 = “0037
t2 = 1.05

86
Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.1n Test of hypothesis D14

Ho: P1=P2 Ha: P1<P2

the proportion of telephone calls or

Where P1
visits (to the office being audited)
from recipients of confirmation
requests which reflect correct amounts
(sample k1) and

P = the proportion of telephone calls or
visits (to the office being audited)
from recipients of confirmation requests
which reflect amounts that are less than
the amounts shown on the recipients'
records (sample k3).

1

4

p1 = 0.02

P = 0.13

The t test described in section 4.2.1e was used to

'4 ‘4
N H
II II

test this hypothesis. For this test: x1 = 1

x = 4

p = 5/80 = 0.06
t1 = e0.69
t2 = 1.33
t2

"t1 = 2002

Therefore,

87
the null hypothesis is not rejected at

the 0.05 significance level.

4.2.10 Test of pypothesis D15

Ho: P

1
Where P1 =

P2 =
y1=7
y2=38
P1 = 7/7 =
Samples k2

= P

2 Ha: P1 £ P2
the proportion of proper reSponses among
confirmation request recipients who call
or visit (the office being audited) con-
cerning their accounts (samples k2 and
k3) and

the pr0portion of proper reSponses among
confirmation request recipients who do
not call or visit (the office being

audited) concerning their accounts

(samples k2 and k3).

1.00
= 0.73

and k were used for this test because

3

confirmation requests which reflect incorrect amounts are

the ones of greatest concern to the auditor. The t test

described in section 4.2.1e was used to test this hypothe-

sis.

For this test: x1 = 38

X2=7

s = 45/59 = 0.81
t1 = «7.86

t - 0.86

88
tZ-t1 = 8.72
Therefore, the null hypothesis is rejected at the

0.05 significance level.

4.2.1p Confidence intervals for samples k2 and k3
Confidence intervals were computed by determining

the smallest value of p such that:

and the largest value of p such that:

n x nqx < a
X = - .-
Pr( 2:?) Z N E
n
Where Np = number of successes in population
N = number of items in population
Nq = N-Np
a = i-confidence level
n = number of items in sample

By trial and error the following confidence inter-
vals were computed at the 95% confidence level.

I 3 0.84

Where P1 = the proportion of proper responses

0.50 5 P

to confirmation requests which
reflect amounts that are greater
than the amounts shown on the
recipients' records (sample k2).

0.66 5 P; g 0.94

89

Where P2 = the proportion of proper responses
to confirmation requests which
reflect amounts that are less than
the amounts shown on the recipients!
records (sample k3).

0.02 2 Pg 3 0.27

Where P3 = the proportion of nonresponses to
confirmation requests which reflect
amounts that are greater than the
amounts shown on the recipients'
records (sample k2).

0.01 5 PE 5 0.22

Where P4 = the proportion of nonreSponses to
confirmation requests which reflect
amounts that are less than the

_ amounts shown on the recipients!

records (sample k3).

0.08 S P; S 0.39

Where P5 = the proportion of improper reSponses
to confirmation requests which
reflect amounts that are greater
than the amounts shown on the
recipients' records (sample k2).

0.02 5 Pg s 0.26

Where P6 = the proportion of improper reSponses

to confirmation requests which

reflect amounts that are less than

90
the amounts shown on the recipients!

records (sample k3).

4.2.2 Analysis of Results of Bank EXperiment:

The analysis for the testing of the hypotheses is
presented first, then the confidence intervals are pre-
sented. Because of the high ratio of population to
samples and the large size of the samples, it is assumed
that the normal distribution is a good approximation for

the hypergeometric distribution which correctly applies.

4.2.2a Test of hyppthesis L1
Ho: P = 0.70 Ha: P<0.70
Where P = the proportion of proper reSponses to
the first requests of confirmation
requests which reflect amounts that are
greater than the amounts shown on the
recipients! records (sample b2).
y = 13
p = 0.43
ReSponses from recipients who stated that they
thought the amount was too high but that they didn't
know the correct amount were treated as proper reSponses.

The 2 test was used to test the hypothesis.

 

 

P* = 0014’3

2* a ___ysnP* = 3,19
VnP“ (1~P*)

Z = 1.64

.05

91
Therefore, the null hypothesis is rejected at the

0.05 significance level.

4.2.2b Test of_hypothesis#L2
Ho: P = 0.05 Ha: P>0.05
Where P = the proportion of improper reSponses to
first requests of confirmation requests
which reflect amounts that are greater
than the amounts shown on the recipients'
records (sample b2).
y = 0
p = 0.00
The 2 test was used to test the hypothesis.
2* = 1,25
2.05 = 1.64
Therefore, the null hypothesis is not rejected at
the 0.05 significance level.

4.2.2c Test of hypothesis L3

Ho: P1 = P2 Ha: P1 £ P2

Where P1 = the proportion of nonreSponses to con-
firmation requests which reflect cor-
rect amounts (sample b1) and

P2 = the proportion of nonreSponses to cone

firmation requests which reflect incor-
rect amounts (sample b2).

To test this hypothesis the proportions of reSponses

to the first requests of confirmation requests for samples

92

b1 and b2 were compared. The hypothesis could be restated

8.8!

H08 Pa = Pb

Where Pa = the proportion of nonreSponses to first

Ha: Pa # Pb

requests of confirmation requests which

reflect correct amounts and

'11
II

the proportion of nonreSponses to first

b
requests of confirmation requests which
reflect incorrect amounts.
Y. = 51
Yb = 17
Pa = 51/100 = 0.51

The 96 test was used to test the hypothesis.

2
”)(obs = 0'17

2 _
Ct.05.1 - 3'8“
Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.2d Test ofphypothesis L4
Ho: P1 = P2 Ha: P1 2 P2
Where P1 = the proportion of nonreSponses to con-
firmation requests which use the standard
confirmation form (sample b1) and
P2 = the proportion of nonresponses to con-
firmation requests which use the short

form (sample b4).

93

y1=28
Y2 = 31
p1 = 0.28
p2 = 0.31

The'XE test was used to test the hypothesis,

libs a 0.22

2 -
76.05.: " 3'8“
Therefore, the null hypothesis is not rejected at

the 0.05 significance level.

4.2.2c Test of hypothesis L5

Ho: P1. = P2 Ha: P1 9‘ P2

Where P1

 

the proportion of nonreSponses to con-
firmation requests which provide the
recipients with the data concerning

their accounts (sample b1) and

the proportion of nonreSponses to con-

2

firmation requests which ask the recipiu
ents to provide the data concerning
their accounts (sample b3).

y1 = 28

y2=57

p1 = 0.28

P2 = 0.57

5 = 0.42

Responses which did not provide the amount of the
account were treated as nonresponses. The hypothesis was

2
tested by means of the‘xj test.

94
ngbs = 17°21

2 _
1.05.1 - 3084
Therefore, the null hypothesis is rejected at the

0.05 significance level.

4.2.2f Test of_hypothesis L6
Ho: P1=P2 Ha: P1<P2
Where P1 = the proportion of telephone calls (to
the office being audited) from recipiu
ents of confirmation requests which

reflect correct amounts (sample b1)

and
P2 = the proportion of telephone calls (to
the office being audited) from recipi-
ents of confirmation requests which
reflect incorrect amounts (sample b2).
V1 = o
y2 = 6

The‘X? test was used to test the hypothesis.

gtgb, = 19.47

2
%.05.1 = 3084
Therefore, the null hypothesis is rejected at the

0.05 significance level.

4.2.2g Test of_hypothe§is L7

Ho: P1 = P2 Ha: P1 £ P2

95

Where P1 = the proportion of proper reSponses among
confirmation request recipients who call
(the office being audited) concerning
their accounts (sample b2) and

P2 = the proportion of proper reSponses among

confirmation request recipients who do
not call (the office being audited) con-
cerning their accounts (sample b2).

y1=o

Y2 = 13

p1 = 0.00

p2 = 0.54

Sample b2 was used for this test because confirma-
tion requests which reflect incorrect amounts are the ones
of greatest concern to the auditor. The 15 test was used

to test the hypothesis.
2

2 - .
1.05.1 " 3'8“
Therefore, the null hypothesis is rejected at the

0.05 significance level.

4.2.2h Confidence interv§l§_for samplgypz

Confidence intervals were computed at the 0.95 con-
fidence level for the proportion of proper reSponses and
nonreSponses to the first requests of confirmation requests
reflecting incorrect amounts. The confidence interval for
imprOper reSponse was not computed because there were no

improper reSponses. .A normal distribution was assumed to

96

be a good approximation of the sample distribution. The

confidence intervals were computed from the formula:

0.2.3

 

 

i- 2m 4% u-i-i-Vn s a s + we new

The confidence intervals were computed as:

0.26 5 P? S 0.61

Where P1 = the proportion of proper reSponses to
first requests of confirmation requests
which reflect incorrect amounts.

0.39 5 P3 3 0.74

Where P2 = the prdportion of nonresponses to first
requests of confirmation requests which
reflect incorrect amounts.

Analysis of Relationship Between Credit Union

Experiment and Bank EXperiment:

This subsection will present the analysis of the

four hypotheses on the relationship between the credit

union experiment and the bank experiment. Chapter five

will begin with a composite review of the analysis in

this chapter and then proceed to propose solutions to

correct the deficiencies disclosed by this analysis.

4.2.3a Test of hypothesis DL1

HO! P1 = P2 Ha: P1 # P2

Where P1 = the proportion of proper reSponses to

deposit account confirmation requests

which provide the recipients with the

97
correct data concerning their accounts

(samples k and k“) and

1
P = the proportion of proper responses to
loan account confirmation requests which
provide the recipients with the correct
data concerning their accounts (samples
b1 and b“).
The results of these samples were subjected to the

t test described in section 0.2.1e.

y1 = number of successes in samples 1:1 and k4
y2 = number of successes in samples b1 and b}+
V1 = 94

5'2 = 1M

5 = 235/300 = 0.78

t1 = -2.7u

t2 = 4.er

tZ-t1 = 7.16

Therefore, the null hypothesis is rejected at the

0.05 significance level.

u.2.3b Test ofthe_hypothesis DEE
Ho: P1 = P2 Ha: P1 g P2
Where P1 = the pr0portion of nonreSponses to the
first requests of loan account confirm
mation requests which reflect incorrect
amounts (sample b2) and

P = the proportion of nonreSponses to

98
first requests of deposit account confir-
mation requests which reflect incorrect
amounts (sample k3).
The results of the first requests of sample k3 were
compared with the results of sample b2. Sample k3 was
used because the adjustment was not in the customers'

favor and would be comparable to sample b It might be

2.
noted however that hypothesis D7 (the proportion of non-
reSponses to adjustments in the recipients' favor is equal
to the proportion of nonreSponses to adjustments not in
the recipients' favor) was not rejected. The t test
described in section h.2.1e was used to test this hypothe-
sis.

y = number of nonreSponses to sample b2

y2 = number of nonreSponses to the first requests

of sample k3
Y1 = 17
y2=l+
p = 21/60 = 0.35
t1 = -2.43
t2 = 2.22

Therefore, the null hypothesis is rejected at the

0.05 significance level.

0.2.30 Test of hypothesis DL3

HO: P1 =P2 Ha: P1 #P2

99

Where P1 = the proportion of improper reSponses to
loan account confirmation requests which
reflect incorrect amounts (sample b2)
and

P2 = the proportion of improper responses to

the first requests of deposit account
confirmation requests which reflect
incorrect amounts (sample k3).
The test of this hypothesis was performed in the
same manner (and for the same reason) as the test of

hypothesis DL2.

y number of improper responses to sample b2

1
y2 = number of improper responses to the first

requests of sample k3

VI = 0

y2=3

i = 3/60 = 0.05
t1 = -0.50

t2 = 1.07

tz-t1 = 1.57

Therefore, the null hypothesis is not rejected at
the 0.05 significance level.

4.2.30 Test of hypothesis DL4
Ho: P1 = P2 Ha: P1 ¢ P2
Where P1 = the proportion of nonreSponses to loan
account confirmation requests which ask

the recipients to provide the data con-

100
cerning their accounts (sample b3) and
P2 = the proportion of nonreSponses to deposit
account confirmation requests which ask
the recipients to provide the data con-
cerning their accounts (sample k5).
This hypothesis was tested by the t test described

in section 4.2.1e. Those reSponses which did not provide

the requested data were treated as nonresponses.

y1 = number of nonreSponses to sample b
y2 = number of nonreSponses to sample k5
xi = 57

y2 = 1.].

t1 = -3.zu.

t2 = 2.54

tz-t1 = 5.78

Therefore, the null hypothesis is rejected at the
0.05 significance level.

CHAPTER V
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

5.1 Summary of Results

The results of the two eXperiments will be summar-
ized in the order of proper reSponse, nonreSponse, and then
impr0per reSponse. In each subsection the discussion will
be addressed to the results of each eXperiment and to the

relationship between the two eXperiments.

5.1.1 Summary of Proper ReSponse:

The pr0portions of proper reSponses differ signifi-
cantly between the bank's loan accounts and the credit
union's deposit accounts (DL1). This difference is exem-
plified by the fact that there was a significantly smaller
proportion of proper reSponses to loan account confirma—'
tions which were incorrectly stated in the bank's favor
than to deposit account confirmations which were incorrectly
stated in the credit union's favor (D2 and L1). Although
second requests for incorrect loan confirmations were not
sent, the adjustment of test criteria would appear to be
valid in view of the fact that no difference was found in
the proportion of proper responses between first and
second requests to deposit account confirmations reflect-

ing incorrect amounts (D10). There was also a distinct

101

102
difference in the proportion of proper reSponses caused by
the direction of error in the confirmation (Di and D2)
with a greater proportion of proper responses to those
confirmation requests which were in the credit union's
favor. This difference is so pronounced that the lower
limit of the interval estimate of proper reSponses to
confirmations which were incorrectly stated in the credit
union's favor (0.66-0.94) was only one percentage point
below the midpoint of the interval estimate of proper
reSponses to confirmations which were incorrectly stated
in the recipients' favor (0.50-0.84).

Neither the age of the recipient nor the size of
the account has a significant influence upon the propor-
tion of proper reSponses (D11 and D12).

There is a marked difference between the two experi-
ments as they relate to telephone calls or visits. In the
case of the credit union eXperiment, there was no signifi»
cant difference in the proportion of calls or visits
between incorrect confirmation requests and correct con-
firmation requests (D13 and D10). However, the proportion
of proper reSponses among those who did call was signifi-
cantly greater than among those who did not call (D15).
Just the reverse was true for the bank experiment. The
incorrect confirmation requests generated significantly
more calls than did the correct requests (L6); but, the
proportion of proper reSponses was significantly less

among those recipients who called than among those who

103
did not call (L7).

5.1.2 Summary of NonreSponse:

The results of the eXperiments supported each other
as to the effect of incorrect confirmation requests upon
the proportion of nonreSponses. There was no significant
difference in the proportion of nonresponses to correct
confirmation requests and incorrect confirmation requests
(D5 and L3). The direction of error also did not sig-
nificantly affect the proportion of nonreSponses (D7).
However, the proportion of nonreSponses was greater for
loan account confirmation requests than for deposit
account requests (DL2).

There was no significant difference in the propor-
tion of nonreSponses between the short form confirmation
requests and the standard form (D8 and L4). However, the
blank confirmation form produced a greater proportion of
nonreSponses than did the standard form (D9 and L5). The
proportion of nonreSponses to loan account confirmation
requests was greater than to deposit account confirmation
requests; this difference was significant for blank form
requests (DL4) just as it was for requests reflecting

incorrect amounts (DL2).

5.1.3 Summary of Improper Response:
The proportion of improper reSponses to loan
account confirmation requests was significantly less

than to deposit account confirmation requests (DL3).

104
This may be due in part to the fact that the proportion
of improper reSponses to deposit confirmation requests
which reflect amounts that are greater than the recipi-
ents' records is between 0.08 and 0.39, this is somewhat
higher than the proportion of improper reSponses to
deposit confirmation requests which reflect amounts that
are less than the recipients! records (0.02-0.26).
However, the direction of error on deposit account con-
firmation requests does not significantly effect the
proportion of improper reSponses (D6). Another reason
for the difference is that the proportion of improper
reSponses to loan account confirmation requests which
reflect amounts that are greater than the recipients'

records is approximately 0.00.

5.2 ConcluSions

This study has clearly shown that the assumption
of no improper reSponse is totally invalid. While the
proportion of improper reSponses may vary with the cir-
cumstances it is nevertheless quite high and there appears
to be no basis for assuming that it is affected by the
direction of error; therefore, the notion of conserva-
tism (i.e".the auditor Is concerned only with overstate-
ment of assets or understatement of liabilities) does not
help. In one sample the proportion of improper reSponses
was twenty-one percent and the interval estimate (at a
ninety-five percent confidence level) for the population

was from eight percent to thirty-nine percent. This pro-

105
portion is so large as to make current statistical sampling
models invalid when applied to confirmation techniques.
What is worse, perhaps, is that improper reSponse arises
at the very time when the auditor most needs right answers,
i.e., when the records are wrong.

The only instances of improper responses were on
confirmation requests which reflected incorrect amounts.
This result leads to the conclusion that recipients gen-
erally neither take exception to amounts which agree with
their records nor provide incorrect data concerning their
accounts when asked to provide such data.

Although nonreSponse is a problem which is recog-
nized by many writers in the field of statistical sampling
in auditing, the assumption which is often made that the
proportion of nonresponses to correct confirmation requests
is equal to the proportion of nonreSponses to incorrect
confirmation requests appears to be valid. It also
appears that the direction of error has no effect on the
proportion of nonreSponses. Based on these findings the
statistical sampling models currently being used in audit-
ing would be quite satisfactory if there were no improper
reSponses.

The particular form used to confirm the accounts
seems to have no effect upon nonreSponse if the recipients
are provided the data concerning their accounts. If the
recipients are asked to provide the data, the proportion

of nonreSponses increases significantly.

106

The proportion of proper reSponses appears to be
independent of both the ages of the recipients and the
size of the accounts being confirmed. This lack of
dependence on age should be comforting to auditors since
they often are unable to obtain this information and even
if they could obtain the information the additional work
required to stratify the accounts on the basis of age
would be a burden. The lack of dependence of reSponse
on the size of the accounts in these eXperiments tend to
refute the assumption made by some that larger accounts
are more likely to elicit a reSponse. These two vari-
ables, then, probably can be safely ignored by the auditor.

Although age and account size do not affect the
proportion of proper reSponses, there is a difference in
the proportion of reSponses under differing circumstances.
This difference may be due to any one or combination of
the following factors: (1) the characteristics of the
population being sampled, (2) whether the accounts being
confirmed are receivables or liabilities, and (3) the
attitude of the recipients toward the company being
audited.

There appear to be no diminishing returns from
first to second requests. The results yielded by the
second requests are much the same as those yielded by the
first requests. This study did not go into the extent to
which this conclusion could be carried. It is possible
that third or even fourth requests may continue to yield

comparable results.

107
No definitive conclusions can be drawn concerning
telephone calls or visits to the office being audited.
It is clear, however, that under certain circumstances
the number of calls or visits can be significant. It is
quite possible that the direction given to the callers
determine whether they reSpond to the confirmation

requests.

5.3 Recommendations

These recommendations are based upon the conclu-
sions of the preceding section and upon the three follows
ing assumptions. First, direct communication with the
parties concerned is not always the least efficient and
least effective means of verifying accounts. Second,
each account in the population has an equal probability
of being in error. Third, the probability of reSponse
from a recipient is independent of the condition of the
account. Condition is defined here as any characteristic
which differentiates one account from another except the
accuracy of the account balance, (e.g., date of last
payment, age of account, etc.).

The first assumption is necessary for the study to
be of any practical significance to auditing. If alterna-
tive procedures are always more efficient and effective
than the confirmation procedure, then alternative proce—
dures should be followed: therefore, the effect of improper
reSponse or nonreSponse would make no difference to the

auditor.

108

The second assumption supposes that errors are made
on a random basis and not on a selective basis. If some-
one were deliberately attempting to misstate the accounts
it is possible that he would select the accounts on some
basis. This problem is always prevalent, however, and can
be circumvented by assigning some ratio of error proba-
bility to the different accounts. This in effect is a
stratification of the accounts.

The third assumption supposes the actions of the
recipients are random phenomena as far as the condition
of the account itself is concerned. It does not imply
that certain groups of recipients do not react differently
but only that if they do react differently to confirmation
requests, this difference is in no way caused by the condi-
tion of the accounts.

If the proportion of nonreSponses is independent of
the accuracy of the account balances and if improper
reSponse did not exist, then estimates of the population
could reasonably be made based on the data which are
received. There seems to be no reason to believe that if
the recipients were asked to provide the data concerning
their accounts, the proportion of nonreSponse would be
dependent upon the accuracy of the account.1 The problem

of improper reSponse can be avoided by using the blank.

 

1Note that hypotheses D5 and L3, which in essence
stated that in those instances where the recipients were
provided the data concerning their accounts the propor-
tion of nonresponses was independent of the accuracy of
the account, were not rejected.

109
confirmation form.1 It is avoided at the cost of a greater
proportion of nonreSponses; but, there seems to be no other
satisfactory means of avoiding improper reSponses.

It is therefore recommended that auditors cease
using confirmation forms which provide the recipients with
the data concerning their accounts and in their place use
forms which ask the recipients to provide the data. The
statistical models currently advocated in manuals and
texts should continue to be used except that where esti-
mates (or conclusions) are based on the total sample size,
the size of the reSponse should be substituted for the
sample size. By like manner, models for determining
sample size should be corrected by multiplying the presently
determined sample size by the reciprocal of the proportion
of nonresponses anticipated. This anticipated proportion
of nonreSponses can be determined from prior eXperience.

An alternative solution, which is not considered
generally necessary but, which does not depend upon the
second and third assumptions was developed by Morris H.

Hansen and William N. Hurwitz.2 Their method essentially

 

1Although the recipient may provide incorrect data,
attention is directed toward the account. Improper
reSponses which most concern auditors are those which
arise because the reSpondents failed to take exception to
an incorrect amount. Unless the reSpondent called the
office to get the data, it is unlikely that he would
report an incorrect amount which coincides exactly with
the companys' records.

2Morris H. Hansen and William N. Hurwitz, "The
Problem of NonmReSponse in Sample Surveys," Journal of
the.American StatisticalEAssociation, Vol. 41, No. 236.
(December 1946). pp. 517-529.

110
estimates the population parameters by estimating the
parameters for reSpondents and for nonreSpondents and
then combining the two. The estimate of the parameters
of the nonreSpondents is based on a sample of the non-
reSpondents to the initial request. This method is

explained further in Appendix C.

5.4 Recommendations for Further Research

There are four areas where further research should
be directed. The first and most important area for fur-
ther research is in connection with the first assumption
in section 5.3; i.e., direct communication with the
parties concerned is not always the least efficient and
least effective means of verifying accounts. The valid-
ity of this assumption should be subjected to critical
examination. The second area is improving alternative
procedures. Research directed toward improving alterna-
tive procedures would be eSpecially needed if alternative
procedures are sometimes more effective and efficient
than confirmation procedures. The third area is the test-
ing of the second assumption in 5.3; i.e., each account
in the population has an equal probability of being in
error. The fourth area of additional research is the
testing of the third assumption in 5.3: i.e., the prob-
ability of a response from a recipient is independent of
the condition of the account.

Although the resolution of these questions would

not solve all of the auditors' problems concerning con»

111
firmation of accounts, it would be a major step forward

for the auditing profession.

APPENDIX A

1019 TROWBRIDGE ROAD I EAST LANSING, MICHIGAN 48823 0 PHONE 353-2280

  

MSU EMPLOYEES CREDIT UNION

Dear Member:

Your supervisory committee is making a routine examination of our recordS.
The committee would like you to compare the amount indicated bel1w with
your records and confirm the amount directly to them. This amount
represents your time deposit account on February 29, 1968.

Account Number

 

Date of Certificate

 

Amount of Certificate Account

Please compare the above amount with your records, note differences in
the Space below, sign and return this confirmation directly to the
supervisory Committee, P.O. Box 425, East Lansing, Mich. A return
envelope is enclosed for your convenience.

Sincerely,

a“. c- 44..., ~J-W 4.44“
Frances Lesnieski
General Manager

Exceptions (if any)

 

 

“W

THIS IS A CONFIRMATION REQUEST, N92 A STATEMENT OF YOUR ACCOUNT

1113

MSU EMPLOYEES CREDIT UNION
TIDE DEPOSIT ACCOUNT - CONFIRMATION FORM

Please compare the information
hereon with your records, note
any differences on the reverse
side, sign, and return this
confirmation directly to the
Supervisory Committee, P.0.
Box 425, East Lansing, Mich.
A return envelope is enclosed
for your convenience.
Confirmation Date February 29, I968

 

 

 

Account Date 0? Tresent Signature
Number Certificate Balance

1019 TROWBRIDGE ROAD I EASY LANSING. MICHIGAN 48823 - Flimsy-2280

 

NISU EMPLOYEES CREDIT UNION

Dear Member:
Your supervisory comittee is making a routine examination of our records.

The committee would like for you to examine your records and provide the
information requested below relating to your time deposit acéount';

Certificate Account Number

 

Amount, as of February 29, 1968

Please sign and return this confirmation request directly to the
Supervisory Coxmnittee, P.O. Box 425,East Lansing, Mich. A return
envelope is enclosed for your convenience.

Sincerely,

duo A! . .1964“-.. 415.4

Frances Lesnie ski
General Manager

 

Signature

APPENDIX B

1:15
Cowmnwm armors NMIONAL Damn

awn Mus m Comm on cadence

231 SOUTH LASALLE STREET CHICAGO. ILLINOIS 60690

THIS IS NOT A REQUEST FOR PAYMENT

In connection with the examination of our records, your account

 

shows an unpaid balance of $ on .
Kindly compare this amount and the information below with your
records as of . If correct, please sign below; but

 

if not correct, supply full information on the reverse side of
this letter.

Date of Amount Date of Last Amount of
Note of Note Payment Last Payment

 

 

This request is made in the usual course of our regular audit for
the purpose of verifying your account. This is not a bill or a
statement. An addressed enve10pe is enclosed for your convenience
in furnishing the desired information promptly.

Very truly yours

I..-“

’ ’(’\ ,SC’T-‘z? J - ---""""' *5

\"' \r

G. G. Davenport
Auditor

Signed

1:16
Comma-gum Tumors NMIONAL BANK;

awn Tans r Comm or CHICAGO

231 SOUTH LASALLE STREET CHICAGO. ILLINOIS 60690

THIS IS NOT A REQUEST FOR PAYMENT

In connection with the examination of our records on ,
please furnish the information requested below from your records.

Date of Note

 

Amount of Note

 

Date of Last Payment

 

Amount of Last Payment

 

Unpaid Balance

 

This request is made in the usual course of our regular audit for
the purpose of verifying your accounts. This is not a bill or a
statement. An addressed envelope is enclosed for your convenience
in furnishing the desired information promptly.

Very truly yours

\\_ . ,3 CW~ «Jar/VT
G. G. Davenport
Auditor

Signed

1137
Cormmmmam Tumors Nmronan Baum
awn Mus m Comm or mcaoo

231 SOUTH LASALLE STREET CHICAGO. ILLINOIS 60690

LOAN ACCOUNT - CONFIRMATION FORM

Confirmation Date

Please compare the information
hereon with your records, note
any differences on the reverse
side, sign, and return this
confirmation directly to me.

A return envelope is enclosed
for your convenience.

 

 

Amount Date of
of Note Last Payment

Signed

Present
Balance

- Very truly yours

0 ......
J“- N c x AW 0'?
G. G. Davenport
Auditor

 

 

 

APPENDIX C

APPENDIX C

The method developed by Morris H. Hansen and William
N. Hurwitz,1 put in an auditing environment, is simply to
(1) take a‘random sample of the population, (2) send first
requests to all those selected, (3) take a random sample
of those who do not reSpond, and (4) obtain a reply from
those selected in the second sample. This could easily
be extended to taking the sample of nonreSpondents after
second requests have been sent to the nonreSpondents to
the first requests. The following is from the Hansen and
Hurwitz article.

An unbiased estimate of the population is obtained
by computing:

-_ N I

Where: N _ the number of accounts in the population

n

the size of the original sample

x1 = total of reSpondents to initial sample

s = number of confirmations that were not
returned and

r2 = the average of the sample of nonreSpon-

dents

The sample variance of x is given by:

 

1020. filth, Pp. 517”5290

118

2‘71

'2'
1a.

119

2
2 2 N-n 2 N s s 2
x (N-1)n n (r )s—i b

Where: 02 = the variance in the entire population
between the initial accounts

Ob = the variance among nonreSpondents to
the initial sample

s = the number of accounts in the popula-
tion on which a response would not have
been received to the confirmation

requests

 

r = the number of accounts in the sample
of the nonrespondents

If N/(N-l) s/(s-i) é 1, the formulas for the

Optimum initial sample size (n) and the optimum second

sample size (r) are:

2
n = 02 N0 [1 + (%'- 1)Q]

+ BE.%§%

the average sampling error

 

Where: 6

 

 

 

Q = the rate of nonreSponse to the initial
sample
and
s
r =\[_61 (1-Q)
C1’+ CZ (l-Q)
Where: C1 = the cost of preparing and mailing the
initial sample
C2 = the cost of processing the reSponses

to the initial sample

120
C3 = the cost of obtaining and processing

data on those accounts in the second

sample

 

BIBLIOGRAPHY
Books

Bennett, Carl A. and Franklin, Norman L. Statistical
Anal sis in Chemistry and the Chemical Industry.
New Iork: ’John Wiley & Sons, Inc., 1954.

Dixon, Wilfrid J. and Massey, Jr., Frank J. Introduction
to Statistical Anal sis. Second ed. New York:
McCraw - Hill Book 0., Inc., 1957.

Hill, Henry P., Roth, Joseph L., and Arkin, Herbert.
Samplinggin Auditin . New York: The Ronald
Fress Company,~i9 .

Lenhart, Norman J. and Defliese, Philip L. Montgomery's
Auditin . 8th ed. New York: The Ronald Press
Company, 1957.

Stettler, Howard P. Auditing Principles. 2nd ed.

Englewood Cliffs, N. J.: Prentice - Hall, Inc.,
19 1.

Vance, L. and Neter, J. Statistical Sam lin for Auditors
and Accountants. New York: John WiIey & Sons,

Inc., 1956.
Articles and Periodicals

Accounting Questions. Answer from an unnamed practitioner,

The Journal of.Accountancy, LVIII, No. 5 (November
9 O 910

Bartlett, M. S. "The Use of Transformations," Biometrics,
III, No. 1 (March 1947), 39-52.

 

Blough, Carmen G. "Confirmation Procedure Must Be Adapted
to the Circumstances," Accounting and Auditing
Problems, The Journal of Accountancy, XCVII, No. 3
(March 1954),‘3457—

Broadhurst, W. H. "Follow—up of Accounts Receivable Ciru
cularization," Canadian Chartered Accountant,
LXXXVI, No. 2 (February 19 5 , 1 5.

121

Q P ‘ ‘mq
1]

If"
I

122

Davis, Gordon B., Neter, John, and Palmer, Roger P. "An
EXperimental Study of Audit Confirmations," The
Journal of Accountancy, CXXIII, No. 6 (June 1967),

Hansen, Morris H. and Hurwitz, William N. "The Problem
of Non-Response in Sample Surveys," Journal of
American Statistical Association, XLI, No. 236

TDecember 19467, 517:529.

Healy, Robert E. "Sampling in Auditing is for all Auditors,"
"The New York Certified Public Accountant, XXXVI,
No. 5“(May 1966),‘366:

. "Sampling in Auditing: the Whole Story," Price
Waterhouse Review, IX (Winter 1964), 40.

Lytle, Richard C. "Accounting and Auditing Problems,"
The Journal of Accountangy, CXVIII, No. 3(September

195E).'73-

Maynes, E. Scott. "Minimizing ReSponse Errors in Financial
Data: The Possibilities," Journal of the American
Statistical Association, LXIII, No. 321 (March I968),
214427.

Smith, Alden C. "The Accounting Profession's Growing
Interest in Statistical Sampling," The New York
Certified Public Accountant, XXVII, No. 7 (July

$937).”52-
Reports

Committee on Auditing Procedure. Auditing Standards and
Procedures. New York: American Institute of
Certified Public Accountants, 1963.

Committee on Auditing Procedure. Statements on'Auditing
Procedure, No. 1, Extentions of Auditing Procedure.
New York: —American Institute ofIAccountants,
October 1939.

Committee on Bank Accounting and Auditing. Audits of
Banks. New York: American Institute of Certified
PuElIc Accountants, 1968.

Committee on Practice Review. Departures From Generally
Accepted Auditing Standards and Accountin Prin-
ci les. New York: American Institute of ertIfied
PuEIic Accountants, 1966.

_ . ' fl

123

Committee on Statistical Sampling. Statistical Sampling
and the Inde endent Auditor. New York: American
Institute of CertITied PuBlic Accountants, 1961.

 

   

IIIII

IIIIIIII

   

IIIIIIIIIIEIIIIIIIIIIS

93 031