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A COMPARISON OF SOME
STATISTICAL STUDIES OF
HYBRID CORN TRIALS

Thesis for the Degrce of M. S.
MICHIGAN STATE COLLEGE

Kenneih J. Frey
I945

Jhesns

 

This is to certify that the
thesis entitled
A Comparison of Some etetisticai
Studies of Hybrid Corn Trials.

presented by

henneth J. Frey

has been accepted towards fulfihnent
of the requirements for

M.S. degree in farm CPODS

L2. 3%”

Major professor

 

 

Datenfleptember l; 1945

 

 

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A.COMPARISON OF SOME STATISTICAL STUDIES OF
HYBRID CORN TRIALS

by

KENNETH J. FREY

.A THESIS

Submitted to the Graduate School of Michigan
State College of Agriculture and Applied
Science in partial fulfilment of the
requirements for the degree of

LESTER OF SCIENCE

Department of Farm Crops

1945

'H ESIQ

I |II 'l, I‘Lr

. [‘(lI lr|r|

If

.I\

A COMPARISON OF SOME STATISTICAL STUDIES OF
HYBRID CORN TRIALS

173876

The writer wishes to acknowledge his indebtedness to
Dr. E. E. Down for his guidance and aid in making this
study.

Gratitude is also eXpressed to Mr. H. M. Brown and to
Dr. W. D. Eaten for their willing cooperation and helpful

advice and criticism.

TABLE OF CONTENTS

I. introduction .......................................
II. Review of previous literature ......................
III. Materials ..........................................
IV. Presentation and discussion ........................
A. 1943 data .......................................

1. Emplanation of methods .......................

2. Discussion of results .........................

B. 1944 data 0.000000000000000000000000coo.000000000

1. Emplanation of difference for significance ...
2. Standard error methods explained .............
a. Illustration of method one ................

b. Illustration of method two ................

0. Illustration of method three .............. g

d. Illustration of method four ...............

3. Discussion of standard error comparison ......

4. Ranking of varieties in 1944 trials ..........

a. Explanation of methods ....................

b. Discussion of correlation coefficients ....

c. Discussion of ranking arrays ..............

V. Summary ............................................
VI. Literature Cited ...................................

VII. Appendix: Tables 7-21 inclusive ...................

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INTRODUCTION

In the randomized design used for the Farm Crops Depart-
ment corn trials in 1943, and years previous, half of the
experimental area was used by the check variety. The ques-
tion arises, is it necessary to use half or even a quarter
of the experimental area for checks? This question forms
the basis for part of the investigations that the writer
presents in this paper.

The other part of these investigations deals with the
particular field design for corn used in 1944, and is under-
taken with the hope of finding a method by which the lowest
valid standard error for the whole experiment can be ob-

tained.

-2-
REVIEW OF PREVIOUS LITERATURE

Love (5) states that in the system of randomization and
its analysis of variance, there is a general tendency to
have few or no check plots. He also states, "For many kinds
of experiments it is important to use checks, but although
the deviations are smallest when the checks are placed at
frequent intervals, it may not be necessary to locate the
checks as closely together as indicated by the preliminary
data since this will require a considerable area of land for
the checks."

The method of averaging standard errors has been used
by Down and Brown (1) in wheat studies. Their errors were
based upon percentages of mean yields. .Hays and Garber (2)
feel that the method of obtaining an error is more or less
of an arbitrary matter depending on the degree of accuracy
wanted.

Hayes and Garber (2) quote the following with regard to
using the probable error of the checks for the error of all
varieties. "It is possible to use sufficient check plots so
that the computed probable error of a single determination,
i. 6., SD‘x i.6745, may be reliable for the variety in ques-
tion." .

Down and Brown (1) in wheat investigations consider the
error of checks to be that of the varieties when testing for

significance between varieties.

-3-
HATER IALS

The data on yield per acre used in this investigation

was collected from.corn trials in 1943 and 1944.
1943 data:

In 1943 the corn varieties were planted in randomized
blocks, each replicated five times, with chedks occurring in
every other plot. A.plot consisted of one row ten hills
long, with each hill being thinned to three stalks when the
seedlings were about four inches high. The trials selected
for these studies were: Saginaw County with 28 varieties;
Huron County with 25 varieties; St. Joseph County with 39
varieties. Other trials were not used because they did not
contain sufficient data. The yields were corrected for

missing stalks.
1944 data:

.A different planting plan was selected for use in 1944,
when a design consisting of a series of 6 x 6 Latin squares
was adopted. Five varieties were planted in each square
along with a sixth variety which was common to all squares.
This sixth variety served as a standard. Also, one IOW'Of
this common variety was planted between successive squares.

The plots in these trials were one row wide and 12
hills long, with the two least desirable hills being dis-
carded at harvest time. The corns were thinned to three

stalks per hill as in 1943. Six trials were selected for

-4-
investigation. Huron County trial with five squares; Otsego
County with three squares; Montcalm County with four
squares; Clare County with four squares; Sanilac County with
four squares; Ingham County with eight squares. no yield cor-
redtions were made for missing stalks in 1944.

Yields per acre were calculated on the basis of fifteen
and one-half per cent moisture,so that all varieties regard-
less of date of maturity would be on a comparable dry weight
basis. The formula used for calculation considered 70 lbs.
per bushel, because the weights were taken on ear corn.

For the check-standard, a variety was used which was
considered as average for maturity and yield within the 10-

cality in which the trial was conducted.

-5-
PRESENTATION AND DISCUSSION

1943 data:

Discussion of 1943 data

The order of ranking by actual and coefficient of yield
values is given in tables 7, 8, and 9, for the 1943 trials
investigated. Coefficient of yield values, often referred
to as P/C, were calculated according to Spragg's method (5),
wdth the "C", or theoretical plot yields, being obtained by
grading the soil between check plots. The arrangement of
checks used in calculating P/C values were as follows:

(1) check in every second plot; (2)check in every fourth
plot; (3)check in every sixth plot.

It is very apparent from.a study of these tables that
within the same trial, the P/C rankings of the first and last
few varieties conform very closely with the actual yield
ranking of the same varieties. In the Saginaw trial (table
7) five of the first seven varieties are common to all four
methods of ranking. The same variety, Funk 303, occurs in
first place for all methods of analysis, while Funk G12 oc-
curs three times in second place and once third, and Pio-
neer 373 ranges from second to fourth place. The other two
varieties of the five are Walters 274 and 368, with the for-
mer dropping to seventh place in the case of checks every
second plot. Also in this same trial, five of the last
seven places are occupied by varieties common to all methods
of ranking, and the arrangement is almost identical to that
described for the top ranking varieties. Funk G174 occurs in

-6-
last place each time.

The trial in Huron County gave results similar to those
found in the Saginaw trial. Five of the first six places
were accupied by varieties common to all methods of ranking,
and the top three varieties were the same for each method,
except that they changed order in two cases. Fourth spot
was held by the same variety by each method. The last four
spaces were occupied by varieties common to all methods of
ranking, but the order is different in each case.

Again, in the St. Joseph trial, the results conform to
those already described. As shown in table 9, four of the
first seven places are held by varieties common to actual and
to the three P/C rankings, and the top variety is Pioneer 314
in all cases; but the bottom place standings do not show
quite the unanimity of ranking by the different methods as
do the previous trials. Only three of the last seven places
are held by varieties common to all methods of ranking.

The central portions of these ranking arrays ShOW'nO
uniformity whatsoever. Within the same trial, the varieties
may fluctuate up and down as much as twelve or fourteen
places from one method of ranking to another. However, this
is to be expected because the difference which distinguishes
between two varieties five places apart may be such that if 0.3cf
a bushel were added to the lower one, it would supplant the
one five places above it. A.very small change induced by a
different method of analysis could send a variety either way

up or way down in the central portion. As a whole,the

-7-
checks do not seem.to facilitate the selection of top or bot-
tom ranking varieties. Actual yields are about as reliable
in picking them, and, if checks are desirable, the results
bear out that they give as reliable data from which to draw
conclusions when planted every sixth plot as when planted

every second or fourth plot, and much less land is used.
1944 data:

1944 tests for significance

Tables 10, 11, 12, 13, 14, and 15 give the varieties
ranked in order of decreasing magnitude of actual yield per
acre for each trial. In the keys of these tables are given
the differences needed between variety means for signifi-
cance as calculated from standard errors, as obtained from
the different methods of analysis.

The difference for significance is calculated from.the

following formula:
diff. for sig. = st‘hzf

In the formula, "s” is the standard error as determined from
the error line, "t", for the degrees of freedom.of the error
line, is obtained from.a table of "t" values, and "n” is the
number of determinations that are included in a variety mean.
Analyzing differences between variety means is facilitated
by calculating the "difference for significance."
1944 standard error comparison
The standard errors for 1944 data were worked by four

different methods of analysis for each trial.

-8-

Table 1. Table showing layout and analysis of Square 1,

Otsego County
-Fie1d arrangement:

 

 

Rows
Columns A B C D E L_ Total
1 70.2 85.6 73.2 66.6 61.2 65.5 422.3
2 80.8 83.3 69.7 60.4 58.8 63.5 416.5
3 72.8 85.5 60.9 58.8 53.2 51.0 382.2
4 84.5 72.9 52.5 61.9 39.0 74.7 385.5
5 94.3 86.6 58.2 51.1 56.0 67.2 413.4
6 89.9 76.9 63.9 62.0 4711 80.1 419.9
S 492.5 490.8 378.4' 360.8 315.3 402.0 2439.8
82.1 81.8 63.1 60.1 52.7 67.0
Arrangement by varieties:
.A B C D E fi;_E Av
G176 70.2 76.9 58.2 60.4 39.0 51.0 355.7 59.3
177 80.8 86.6 60.9 61.9 47;1 65.5 402.8 67.1
Kin. 72.8 72.9 63.9 66.6 58.8 67.2 402.2 67.1
51B 84.5 85.5 73.2 62.0 56.0 63.5 424.7 70.8
F40 94.3 83.3 52.5 58.8 61.2 80.1 430.2 71.7
11A. 89.9 85.6 69.7 51.1 53.2 74.7 424.2 70.7
2439.8
CT : 165,350.67
sstot = 171,499.14 - 165,350.67 = 6,148.47
88001 = 165,618.70 - 165,350.67 = 268.03
ssrow = 169,637.03 - 165,350.67 = 4,286.36
ssvar = 165,987.10 - 165,350.67 2 636.43
Analysis:
Source D.F. S.S. M.S. Error
Total 35 6,148.47
Col 5 268.03 53.61
ROW’ 5 4,286.36
Var 5 636.43 127.29
Error 20 957.65 47.88 6.98

Table 2 0

Field arrangement:

Columns

mmO‘HPCfiNI-J

Arrangement by varieties:

F21
K12
W225
M32
S4
Ck

CT
SStot

SScol
SSrOW'

SSvar

Analysis:
Source
Total
001
ROW'
Var.
Error

-9-

Otsego County

 

 

 

Rows

4A B C D E F
79.1 77.7 72.0 59.3 65.9 72.3
80.9 85.9 67.1 77.5 49.5 79.2
77.1 79.8 80.0 62.3 48.8 80.7
81.4 80.6 75.7 61. 58.0 66.4
84.1 65.4 77.3 53.6 60.4 71.9
81.3 75.7 70.2 63.5 64.5 67.7
483.9 465.1 442.3 378.1 347.1 438.2
80.7 77.5 73.7 63.0 57.8 73.0

,A g, C D E F
79.1 75.7 77.3 77.5 58.0 80.7
80.9 65.4 80.0 61.9 64.5 72.3
77.1 80.6 70.2 59.3 49.5 71.9
81.4 79.8 72.0 63.5 60.4 79.2
84.1 85.9 75.7 62.3 65.9 67.7
81.3 77.7 67.1 53.6 48.8 66.4
181,291.45

184,716.84 - 181,291.45 = 3425.39
181,357.51 - 181,291.45 - 66.06
183,593.96 - 181,291.45 = 2502.51
181,644.35 - 181,291.45 = 352.90
D.F. 8.8. M,S, Earp:

55 5,425.59

5 66.06 13.21
5 2,502.51
5 352.90 70.60
20 703.92 35.19 5.93

Table showing layout and analysis of Square 2,

Total

426.3

440.1
428.7
424.0
412.7
422.9
2554.7

448.3
425.0
408.6
436.3
441.6
394.9

Av
74.7
70.8
68.1
72.7
73.6
65.8

Table 5 0

Field Arrangement:

Columns

ClJCJ‘JCJ'IrF‘CfiINI-flI

Arrangement by varieties:

KFl
KF2
W255
240
M34
Ck

CT
SStot
SScol
SSrow

ssvar

Analysis:
Source
Total
Col
Row
Var
Error

-10..

Otsego County

 

Table showing layout and analysis of Square 3,

 

Rows
__§: 7__B ,9: D E F Total
83.4 79.2 83.8 61.4 63.1 .62.5 433.4
75.9 84.0 70.1 67.0 71.2 54.4 422.6
78.9 68.1 76.9 69.2 64.0 68.8 425.9
74.4 75.7 62.1 65.2 74.9 59.0 411.3
80.7 71.5 61.5 57.5 52.1 59.2 382.5
76.2 57.9 63.3 70.6 59.6 51.1 378.7
469.5 436.4 417.7 390.9 384.9 355. 2454.4
78.3 72.7 69.6 65.2 64.2 59.2
A B C D .E F ‘:_
83.4 57.9 61.5 67.0 74.9 68.8 413.5
75.9 71.5 76.9 65.2 59.6 62.5 411.6
78.9 75.7 63.3 61.4 71.2 59.2 409.7
74.4 68.1 83.8 70.6 52.1 54.4 403.4
80.7 84.0 62.1 69.2 63.1 51.1 410.2
76.2 79.2 70.1 57.5 64.0 59.0 406.0
167,335.53
170,261.66 - 167,335.53 = 2,926.15 L
167,784.12 - 167,335.53 = 448.59
168,720.72 - 167,555.55 : 1,595.19
167,347.08 - 167,555.55 = 11.55
D.F. S.S. ‘M.S. £239;
55 2,926.13
5 448.59 89.72
5 1,395.19
5 11.55 2.31
20 1,070.80 53.54 7.31

Av
68.9
69.6
68.3
67.2
68.4
67.7

-11-

method_one or "individual squares average" method, is
the method where each square of a trial is analyzed individ-
ually, giving a standard error for each. From.these, an av-
erage of the standard errors of all the individual squares
is obtained and this average is used as the error for the
whole experiment. This method is illustrated by the data
from Otsego County. Analyses of these squares are given in

tables 1, 2, and 3. The averaging is done as follows:

89, No, Error gbtained
l 6.98
2 5.93
3 7.31
Average 6.35

Method 17.179- or "as a randomized experiment" is illustra-
ted by data obtained from Otsego County as given in table 4.
The analysis table is aa'follows: ‘
Analysis of variance

 

 

 

Source D.F. _:S.S. M.S. Error
Total 107 12726
Between Rep. 5 6493
Between Var. 15 1146 74.40
Within stand. 12 403 33.55
RxV (error) 75 4684 62.45

Error + Within St. 87 5087 58.47 7.64
"Within standards" is obtained from.an "analysis of standards"

table:

Analysis of variance on standards

Source D.F. 3.8.
Total 17 2596
Rep. 5 2193
‘Within st. 12 403

In this design, the rows of the Latin squares become the re-

plications, so all rOW'AJs in the squares are included in

replication one, B's in replication two, etc., thus making

lysis by method two.

for ana

. Ct uo

Table showing how data is

Otsego County data.

Table 4.

A

from square
1

Varieties

 

073 saeqsem

819 9015

13X QSOJOSflYCUOJN\OH)

[[10 runs,

9115 runs
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of
standards

N

Standards from
square

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1.9
47.1
65.5

80.5
86.6
355.7 402.8

60
6

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9
2
n
0

0.
6
68
60
39

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242
206
162.2
166.0
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-12-

Varieties from square

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one 0816

593 081151 EOLLWMHH

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3131 350,103,331 L:\r-I\O mmm H

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Var 8 448.3

 

-15-
the replications continuous across the field. The randomized
design formed is very special in that each variety occurs
within a width of six plots for all replications.

Methqg three treats the whole experiment as one unit,
but the squares making up the trial retain their individual-
ity. This type of analysis will be illustrated by data from
Otsego County. The complete analysis is as follows:

Analysis of variance

 

Source D.F. S.S. MQS. Error
T0tal 107 12726
Between Sqa. 2 218
Between Rep. 5 6493
S x R 10 1107
Between Col. 15 783
Between Var. 15 1146 76.46
Error 60 2979 49.65 7.05

S x R is obtained from the two-way table, analysis of R by 3.

Analysis of variance for S x R

Source D.F. S.S.
_Total 17 7818
Sq. 2 218
Rep. 5 6493
S x R 10 1107

001.8.8. is obtained by adding the "Column Sums of Squares"
from.individua1 analysis. Var. S.S. is obtained the same as
Col. S.S.

Method.£ggr_(checks and standards) urrors are calculated
from the assembled data of checks and standards, with each
being considered as a variety, so that between x’s (vari-
eties) and "between replications" sums of squares can be ex-
tracted from.the total. The table of analysis worked on

Otsego County data by this method is as follows:

-14-

Analysis of variance of checks and standards

 

Source D.F. S.S. M.S. Error
Total 41 5667
Between Rep. 6 3769
Between x's 5 687
Error 30 1211 40.37 6.35

Discussion of standard error comparison

Table 5. 1944 overstate corn trials. Standard errors given in
bushels as obtained by different methods of analysis.

a __v County trials
M6§§?d_§ature of method Huron 1:33 Otsego Slag: Clare Ingham
I Individual sqs.
(Av.) 10.02 9.55 6.74 8.03 7.75 8.17
11 Randomized eXp. 9.94 8.54 7.64 7.60 8.81 9.02
III As unit with sqs.
retaining indi-

 

 

 

viduality 10.10 9.88 7.22 8.34 7.44 8.14
IV Checks and stand-
ards 9.81 6.34 6.35 5.66 7.55 10.00

AmJt needed for

sig. between

methods at 5%

level 4.00 3.90 3.68 3.37 3.57 2.79

The standard errors as obtained by these foucmethods of
analysis are assembled in table 5.

Table 5 shows that the errors obtained by the average of in-
dividual squares are higher than the "checks and standards" er-
rors in every case but one, that being in Ingham.County where a
reversal occurred. Huron County trial with a difference in er-
rors of 0.21 bushels between methods one and four represents the
smallest difference, while Montcalm.County with 3.21 bushels re-
presents the largest, the difference being in favor of method

four in each case. This latter difference approaches the amount

needed for significance between methods.

-15-

When comparing methods two and four, the same relation-
ship holds as did with the former case. Ingham.County again
was Opposite the other five trials. It is of interest to
note that even before calculations were started, Ingham
County trial was labeled as a poor experiment, for the trial
'was non-uniform. The differences between standard errors
for methods two and four range from 0.13 bushels in Huron
County to 2.2 bushels for Montcalm.County. This shows that
a somewhat closer relationship exists between methods two
and four than exists between methods one and four.

Errors by method one are higher than those by method
two in three trials, Huron, Montcalm, and Sanilac; while er-
rors occur lower by method one than by method two in three
trials also, Otsego, Clare, and Ingham. Errors by "average
of individual square" analyses range from.1.01 bushels high-
er in Montcalm County to 1.06 bushels lower in Clare County
than errors by the randomized experiment.

Under method three, lowest errors of any method are
gotten in two county trials, Clare and Ingham, and in three
of the trials, Huron, Montcalm, and Sanilac, the highest er-
ror is obtained by this method. In Otsego County trial, the
randomized experiment analysis gives a slightly higher error
than any other method used. Errors by methods one and three
are very close together, ranging from 0.48 bushels below in
Otsego County for method one than method three, to .31 bushel

above in Clare County. This latter statement is to be ex-
pected because the methods are very similar; only one dif-

ference is present: replications are considered in method

~16-
three as they are in method two. Errors obtained by method
three are lower than those by method one in two out of the
six cases, being 0.31 bushels lower in Clare County and 0.06
bushels lower in Ingham County. .A comparison of methods two
and three shows that the errors by the latter are smaller in
three out of six counties, these being Otsego, Clare, and
Ingham. Differences between methods three and four approach
significance in Montcalm, Sanilac, and Ingham counties.

Errors obtained by method four are smaller than errors
by any other method in Huron, Montcalm, Sanilac, and Otsego
Counties.

No significant difference is present between the errors
as obtained by different methods within any of the trials.
This was tested at the 5%jpoint, and the differences needed
for significance are given in the lower line of table 5.

Probably the greatest disadvantage of obtaining an er-
ror by method one is that if one square has an exceptionally
large error, the average error is boosted enormously.

The corn experiments here in.Michigan are laid out so
that varieties of about equal maturity occur in the same
square. This means that early maturing varieties occur in
one square, medium.maturing varieties in another, and late
maturing in still another, and the early maturing square is
not expected to yield as well as is the late maturing one.
The varieties so arranged in a square will need heavy mois-

ture and high temperatures at approximately the same time,

so weather conditions will be either beneficial 0r detrimen-

-17-
tal to a whole square. From.this, it becomes apparent that
a difference is apt to occur between squares, and if this
does occur, it would be eliminated by extracting the differ-
ence between squares as in method three. This method takes
out "difference between squares", which is lacking in the
randomized experiment method.

The method of analysis giving the lowest error in Huron,
Montcalm, Otsego, and Sanilac Counties is "checks and stand-
ards," which is in reality a measure of soil heterogeneity
of the experimental field. If all varieties are expected to
respond nearly the same to environmental factors as the
standard variety, an error obtained from the standard and
check variety would be a logical one to use when testing for
significance between variety means, but if all varieties
throughout the experiment do not respond alike, as they sel-
dom.do, some other method for analyzing should be used.

Ranking of varieties in 1944

Tables 16, 17, 18, 19, 20, and 21 give ranking of vari-
eties in 1944 trials in bushels per acre according to de-
creasing magnitude. Section one in each table contains the
varieties as they ranked with yield per acre calculated by
what will be referred to here as method one or the "add and
subtract" method. This is done in the following manner:
the mean yields of the checks on either side of the square
and the mean yield of the standard within that square are
averaged. The amount that this average is above or below
the average yield of all checks and standards in the trial

is added to or subtracted from the mean of each variety

-18-
‘within this particular square. The method proceeds for all
squares in like manner.

Method two or actual yield ranking of varieties given in
section two of each table is from the raw data, letting each
variety stand as it yielded with no corrections.

Method three or 78 method of ranking varieties is given
in section three of each table. 35 yields in 1944 were de-
rived by dividing-the mean yield of each variety in a square
by the mean yield of the standard within that square.

First place is held by the same variety for all three
methods of ranking in four of the trials; Mich 30 in Huron,
Ohio 1415 in Montcalm, Master F21 in Otsego, and Mich 59 in
Sanilac, but in Clare trial, Mich 20 ranks first in sections
one and two, and drops to third place in section three.
Ingham County shows no consistency of first place holders.

It is of interest to note the Otsego trial where the
first three and last three places are occupied by the same
varieties in all sections.

Rankings by the add and subtract method conform.more
closely to actual yield rankings than do those by 35 method,
but section one seems to be more closely related to section

'I'

three than does sectionfto section three. In other words,

the add and subtract method seems to form "a happy'medium”

between the other two methods.

-19..

Table 6. 1944 data.

Correlation coefficients between

different meth0ds of ranking varieties.

Between methods

 

 

Cor. coef. needed

 

 

County trial ‘2: for sig. at
_ 18621803 2&3 Zlevels
5’0 10
Huron 0.551 0.818 0.556 0.396 0.505
Iflontcalm. 0937 0358 0109 04:44: .561
Otsego .899 .938 .876 .514 .641
Sanilac .890 .719 .394 .444 .561
Clare .952 .527 .345 .444 .561
Ingham .888 .835 .580 .325 .418
Key: Method No. Method
1 .Add and subtract
3 .Actual yield

Discussion of correlation coefficients

For further evidence as to which method of ranking
proves best, correlation coefficients have been worked be-
tween the yields as obtained by methods one and two, one and
three, and two and three for the six trials,and these coef-
ficients are assembled in table 6. All values are positive.

The correlation coefficients between methods one and
two, given in column one, all prove to be highly significant
when tested against the values needed for significance given
in column.four. Huron trial gives the lowest value in this
comparison with a coefficient equal to 0.551, and the next
lowest coefficient value is 0.888 for Ingham County.

In the comparison between methods one and three, the
correlation coefficients are highly significant in four

cases and significant in one case. The Montcalm.trial co-

efficient is not significant at either the 5% or the 1%

ILevel. In only two instances did the coefficients for

-20-

methods one and three exceed the coefficients for methods one
and two, these being Huron and Otsego counties. It can be
said, in general, that the doefficients in column two are
lower than those in column one.

The correlation coefficients between methods two and
three are high enough for significance in only three coun-
ties, Huron, Otsego, and Ingham, and all of these are highly
significant. The coefficient for Montcalm is 0.109, and
only one coefficient goes above the 0.580 of Ingham, this
being Otsego with 0.876. Correlation coefficients obtained
between methods two and three are lower in every case than
either of the first two comparisons'with the exception of
Huron County, where the coefficient in column three is 0.556
and in column one is 0.551.

From.the foregoing discussion 0n the correlation coef-
ficients, it can be seen that a closer relationship exists
between the add and subtract and actual yield methods of
treating varieties than exists between either of these two
methods and the Pfismethod. .A closer relationship also ex-
ists between add and subtract and P/S methods than exists
between actual yield and Rs methods of treating varieties.
The statements made in this paragraph further substantiate
the fact that method one places varieties on a plane between
the other two methods.

W

A true picture of why a drop occurs in correlation co-

efficient when.P§:method enters into it, can be better shown

Table 6a.

1.

Add
and
subtract

2.

3.

Add
and
subtract

-21-

Scatter diagrams showing relationship between the
placement of varieties by the three methods of
ranking. Montcalm County data.

Actug; yield
82 80 78 76 74 72 70 68 66 64 62 60
80 1

05
CD
l—‘N
Oil-J

r I 0.937

Aotugl yield
82 80 78 76 74 72 70 68 66 64 62 60
74 1 l

r = 0.109
its
74 72 70 68 66 64 62 60 58 56 54 52
80 1

0%
oz C)
H

one
+4 to
H

r = 0.358

-22-
by the accompanying tables 6a1, 2, and 3. These tables are
called scatter diagrams and are designed to present graphical-
ly the relationship between variety placement by two methods
of ranking, for each diagram.

In table6al, it can be seen that the population forms
a homogeneous group running diagonally from.the upper left
hand corner to the lower right hand corner, and this makes a
high correlation coefficient. In table 682, a large group
of the population runs the same as in table 6a1, but in the
upper right hand corner is a group of five varieties. When
the original data of these particular varieties is examined,
it is found that they all occur in the same square. The
same group of five varieties are found in a group by them-
selves in the lower left hand corner of table 6a3. A group
of values separated in this manner will cause the correlation
coefficient to be reduced considerably. The value worked
from table 6a2 gave a coefficient 0.109 and table 6a: gave a
coefficient of 0.358, neither of them being high enough for
significance.

As mentioned above, each of those small groups that are
apart from the rest of the population are the same group, and
the group is composed of five varieties from.the same
square. In this particular square the standard had an ex-
ceptionally low value, so all P/g values in this square were
boosted up enormously. The same thing occurred in several

of the other trials. This provides a limitation on the use
of the P4, method of ranking varieties.

-23-

The "add or subtract" method has an advantage over the
3/5 method, because an average of 18 plots is used to deter-
mine how much will be added to or subtracted from variety
means, while in the latter, the corrections are based upon
the average of only six plots. In the first method, use is
made of the six plots used in.Bé determinations plus the 12
check plots, six on either side of the square. Itis better
to draw conclusions from results where more determinations
are used, in order to obtain more accuracy.

When ranking by actual yield, the varieties are allowed
to fall wherever in the ranking array they will, with no cor-
rections. If one of the plow; does fall down, the whole av-
erage is dragged down with it. If a square should happen to
occur on a poor part of the field, all of the varieties in
that square will be dropped down in the ranking array, but
if corrections are made according to checks and standards,
which will also probably be low, the varieties will be
raised to an equal basis with the remainder of the field.

-24-
SUMMARY

For this investigation there were available data from
three hybrid corn trials grown in 1943 and from six trials
grown in 1944. The investigation was carried on to attempt
an answer to tWo questions: (1) does a check planted every
sixth plot give as valid results upon which to judge vari-
eties on test as if planted every second or fourth plot?

(2) what is the method of analysis by which the lowest valid
error can be obtained from the design composed of 6 x 6 Latin
squares?

Calculations have been worked on the data and from the
results given in this paper, the following conclusions may
be drawn:

(1) The first few and last few varieties of the ranking
array, as ranked by actual yields and by'gb values calculated
from.0hecks every other plot, checks every fourth plot, and
checks every sixth plot, are approximately the same. This
fact leads one to believe that if checks are needed at all,
it is quite sufficient if they are placed in every sixth
plot.

(2) Varieties within the central portion of these
ranking arrays do not show the uniformity of placement as
mentioned in conclusion number one. However, they behave as
would be expected, because 0.32 bushels added to a variety
yield by another method of ranking could boost that variety
five places or even more.

(3) 0f four methods of analysis used on 1944 data, the

method which treated the experiment as a unit but left the

-25-
squares with their individuality, gave the lowest errors in
two cases, and the "checks and standards" errors were lowest
in four cases. The "as a unit with squares retaining indi-
viduality" errors were lower than the "average of individual
squares" errors in two out of six cases, and lower than
"randomized experiment" errors in three out of six cases.

(4) "Checks and standards" errors are lower than errors
from either "average of individual square" errors, or gran-
domized experiment" errors in five out of six cases.

(5) No significant differences were found between any
two of the methods of analysis within the same trial, but in
several cases, the differences approach significance.

(6) From.the methods of ranking 1944 varieties, the
"add and subtract" method seems to place varieties somewhere
between.3§ and actual yield ranking. This conclusion is
based upon data given in tables 16, 17, 18, 19, 20, and 21,
and upon correlation coefficients worked between the differ-
ent methods of ranking the varieties.

(7) A.limitation occurred in use of the 2g method, be-
cause several trials were found, where a poor standard yield
would boost all of the varieties of a square way out of line

with the remainder.

-25-
LITERATURE CITED

(1) Down, E. E. Brown, H. M. Patten, A. J. Winter, 0. B.
and Coons, G. H., Investigations on Winter Wheats
in Michigan. Mich. State College Tech. 5ul. No. 88.
1928.

(2) Hayes, H. K. and Garber, R. J., Breeding Plant Crops.
McGrawéHill 2nd ed. 1927.

(3) Love, H. H., Application of Statistical Methods to
Agricultural Research workers. Shanghai: The Com-
mercial Press 1937.

(4) Snedecor, G. W., Statistical Methods. Collegiate Press
3rd ed. 1940.

(5) Spragg, F. A., The coefficient of yield. J u e
Soc, 9f égron, 12:168—74. 1920.

APPENDIX

Tables 7 - 21 inclusive

In the following tables Hoosiercrost and Kingscrost

are abbreviated respectively as Hsrcrost and Kgscrost.

-27-

 

 

 

N.w6 :NHw Mczm 0.66 dNHw Mada w.mw :NHS MCSh 6.N6 :NHw xcsa
6.66 6H66H 6666666 6.66 6H66H 6666666 6.66 66 66H6 H.66 quoH 6666666
m.66 6 66Hs 6.66 6H6 66H6 6.66 qH66H 6666666 6.66 6H6 66Hs

.66 6H6 66H6 6.H6 66 66Hs 6.66 6H6 66H6 H.6N 6 66H6
6.66 6 66Hs 6.66 6 66Ha 6.66 666 666H6 6.66 66 66H6
6.66 66 66H6 6.66 66 66H2 6.66 66 66Hs H.H6 66 66H6
6.66 66 666H6 6.66 66 666H6 6.66 66 666H6 6.66 66 666H6
6.66 666 666H6 6.66 666 666He 6.66 666 66Hs 6.66 666 666H6
6.66 666 66666H6 6.66 666 66666H6 6.66 666 66666H6 6.H6 666 66666H6
N.H6 6mm 66666H6 6.66 666 66666HH 6.66 666 66666H6 6.66 666 666He
6.66 666 6H66 6.66 666 666H6 6.66 666 666H6 6.66 666 66666H6
6.66 666 66666H6 6.66 666 66666Hm 6.66 H66 666H6 6.66 66 66H:
6.66 66 66H6 6.66 H66 666H6 H.66 66 66H6 6.66 666 6H66
6.66 666 66666 6.m6 66 66H6 6.66 666 66666H6 6.66 H66 666HH
6.66 H66 666H6 6. 6 6H6 6H66 6.66 6H6 6666 6.66 6H6 H666
6.66 mm 66Hs 6.66 m: 66Hs 6.66 666 66666Hm 6.m6 6m HoHs
m.ww 6m Seas N.Nm m a oaflo 6.66 6H3 oano w. w 6 sedfi
6.66 o 56H2 6.66 am 6656 6.66 ems OHSO v.66 mmm ammcon
6.66 6H2 6H66 6.66 mm 66H6 6.66 mm 66Hs 6.66 66 66Hs
6.66 6H6 6666 H.66 666 66666H6 6.66 66 66Hs 6.66 666 66666HH
6.66 666 66666H6 6.66 66 66H: 6.H6 666 6666H66 6.66 6H6 6H66
m.H6 66 66H6 6.66 666 6666H66 6.66 666 6666H66 6.66 66 66H6
6.H6 666 6666H66 H.66 66 66H6 6.66 66 66H6 6.66 666 6666H66
6.66 666 6666H66 6.66 666 6666H66 6.66 666 66666Hm 6.66 66 6666H66
6.66 N 6 66666H6 H.66H 6H6 6666 6.66. 66 66Hs 6.66. 66 66666H6
6.66 6H6 H666 6.66H 666 66666H6 6J66. 6H6 6666 6.66_ 6H6 H666
mhmmw 666 6666 MhHmw 666 6666 mhmmw . 666 6666 H.66H 666 6666
.53 CH .53 CH .52 ca .59 CH
6H6Hw . 6H6Hw 6H6H6 6H6Hs

mpoamwxam mpOHQ 550m mpOHC 05p
66m>m 660656 3 66¢>6 666650 0. mao>e mxomno 6 camaz Hm5po<
soak 665H6> (m 5066 665H6> \m 8666 665H6> {m

umcH656H we ooxpmfi

.mmapmapm> wcaxcmp 6o wooflpee mo 6066665500 .6566 6pc5co amchmm

.6 6H666

 

-28-

 

 

 

6.66 4666 6666 6.66 666 6626 6.66 626 6626 6.66 46H6 6666
6.66 6H6 6666 6.66 64 6666 6.66 46 66626 6.66 46 66666
H.66 64 6666 6.66 46 66666 6.66 4666 6666 6.66 6H6 6626
6.66 46 66626 6.66 666 6666626 6.H6 64 6666 6.66 6 6626
4.66 666 6666626 6.H6 46H6 6666 6.H6 666 6666626 6.66 66 6626
6.H6 6 6666 H.66 6 6666 H.66 6 6666 6.66 64 6626
6.66 66 6626 6.66 66 6666 6.66 6H6 6666 H.66 666 6666666
6.66 66 6626 6.66 6H6 6666 6.66 666 6666 6.66 626 6666
6.66 666 6266 6.66 66 6626 4.66 66 6626 6.66 H66 66626
6.66 66.6626 6.66 66 6666 6.66 66 6626 6.66 66 6626
6.66 466 6266 6.66 666 6666666 6.66 666 6666 6.66 66 6626
6.66 466 6666H66 6.66 666 66666 6.H6 666 6666626 6.66 666 6666666
6.H6 H66 66626 6.H6 466 6666 6.26 666 66666 6.66 666 66666
6.66 66 6626 6.66 H66 66666 6.66 666 6666666 H.66 666 6666666
m.66 666 6666626 6.66 666 6666666 6.66 a 66 6666 6.66 66 6626
.66 666 6666 6.66 666 6666626 H.66 466 6666H66 6.66 666 6666626

6.66 666 6666666 6.66 666 6666 H.66 466 6666 6.66 666 6666
6.66 666 66666 4.66 666 66666 6.46 666 6666626 6.66 466 6266.
6.66 666 6666666 6.66 66 6626 H.M6 H26 66626 6.46 666 666266
6.66 666 66626 6.66 66 6666666 6..6 666 66626 6.46 666 6666626
6.66 666 6666666 6.66 66 6666666 4.66 666 6666626 6.66 666 66666
6.66 66 6626 6.66 66 6626 4.66 66 6626 6.66 66 6626
6.66 666 666H66 6.66 666 6666266 6.66 6H6 6666 6.66 6H6 6666
6.66 626 6666 6.66 66H6 6666 6.66 666 666H66 6.66 666 666266
H.66 6666 6666 6.66 626 6666 6.66 66H6 6666 6.66 6666 6666
.66 62 .66 62 .66 62 .66 66

6H666 66666 6H626 6H666

6p066.x66 mpcam 6506 muoag 03p
66m>m 660650 a. 666>6 mxomso 0\ 666>6 mxomgo o UH666 stpod
8066 665H6> .\w 5066 66566> m 5066 665H6> \m

”6666666 60 606663

.666p6666> mcdxcmh 60 mcofipwe mo :06666mnoo .6666 6pc500 2065m .m mHnma

 

 

Table 9. St.

Actual yield

JOSGDh County data.

Method of renking:

 

Pioneer 314
Funk G21
Funk G20
Funk 6114
Funk F138
Funk G67

It'll Ch. 1 6

‘ Lowe 14

Pioneer 341
Ohio M34
I‘v’liCh 12
Mich 18
Mich 28
Mich 34
Pioneer 322
1nd 4160
Lowe 6W
hich 26
Mich 31
MiCh 27
Kgscrost KY
Lowe 15
Pioneer 324
1111011 13
Ohio M34
Mich 17
11511011 21
31110171 29
Lowe 22
Mich 2O
MiG/h 22
Jacques 11573
Mich 32
Indiana 210B
W150 648
Kings KR2

P ioneer 353A
Ohio M15
Mich 248

YiéTE
in bu.

 

.fig
(.6.

O O O O

O . o

109\”\OO l—‘mW-F'U" O\
O
womww H ON [\3 W

wwwwmmwmmm$
wmwommmmomwwmwmmmmwwmwmmzmmm

O 9 O O O

*1 O\O\O\O\\i‘\l“\l'\l C“
O

tn

3 O C . .

I O c o

O O Q C C O

gn0\own0\Ora«kw~¢xhq«hqxrqxr0~r<~¢\hqxrq~¢w

m-QKJmA0230CDFJHrovAqufl4r¥%
0

Oomoer

 

Ba values from PA values from
U checks every 9 checks every
two_p10ts _ _ four plots

Yield "““7ff§fa

12-22- in by.
Pioneer 314 .82.2 Pioneer 314 62.-
Funk G20 79.7 Funk 620 82.1
nicn 28 79.7 hich 26 *81.8
Pioneer 322 76.6 Funk 6114 77.2
Funk c21 76.0 Pioneer 322 76.9
Funk 667 75.8 hioh 16 76.6
Funk 6114 75.2 Funk G21 76.4
Mich 16 71.4 Lowe 14 74.2
Mich 12 74:7 9mmh 2132 73.2
Funk 613$ 'Wifli Rich 1% 73.6
hich 31 73.1 Funk 667 73.&
Lowe 14 72.9 hich 27 73.3
Pioneer 341 71.6 chic M34 72.7
Mich 34 71.4 hich 34 72.0
mich 27 71.3 Mich 31 71.7
1nd. 4160 71.1 Pioneer 341 71.3
hich 12 71.0 ohio h21 69.9
Ohio M34 71.0 Mich 13 69.7
Lowe 15 70.5 1nd. 4160 69.5
hich 21 7:.2 Lowe 15 69.&
Mich 29 70.0 hich 12 69.2
Jacques 10013 69.9 Mich 22 69.1
Lowe 6W 6C.8 Lowe 6H 63.9
hich 13 69.8 Pioneer 353A 66.6
on io 1.1314- 69 . .3 hich 21 6s . t
Pioneer 324 69.4 Pioneer 324 65.4
hich 26 69.3 hich 32 62.2
Kings KY 68.9 Kings KY 63.1
1nd 2102 67.8 hich 17 62.)
Mich 17 67.5 Mich 26 67.9
hich 22 66.6 hich 29 67.6
Mich 32 65.7 1nd 2102 67.6
Pioneer 353A 63.7 hinge K22 66.6
Kings KR2 0;.9 Jacques 11573 66.2
Ohio n15 64.9 Ohio 115 65.1
Lone 22 65.6 flisc 6M6 64.6
Wise 6&3 62.8 Lowe 22 62.9
hich 20 63.0 Mich 20 61.6
Mich 24B 57.6 hich 24E 57.3

 

 

ison of methods of ranking varieties.

 

1‘7,1 values from
V checks every
six plots
‘Yield
in 9:1
Pioneer 314 “21.7
hich 26 79,7

Funk G21
Funk G20
Pioneer 322
Funk Gllf
Mich 13
Mich 16
Funk 667
Funk F136
Pioneer 341
Mich 31

it‘ll Ch ‘3 -
Ohio M34
Mich 27
chic n24
Mich 29
Lore 14
1nd. it16G
Lowe 6U
Kingff,2f
Mich 12

12.1.1 C31" 2 *3)
Pioneer 324
JRCQUSS 11573
1nd 2108
171.1011 2].

Lowe 15

11711011 13

Mich 17
Pioneer 353A
Ohio M15
Lowe 22

341.1011 32 I

Wisc 646
Mich 20

Kings K32
Mich 246

(

LJ
0 o

O

~FKT’ K)"- O \N f}
o o o o o o o o o o o

“ H HHm r0 03w ~P’

”V
O O C O

(hquUAQwDQ'
O O I O O C

O O C

C?" O\ OW ON 0\ CH O'\ O\ ON O'\ C""\ Ch O‘xC‘ \O\O\\\I’ZF\C‘\C}‘\\J\1':J'\} NNN‘JN NNNNNNN'KJ \i
Q Q
9
‘ kflN‘QKO m O‘Q‘i'rxi r-‘NKOMKIKNKN mmxo HKOKN‘KJJ O9. “3‘an O‘\i‘—" 1“" (ESPN C9. 1" FOWQ Q [0

x} w w +1761 Ox .7 C \~\I -\l \1 xi ca...

 

 

 

Table 10.
yields.
Rfigk Variety

1 Mich 50

2 Pioneer 570

3 Mich 20

4 Hsrcrost 112A
5 Hsrcrost 213
6 Ohio M15

7 Pfister 274
8 Pioneer 575

9 Funk GlA
10 Mich 29

NNNNNmHHHHHHHH:
mmmmwoomqmmpmm

Pioneer 555
Kingscrost D4
Funk G175
‘Wisc 464

Mich 51B

Funk G177

Wise 416
Pioneer 359
Kingscrost KNl
Kingscrost KS6
Wise 412
Master F60
Kingscrost K32
Mich 57

Mich 56

Yield
jg bu.

97.7
90.6
89.1
88.8
88.3
86.9
86.8
86.7
86.7
86.5
86.0
84.8
85.8
83.0
82.0
81.6
81.5
81.0
80.5
79.8
78.2
77.3
76.9
76.7
76.2

-30-

Huron County data.

Varieties ranked by actual
Differences needed for significance in
bushels given for different methods of analysis.

Method used

 

Av. of Ind. sqs.
Randomized exp.
‘As a unit with

sqs.
uals

as individ-

Checks and
standards

Bu. differ-
ence for

t

significance

e

5" 1”

11.5
11.5

11.6
11.4

15.2
15.0

15.3
15.2

-31-

Table 11. Montcalm County data. Varieties ranked by actual
yields. Differences needed for significance in
bushels given for different methods of analysis.

 

Bu. differ-
ence for
Rank Yield Method used significance
No Variety , in bu. at g “1%“
I Ohio M15 82.5 5 o 1
2. Funk GlA 78.0 1. Av. of Ind. sqs. 11.2 14.9
5 Mich 20 74.9 2. Randomized exp. 9.7 12.9
4 Master F60 70.8 3. As a unit with
5 Funk G174 70.1 sqs. as individ-
6 Kingscrost KA4 69.4 uals 11.5 15.0
7 NIiCh 52 6809 40 Cheeks and
8 Mich 56B 67.9 standards 7.4 9.9
9 Mich 56 67.7
10 Funk G177 67.2
11 Pioneer 359 67.1
12 Mich 57 66.2
13 Pioneer 375 66.1
14 Mich 50 64.0
15 Mich 29 63.7

16 Kingserost D4 65.4
17 Kingserost Km 65.0
18 Wise 464 61.4
19 Wise 416 61.2
20 Kingscrost KE2 59.4

-32..

Otsego County data.

Varieties ranked by actual

Differences needed for significance in

bushels given for different methods of analysis.

 

Table 12.
yields.
Rank ,
No Variety
1 Master F21
2 Mich 54
5 Mich 52
4 Master F40
5 Kingscrost KE2
6 Mich 51B
7 Kingscrost KF2
8 Kingscrost KFl
9 Mich 54
10 Wise 255
ll Wise 255
12 'Wise 240
15 Funk G177
14 Kingscrost KELL
15 Funk 0176

Yield
in bu.

74.7
75.6
72.7
71.7
70.8
70.8
69.6
68.9
68.4
68.5
68.1
67.2
67.1
67.1
59.5

Method used

 

l.
5.

4.

Av. Of Ind. sqs.
Randomized exp.
As a unit with
sqs. as individ-
uals

Checks and
standards

ence for
significance

2
55
7.8
8.7

8.5
7.5

10
10.4
11.5
11.1

10.1

-33..

 

 

 

Table 13. Sanilac County data. Varieties ranked by actual
yields. Differences needed for significance in
bushels given for different methods of analysis.

Bu 0 differ"
ence for
Rank Yield 3M9th°d used significance
No, Variety ‘ip bu. at 2 levels
1 Mich 59 87.4 5% 1%
2 Kingscrost D4 85.5 1. Av. of Ind. sqs. 9.6 12.7
3 Funk 0175 85.5 2. Randomized exp. 8.7 11.5
4 Mich 54 83.8 3. As a.unit with
5 Funk G177 83.6 sqs. as individ-
6 Kingscrost KA4 82.5 uals 9.6 12.7
7 Pioneer 370 82.3 4. Checks and
8 Mich 36B 81.6 standards 6.6 8.8
9 Funk GlA 80.1

10 IMaster F60 80.1

11 Wise 416 79.7

12 Pioneer 373 79.1

13 Mich 30 78.7

14 IMich 57 78.2

15 Kingserost KS6 76.1

16 Pioneer 359 75.3

17 IMich 11A 75.1

18 Kingscro st KM 75 .0

19 Wise 255 74.9

20 Kingscrost K82 70.4

Clare County data.

Varieties ranked by actual

Differences needed for significance in

bushels given for different methods of analysis.

 

Table 14.
Yields.

fig? Variety

1 Mich 20

2 Funk GlA

3 Master F60

4 Mich 30

5 Mich 57

6 Ohio M15

7 Mich 56

8 Mich 52

9 Funk G174
10 Kingscrost KA4
11 Mich 54
12 Funk G177
13 Mich 11A
14 Kingserost D4
15 Wise 416
16 Pioneer 359
17 Kingscrost‘KEl
18 Kingserost H2
19 Mich 29

Wise 464

Yield
39 .---

74.4
75.7
75.6
69.5
68.8
68.6
68.5
67.6
66.9
65.4
65.1
65.7
65.0
65.0
65.0
62.8
62.5
59.6
59.0
57.1

 

Bu. differ-
ence for
Method used significance
at 2 levels
5p 10
10 AV. 0f Ind. sqs. 9.1 12.0
2. Randomized exp. 10.0 13.3
3. As a unit with
sqs. as individ-
uals 8.5 11.3
-4. Checks and
standards 8.8 11.7

-35...

Ingham.County data.

Varieties ranked by actual

Differences needed for significance in

bushels given for different methods of analysis.

Table 15.
yields.
Rank
No. Variety

GammammummmmwmmmwmmmHHHHHHHH H
omqmmpumwoomdmmpmmHoomsmmwumEoomqmmpmmH

P
O

 

Hsrcrost F138
Pioneer 322
Mich 16

Mich 24B
Pioneer 373
Mich 22

Mich l2

Mich 18

Mich 31

Mich 32

Ohio M15
Kingscrost KR2
Mich l9

Mich 55

Wise 643
Mich 39

Mich 34

Funk G12

Ohio M34

Mich 28

Mich 59

Mich 55

Wise 608
Mich 43

Mich 20

Mich 30
Kingscrost KNl
Mich 58

Mich 29

Mich 21
Pioneer 355
Mich 51B

Funk G550W
Wise 412

‘Wisc 464
Kingscrost KS6
Mich 54

Mich 36B
Mich 11A

Mich 57

Yield
in bu.

69.7
69.5
66.7
66.5
65.8
65.2
64.7
64.4
64.2
65.8
62.1
62.1
62.1
62.1
61.7
61.7
61.5
61.4
61.5
61.5
61.1
61.1
60.5
59.8
59.5
58.1
57.7
57.5
57.1
56.4
55.8
52.9
51.5
49.8
48.0

748.0

47.7
47.5
46.2
40.7

 

Bu. differ-
ence for
MGthOd used Significance
f at 2 levels
500 1 o
1. Av. of Ind. sqs. 9.2 12.2
2. Randomized exp. 10.5 13.8
3. As a unit with
sqs. as individ-
uals 9.2 12.2
4. Checks and
standards 11.5 15.2

-36..

Table 16. Huron County data. Varieties ranked by different
methOdSo

Methods ranked by:

 

 

 

 

 

 

Add and subtrget Actual yields P/S Y
Rank ield Yield ield
No Variety in bu. Variety 1.2: bu. Variety 1.11.. b .
l Mich 30 94.9 Mich 30 97.7 Mich 30 86.4
2 Mich 51B 90.5 'Pioneer 370 90.6 Pioneer 373 84.7
3 Pioneer 373 88.9 Mich 20 89.1 Hsrcrost 112A 84.2
4 Pioneer 355 88.2 Hsrcrost 112A 88.8 Pioneer 355 84.1
5 Pioneer 370 87.8 Hsrcrost 213 88.3 Mich 5113 84.0
6 Wise 412 86.7 Ohio M15 86.9 Hsrcrost 213 83.7
7 Hsrcrost 112A 86.5 Pfister 274 86.8 Pfister 274 82.3
8 Mich 20 86.3 Pioneer 373 86.7 Funk GlA 82.2
9 Hsrcrost 213 86.0 Funk GlA 86.7 Wise 464 81.1
10 Master F60 85.8 Mich 29 86.5 Pioneer 370 80.2
11 Kgscrost K82 85.4 Pioneer 355 86.0 Wise 412 80.0
12 Wise 464 85.2 Kingscrost D4 84.8 Wise 416 79.6
13 Mich 57. 85.2 Funk G175 83.8 Master F60 79.1
14 Pfister 274 84.5 Wise 464 83.0 Mich 20 78.8
15 Funk GlA 84.4 Mich 513 82.0 Kingscrost D4 78.7
16 Ohio M15 84.1 Funk G177 81.6 Kgserost KS2 78.7
17 Mich 29 83.7 Wise 416 81.5 Mich 57 78.5
18 Wise 416 83.7 Pioneer 359 81.0 Kgscrost KS6 78.0
19 Kingscrost D4 82.8 Kgserost m 80.5 Funk G175 78.0
20 Kgscrost K86 82.0 Kgscrost KS6 79 .8 Funk G177 77 .4
21 Funk G175 81.8 Wise 412 78.2 Ohio M15 76.8
22 Funk G177 79.5 Master F60 '77 .5 Mich 29 76.5
2:5 Pioneer 359 79.0 Kgscrost K82 76.9 Pioneer 359 75.2
24 K serost KNl 78.5 Mich 57 76.7 Kgserost KNl 74.7
25

M ch 56 74.2 Mich 56 76.2 Mich 56 70.8

Table 17 0

Rank

(DmQOSOHF-OVNHIS

Montcalm County data .

methods .

Methods ranked by:

Add and subtract

e

 

Variety in bu. Variety
Ehio Ml5 $79.6 OLhio M15
Funk GlA 75.1 Funk GlA
Mich 20 72.0 Mich 20
Master F60 70.7 Master F60
Mich 52 69.7 Funk G174
Kgserost KA4 69.1 Kgserost KA4
Mich 36B 68.7 Mich 52
Pioneer 359 67.9 Mich 36B
Mich 56 67.6 Mich 56
Funk G174 67.2 Funk G177
Mich 29 67.2 Pioneer 359
Mich 57 67.0 Mich 57
Kgserost KEl 66.5 Pioneer 373
Pioneer 373 66.0 Mich 3O
Wise 464 64.9 Mich 29
Wise 416 64.7 Kingscrost D4
Funk G177 64.3 Kgserost KEl
D4 (N) 64.2 Wise 464
Mich 30 63.9 Wise 416
Kgserost KE2 62.9 Kgserost KE2

Actual iel ds
Yield

in bu.

 

Varieties

82.5
78.0
74.9
70.8
70.1
69.2
68.9
67.9
67.7
67.2
67.1
66.2
66.1
64.0
65.7
65.4
65.0
61.4
61.2
59.4

ranked by different

 

 

PjS Y

Vari ety 136%: .
Ohio M15 74.2
Mich 29 73.8
Kgserost KEl 73.0
Wise 464 71.1
Wise 416 70.8
Funk GlA 70.2
Kgserost KE2 68.8
Mich 20 67.4
Mich 52 64.9
Mich 36E 64.0
Pioneer 359 63.2
Funk G174 63.1
Master F60 62.9
Mich 57 62.4
Kgserost KA4 61.5
Funk G177 60.4
Mich 56 60.2
Kingscrost 134- 59.7
Pioneer 373 58.8
Mich 30 56.9

Table 18 .

Rank

‘OGTQCDUH§CRNH4E§

'4
C)

3:555

Otsego County data.

methods .

Methods ranked by:

Add and subtract

 

Yield

Variety in bu.
Master F21 74.8
Mich 54 73.7
Mich 52 72.8
Kgserost KE2 70.9
Kgserost KF2 70.9
Kgserost KFl 70.2
Mich 54 69.7
Wise 255 69.6
Master F40 69 .1
Wise 240 68.5
Mich 51B 68.2
Wise 255 68.2
Funk G177 64.5
Kgserost KEl 64.5
Funk G176 56.7

-38-

Actual ields
Yield

1g bu.

Variety

Master F21

Mich 54
Mich 52
Master F40
Kgserost KE2
Mich 518
Kgserost KF2
Kgserost KFl
Mich 54

Wise 255
Wise 255
Wise 240
Funk G177
Kgserost KEl
Funk G176

74.7
73.6
72.7
71.7
70.8
70 .8
69.6
68.9
68.4
68.3
68.1
67.2
67.1
67.1
59.5

Varieties ranked by different

 

 

P/S Y

d

Variety 13169311.
Master F21 79.2
13111011 54: .7800
Mich 52 77.1
Kgserost KE2 75.1
Wise 255 72.2
Kgserost KFl 71.1
Kgserost KF2 70 .8
Master F40 70.8
Mich 54 70.5
Wise 255 70.4
Mich 51B 69.9
Wise 240 69.4
Funk G177 66.5
Kgserost KEl 66.2
Funk G176 58.3

Table 19 o

Sanilac County data.

methods .

Methods ranked by:

-59...

Varieties ranked by different

 

 

 

Add and subtract Actual yields P/S

Rfigk ‘Variety 1:653. Variety iiaég. Variety §:e%3.
1 Mich 59 87.3 Mich 59 87.4 Mich 59 88.7
2 Mich 54 85.7 Kingscrost D4 85.5 Master F60 86.5
3 Funk G175 82.7 Funk G175 85.5 Wise 416 85.8
4 Kingscrost D4 82.7 IMieh 54 83.8 Mich 54 85.0
5 IMieh 36B 82.7 Funk G177 85.6 ‘Mich 57 84.2
6 Kgserost KA4 82.4 Kgserost KA4 82.5 Kgserost KA4 83.7
7 Master F60 81.7 Pioneer 370 82.3 'Mich 56E 82.4
8 Wise 416 81.3 Mich 36B 81.6 Kgserost KM 80 .8
9 Funk G177 80.8 Funk GlA. 80.1 Pioneer 573 79.9
10 Pioneer 373 80.2 Master F60 80.1 IMich 30 79.6
11 .Mich 30 79.8 Wise 416 79.7 Funk G175 78.6
12 JMich 57 79.8 Pioneer 373 79.1. Kingscrost D4 78.6
13 Pioneer 370 79.5 IMich.3O 78.7 Funk G177 76.9
14 Funk GlA 77.3 Mich 57 78.2 Kgserost KS6 76.8
15 Kgserost KS6 77.2 Kgserost KS6 76.1 Mich 11A 76.1
16 Kgserost KEl 76.6 Pioneer 359 75.3 Pioneer 359 76.0
17 Pioneer 359 76.4 IMich 11A 75.1 Wflse 255 76.0
18 Mich 11A 75.0 Kgserost KEl 75.0 Kgserost K32 75.9
19 Wise 255 74.8 Wise 255 74.9 Pioneer 370 75.7
20 72.0 ‘Kgscrost‘KSZ 70.4 Funk GlA 73.7

Kgscro st KS2

Table 20. Clare County data. Varieties ranked by different
methOdB 0

Methods ranked by:

 

 

 

 

 

_Add and subtract Actual yields P18

Haws—V Yield Yield , Yield
No Variety in bu. Variety in bu. Variety .19 bu.
l Mich 20 74.1 Mich 20 74.4 Mich 52 72.1
2 Funk GlA 73.4 Funk GlA 73.7 IMich 54 69.5
3 Master F60 71.6 Master F60 73.6 .Mich 20 67.8
4 Mich 52 69.5 Mich 50 69.5 Master F60 67 .4
5 Ohio M15 68.5 Mich 57 68.8 Funk GlA 67.2
6 Mich 30 67.5 Ohio M15 68.6 Kingscrost D4 67.2
7 Mich 54 66.8 Mich 56 68.5 Mich 11A 67.2
8 lMieh 57 66.8 Mich 52 67.6 Pioneer 359 67.0
9 Funk G174 66.6 Funk G174 66.9 Wise 416 66.0
10 Mich 56 66.6 Kgscro st KA4 65.4 Kgserost KEl 65.5
11 Kingscrost D4 64.7 Mich 54 65.1 Mich 30 63.7
12 ZMich 11A 64.7 Funk G177 63.7 IMich 57 63.1
13 Wise 416 64.5 ZMich llA. 63.0 IMich 56 62.6
14 Pioneer 359 64.5 Kingscrost D4 63.0 Ohio M15 62.6
15 Kgscro st KE]. 64.0 Wise 416 63.0 Kgserost KE2 62.5
16 Funk G177 65.4 Pioneer 559 62.8 Mich 29 61.9
17 Kgserost KA4 63.4 Kgserost KEJ. 62.5 Funk G174 61.0
18 Kgserost KE2 61.1 Kgserost KE2 59.6 Kgserost KA4 59.9
19 Mich 29 60.5 Mich 29 59 .0 Wise 464 59.9

20 Wise 464 58.6 Wise 464 57.1 Funk G177 58.1

-41-

Table 21. Ingham County data. Varieties ranked by different
methods.

Rank
No .

OGDQO>UHI>UJNH

Methods ranked by:

Add and subtract

Variety

Pioneer 322

Hsrcrost F138
Pioneer 373
Mich 24B
Mich 16
Kgserost KR2
Mich 55
Mich 39
Mich 12
Mich 34
Ohio M34
Mich 31
Mich 18
Mich 32
Mich 22
Mich 55
Mich 59
Pioneer 355
Mich l9
Mich 28
Mich 30

Funk G12
Mich 513
Mich 20

Ohio MlS
Wise 643
Mich 21
Kgserost KNl
Wise 608
Mich 58
Mich 29
Mich 43

Wise 412
Kgserost KS6
Wise 464
Funk G55OW
Mich 56B
Mich 54
Mich 11A
Mich 57

e
in bu.

67.9
67.8
67.5
65.8
64 .8
64.0
65.6
65.4
65.5
65.2
65.2
62.8
62.5
62.4
61.9
60.6
60.5
60.5
60.2
59.9
59.8
59.5
59.4
59 .0
58.8
58.4
58.5
57.7
57.0
56.7
56.6
56.6
56.5
54.5
54.5
55.4
49.4
47.1
45.6
40 .1

 

 

Actual yield; P/S

Variety 13911.3. Variety i353.
Hsrcrost Pisa 69.7 Pioneer 375 70.4
Pioneer 322 69.3 Mich 243 70.3
Mich 16 66.7 Pioneer 355 66.6
Mich 24B 66.3 Mich 55 66.2
Pioneer 373 65.8 Mich 39 66.0
Mich 22 65.2 Mich 34 65.8
Mich 12 64.7 Mich 513 65.5
Mich 18 64.4 Mich 59 65.4
Mich 31 64.2 Kgserost KR2 64.8
Mich 32 63.8 Pioneer 322 64.7
Ohio M15 62.1 Mich 55 64.7
Kgserost KR2 62.1 Hsrcrost F138 64.3
Mich 55 62.1 Mich 20 63.0
Wise 643 61.7 Mich 30 62.2
Mich 39 61.7 Wise 412 61.7
Mich 34 61.5 Mich 16 61.5
Funk G12 61.4 Mich 58 61.3
Ohio M34 61.3 Kgserost KNl 61.2
Mich 28 61.3 Mich 29 60.5
Mich 59 61.1 Mich 12 60.5
Mich 55 61.1 Mich 31 59.9
Wise 608 60.3 Mich 22 59.8
Mich 43 59 .8 Mich 32 59.6
Mich 20 59.5 Wise 464 59.5
Mich 30 58.1 Kgserost KS6 59.4
Kgserost KNl 57.7 Mich 18 59.3
Kingscrost 58 57.3 Mich 21 58.9
Kingscrost 29 57 .1 Mich 19 57.
Kingscrost 21 56.4 Mich 28 57 .2
Pioneer 355 53.8 Ohio M15 57 .O
Mich 51B 52.9 Funk G12 56.6
Funk G55OW 51.5 Wise 643 56.6
Wise 412 49.8 Wise 608 55.3
Wise 464 48.0 Mich 43 54.8
Kgserost KS6 48.0 Funk G55OW 53.7
Mich 54 47.7 Mich 54 51,0
Mich 36B 47.5 Mich 36B 49.6
Mich 11A 46.2 Mich llA 49.4
Mich 57 40.7 Mich 57 43.5

h'li

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