9 WW I,” ll .fiN ENVESNQM‘EQN OF ”E‘E‘ZE 9999179 Tia-9929 its): $9 {399599 9% M. A. MECMGAN STA‘E‘E CZQLLEEQE 3:99-99 $993: 1999 Inflvla , I This is to certify that the thesis entitled “An Investigation of the Validity of Certain Practices in Stop Watch Timing" presented by Buford. Beck has been accepted towards fulfillment of the requirements for Master Mdegree mm Education 999W \figjor professor H IMSIIGAIIOH 01' In VALIDITY OF CERTAIN PRACTICES III 810? WAICE IIMIHG 3: BUIOBDLH A IBISIS Submitted. to the School of Graduate Studies of lichigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of worms Department of Plursical Education. Health. and Recrentton for lien 1950 TH gem ACKNOWLEDGWS the author expresses sincere appreciation to Professor Henry J. Montoye whose inspiration and guidance made this thesis possible. Ihanks are expressed to the many persons who acted as timers. starters. runners. etc. i'he complete cooperation of the Department of Physical Education at lichigen State College in providing watches and other necessary squipent is also acknowledged. 237370. TABLE 01' COWS Page Amms O O O O O O O O O O O O O O O O 11 LIST or m C O O O O O O O O O O O O O O 0 O 1' Chapter I. IWWMION O O O O O O O O I O O O 0 O O 1 Importance of Precision in Stop latch fining . . . . 1 Purpose of the Investigation . . . . . . . . . 2 may at the Litcratm 0 e e e e e e e e e 3 Organisation of the Remainder of the l'hesis . . . . 7 II. METHODS 01' new . . . . . . . . . . . . 8 lethod of Collecting Data . . . . . . . . . . 8 Possible Sources of Errors . . . . . . . . . . 10 Hethod of Analysing Date. . . . . . . . . . . 13 III. ”SUI-18 e e e 0 e e e e e e e e e e e e e e 1" Comparisons of Individual Stop Watch fines . . . . I“ Comparison of Estimates of true the . . . . . . 15 Iv. DISCUSSIOR or MES e e e e e e e e e e e e 19 Comparisons of Individual Stop watch files . . . . l9 Comparisons of llethods of lstimating True line . . . 22 Y. W. CONCLUSIONS. ADDRDCOWAIIONS . . . . . 25 Sonar: . . . . . . . . . . . . . . . . 25 conclm1°u . O O O O O O O O 0 O O O O O % Recommendations . . . . . . . . . . . . . 27 DIDLIOGRAPBI . . . . . . . . . . . . . . . . . 29 APPENDIX A. Diagram of Electric Timing Device . . . . . . 31 mu B. Data Sheet of True and Stop Watch fines . . . . 32 1318! 01' was fable Page 1. Characteristics of the Distribution of hrors by Imfldm Stop Watch an”. e e e e e e e e e 1“ II. Conparisons of Means and Variances of the lrrors of Individual Stop Vatch Eines . . . . . . . . 16 III. Characteristics of the Distribution of lrrors Inploying Three Methods of lstmating true ”1‘0 0 O O O O O 0 O O O O O O O O O O 17 IV. Comparisons of Estimates of True Tine Computed by MOO Math“. 0 e e 0 e e e e e e e e e 18 CHAPTER! IMBODUCIIOH Imrtancs __f_ e- Stop watches are used by officials in man cision i_ fitop latch 23113 modern sports. especially those involvixg speed. In sports like wrestling and boxing. precision is not a factor of utmost importance. mu. in others. swimming and track for exasple. pre- cision is a matter of primary concern. It is frequently necessary to run preliminary 'heats' in both track and swimming nests. Iroquently it is necessary to time the first several contestants in each heat in order to determine who is to swim or run in the finals of the event. In addition to the importance of precise timing in the heats. occasionally official records are involved. It has been realised for many years that the accuracy of step watch timing is limited by a number of factors. It is also recognised that electric or mechanical timing devices reduce the errors in timing speed events. A number of such devices have been developed but as yet they are impractical for use in the average high school or college situation. As a result. even though it is fully realised that stop watch timing is inac- curate. stop watches are usually used in timing athletic events such as swimming races. certain track events. rope climbing. ice skating. skiing. etc. It is customary for several timers equipped with stop watches accurate to a tenth of a second to mark the times of the contestants. fhe method of determining official times from the times marked by the timers is an important factor. Certain practices are required by the rules adapted s... 2 by the national Collegiate Athletic Association and the rational Amateur Athletic union for various speed events. A typical example is taken from the 19118 1.1.11. 9:11am mg; 24 lield Hgboo . The rule is as follows: mm VII Eimekeepsrs l. i'here shall be three official timekeepers who shall time every event. In case two of their watches agree. an! the third disagrees. the time marked by the two shall be official time. If all watches disagree. the time marked by the watch giving the middle time shall be the official time. rims shall be taken from the flash of the pistol. 2. Should alternate timekeepers be provided. they shall perform like duties. but the time recorded by their watches shall only be accepted in the event of one or more of the watches held by the official timekeepers failing to mar]: the time. in which case they shall be called upon in such order as may be previously decided upon. so that on all races. where possible. three watches shall record the time. 3. If only two of the three watches record the time of an event. and they fail to agree. the longest time of the two shall be accepted as official time. the 1.0.1.1. and 1.1.13. rules require that stop watch times marked by timers in swimming and track events be handled in exactly the same manner as specified in the rule quoted above. m of he he validity of the above practice as well as nvest a ion other similar practices of handling stop watch time is questionable. rho purpose of this investigation is to compare the validity of several of these practices. The officials of each of the sports are interested in using the most valid methods of determining 1mm.- m Mam mm gamma. (m York: an. Amateur Athletic Union of the United States. 19%). Pp. 158-9. ,-.—-'~..'-. 3 official times from the marked stop watch times. the need for such a study seems obvious in view of the fact that the popularity of track and Manning events at all levels is increasing. the most valid techniques in marking times and the most valid methods of handling the times marked should be employed. Survey 93 the Several articles have appeared in the literature Literature in regard to the inaccuracies of stop watch timing. 3. K. Dumberger2 reported the results of an experiment conducted to show the extent of these errors. In his experiment. the data were gathered in a laboratory situation. timers marked the times between two successive appearances of a red signal flash. “true“ times were recorded on a ky- mograph ami compared with the stop watch times for each trial. the average errors of individuals ranged from 0.051 to 0.261 seconds. Indi- vidual errors as great as 1.01 seconds were reported. It was not stated whether or not the times recorded by the step watches were faster or slower than true times. this study substantiates the claims that step watch times are quite inaccurate. the particular experiment is of only limited value in so far as this study is concerned since the situation was unlike an actual track situation. In 1932. c. s. l'etter3 published an article in the 33;; telephone mg; in which the errors of stop watch timing are briefly discussed. He describes the construction and uses of a photographic-electric timing Zn. 1:. numberger. “the Accuracy of timing with a Stop Vatch.‘ gournal 21:: lgerimental Pszghelegz. 10:60-61. February. 1927. 3C. 8. letter. '1 New Way of Splitting Seconds.“ Dell telephone m. 11:293-300. October. 1932. 1. device developed in the Dell telephone Company laboratories for timing track events. the times recorded by this device and the official Olym- pic times recorded on a number of events in the 1932 Olympic games are quoted for comparative purposes. the deviations between official am camera times recorded by this piece of apparatus ranged from - 0.1 to 0.08 seconds. In the six cases cited. the official times were longer than cuera times in four cases and shorter in only two. tho device. though apparently very accurate. is impractical for use in the average high school or college. In 1933. t. K. Cureton and D. l. Cos“ reported the findings of a series of experiments on the nature and magnitude of errors involved in timing a sprint race. the method used in collecting the data was quite similar to actual track conditions. Actual race situations were repro- duced with groups of three timers marking the times of runners over 30 an! 100 yard distances. the times of each timer were compared with the true time as recorded by an electrical timing device. A total of 61+ timers were reported to have had an average error of - 0.302 seconds with a range of errors from - 0.01 to - 1.07 seconds. In every case. the times recorded by the stop watches were faster than true times. In the discussion. the authors considered the following as sources of error: Intent of flash of the starting pistol. timers reacting to sound rather than to the flash of the pistol. timers reacting to smoke rather than the flash. varying resistances of stop watch starting mech- anisms. position of the watch in the haul of the timer. mechanical errors within the individual watches. acuity of vision of the timers. the ht. I. Cureten and D. 2|. Cos. “in Analysis of the more in Step 'atch timing.’ Research My. l4499-109. Hay 1933. 5 reaction times of the various timers. timers reacting to minimal queues of movements of other timers or sounds of other watches. experience of the timers. and the tendency of most timers to acticipate the finish. It was concluded that the greatest error was due to reaction delay in starting the watches. this. combined with the fact that most timers teni to anticipate the finish. was thought to account in great part for the results reported. In a recent report. Dranklin Henrys discusses the possibility that current practices of estimating true times from stop watch times are invalid. In his study. he reports the results of an experiment involvizg the handling of stop watch times. the primary objective of the study was to determine the loss of precision by discarding discrepant data. the experimenter timed lo-second intervals with a stop watch using the move- ments of the sweep second hand of an electric clock as a stimulus. Henry was not directly interested in the sources of the errors but rather in the validity of various methods of hauling the data. A total of 150 serial times were recorded. the true time in each case being 10 seconds. the mean time of the 150 trials was 9.99 seconds and the standard deviation 0.162. After grouping the data in pairs. triplets. an! quintuplets. he handled them in a variety of ways. When the middlemost score for each triplet was taken as official time he found the standard deviation to be 0.112 as compared with a standard deviation of 0.081!» when the average of all three times was taken. the average of the two most discrepant times in each triplet had a staifiard deviation of 0.087 stranklin Henry. “the Loss of Precision from Discarding Dis- crepant Data.‘ gesearch W. 21:195-152. new. 1950. 6 which is much smaller than the average of the two closest times. which gives a standard deviation of 0.131. He founi that when the average of all five times in each quintuplet was computed the standard deviation was lowest of an other method. 0.064. Iron these reported standard deviations it can be concluded that under the conditions of his experiment the most valid method of computing true time from three stop watch times is to take the average of all three. than five times are available. the most valid method is to take the average of all five. Rejecting discrepant data led to increased error. which is in agreement with statistical theory. It cannot be concluded from this study. however. that the same results would have been obtained if the times had been marked by sever;l different timers under typical track conditions. is was shown by Cureton and Coe.6 there may be a constant error involved when times are recorded unier actual conditions. It is possible that such an error. if it exists. would have an effect on the results of a similar study. In the laboratory situation used in the study reported by Henry. man of the errors discussed by Cureton and Cos were not involved. the literature to date seems to indicate that stop watch timing is inaccurate to varying degrees depending upon the situations. there is reason to question the validity of the practices required by the 1.1.0. and the H.044. rules for handling stop watch times. to the best know- ledge of the writer. no one has made a statistical study of the validity of methods of handling times marked by several stop watch.timers under typical track or swimming conditions. scureton and Cos. loc. cit. 7 Organization 9; _t_h£ fhe methods of collecting and treating the Remainder of i'hesis data are described in Chapter 11. Chapter 111 contains the results of the statistical treatment of the data. these results are discussed in Chapter 17. the summary. conclusions. and recommendations are found in Chapter V. the final chapter. CHAPTER II METHODS 01' PROM flethod 21.: in actual race situation was reproduced for Collecting Data purposes of collecting the data for this study. in outdoor. 50 yard straightaway lane was marked off. A chalk line marked the starting line and starting blocks were placed in position behind it. in official finish line was constructed. lash runner was started with a gun and was timed by five timers and an electric timing device. Ehs times marked by each of the five stop watches and the true time as recorded by the electric timer were recorded for each trial. he timing device"l used in this experiment was designed and con- struetsd by Robert Clark. a graduate Illsctrical lngineering student at Michigan State College. It consisted of a starting switch operated by the muzzle blast of the starting gun. an electric chronometer which was started by the action of the starting switch. em a photo-electric cell unit at the finish line that stepped the chronometer when the beam was broken. Ehe chronometer was calibrated to a hunlredth of a second and was powered by a synchronous motor. rho starting switch was highly sen- sitive and operated by the muzzle blast of the starting gun. It was located approximately ten feet from the starting line. The starting gun. used was an open muzzled. .22 calibre. eight-shot revolver. 'hen the runner was ready. the starter called out 'Guns up'. We acted as a Llor a diagram of the timing device used. see Appendix '1'. 9 preparatory command for both the timers and the runner. A few seconds after the command. the starter fired the gun in such a way that the flash was visible to each of the timers and at the same time the blast would Operate the switch. it 50 yards. on most occasions it was possible to see the flash of the gun. The runners were cautioned to avoid “Jumping the gun'. In the event that a runner did Jump the gun. the entire trial was discarded. They were also told that it was not necessary for them to run 'all-out' on each trial but were requested to run at a relatively fast and even pace for the last 15 yards of the race. To prevent breaking the photo-electric cell beam prematurely. at the finish each runner carried his arms over his head or behind him. The runners consisted of students enrolled in service courses at Michigan State College and other volunteer groups. The runners ran one at a time. it the finish line. official staulards for holding finish line yarn were erected. The yarn was drawn taut between the stardards approx- imately four feet above the chalk marked finish line. is was previously stated. the photo-electric cell unit was located at the finish line. It was placed so that the beam was direcly over the chalk line and approxi- mately one foot beneath the yarn. The chronometer and the rest of the electrical apparatus with the exception of the starting switch were also located near the finish line. About fifteen feet from the finish line and parallel to it on one side was placed a three step Judges stand. 011 the opposite side. about the same distance from the finish line. a natural slope served the same purpose as the stand. Three'timers took positions on the stand and two took positions on the slaps. The timers chosen had had considerable 10 experience in timing physical events. The same five timers were used throughout the entire experiment and were issued the same watch for each session. Heylan watches calibrated to one tenth of a second were used. lash timer was in such a position that both the starting gun and the fin- ish line were clearly visible. Timers were instructed to start their watches at the flash of the gun. or. in the event that they failed to see the flash. at the first sight of smoke. They were instructed to stop their watches when am part of the runner's body crossed the finish line. In each case. this was the torso of the runner. Timers were requested to refrain from looking at their stop watch times and were told that in no case were they to attempt to compensate for their errors in the event they discovered they were making errors. Inch was considered competent. honest. and conscientious. l'or each of the trials. the writer acted as recorder. reading and recording the times marked by the five stop watches and the electric chronometer. These data were recorded on prepared work sheets. then an of the watches failed to mark the time. the trial was discarded. The interval between trials varied depending upon the time necessary to record the times. reset the electric timer. reload the gun. runners to get set. yarn to be restrurg. etc. All of the data recorded were gathered in three sessions of approximately one and onehalf hours each. The student who designed and built the timizg device operated it at each session. Possible Sources In addition to the possible sources of errors 92 lrrors discussed by Custom and Coe.2 certain errors may have been present in the timing device. Since the chronometer was 2Cureton and Cos. lsc. cit. ll operated by a synchronous motor. changes in frequency in the power source would omse errors. The power company supplying electrical power to the fieldhouse at )lichigan State College where the experiment was conducted assured the writer that there were no fluctuations in frequency during the hours when the experiment was in progress. The llectrical Engineer- ing Department estimated the maximum error of the electrical apparatus (relays. etc.) as considerably less than l/60th of a second. A possible source of error was the starting switch. The starting gun was held ap- proximately one foot from the switch. The average .22 calibre blank cartridge contains .21} grams of powder. The Smithsonian Physical Tables quote the rate of travel of explosive waves in air for a charge of powder this size to be 1102 ft./sec. This being the case. the flash would be seen and the switch operated simltaneously for all practical purposes. Although it is possible that a larger calibre gun would have produced a flash more easily seen. the .22 was not replaced since a gun of this cal- ibre is used in most high school and college meets. In the report by Curaton and Cos.3 it was stated that a personal correspondence from Kirby indicated that the flash and first smoke of a pistol shot smeared within l/250th of a second of each other. This was determined through experi- ments involving motion pictures of a gun being fired. it the finish line. the photo-electric cell unit beam was approx- imately one feet below the yarn and directly over the chalk line. It is possible that a runner could have a body lean great enough that a part of his torso would cross the finish line before the beam was broken. To produce a difference of two inches. a body loan of 10° with the groufl — * 3Custom and Coe. loc. cit. 12 would be necessary. It was estimated that no runner was leaning more than 10° when the finish line was crossed. The average runner was traveling at a speed of approximately 225 inches per second. it this speed. a difference of two inches would be equivalent to less than l/lOOth of a secom. The portion of the beam that had to be broken in order to stop the chronometer varied depending in part upon the intensity of the sun. In the most extreme cases. the full bean. one inch in diameter. would have to be broken. This would introduce a maximum error of approximately 1/ 225th of a second. Iith all errors operating at maximum. the total error would be approximately 1/h5th of a secomi. The errors would cause the electric chronometer times to be longer than actual true time by something less than 1/hv5th of a second. It is extremely unlikely that the errors in the device on any single trial would approach this figure. The stop watches were calibrated in tenths of seconds. Occa- sionally the sweep hand of a watch would stop between two graduation marks. It is questionable whether or not the watches are accurate to less than a tenth of a second. but when the hand stopped immediately between two marks. the times were recorded to 0.05 seconds. lo attanpt was made to read the watches to a more accurate time than a tenth of a second except in such cases as Just mentioned when the hand stopped almost exactly between the graduation marks. it worst. this practice would not introduce an error greater than by reading the watches to the closest tenth of a second. in effort was made to reduce parallax errors by reading the watches from a point directly above and perpendicular to the hand on the watch. 13 Method p_f_ Conventional statistical techniques were used to armada: Lats analyse the data. The error deviations between true time and the time marked by each of the timers for each trial was computed. The arithmetic mean and standard deviations were determined for each timer. The significance of the difference in means and variances among the five timers was determined using the critical ratio and '1" ratio tests respectively. Estimates of true time were determined using three methods. Three timers chosen at random were designated as I'official timers". An estimate of true time using the times marked by these three timers was determined by following the i.i.U. rules.“ 1781118 the same three times. another estimate was determined by computing the average of the three times for each trial. l'inally. the average of all five times for each trial was taken as an estimate of true time. Using these three methods. three sets of estimates for each trial were recorded. Each of the estimates was compared with true time for each trial and the deviations from true time recorded. The mean and standard deviation was then computed for each method. The results determined by using the three methods were analysed by comparing the means and standard deviations of the three methods. ‘93;- onto” Po 2e W III WIS Comparisons of Individual Step 'atch Times rho times recorded for each trial by each of the five timers were analysed using conven- tional statistical techniques. The times marked by each timer were com- pared with true time for each trial. l‘rom these deviations (errors). a mean and standard deviation for each of the five timers were computed. Ihe variance and the standard error of the mean were also computed for each timer. l'hese values are given in table 1 below. ( IAN-II CHARACTERISTICS 01' 1'33 DISMBIRIOI 01‘ mors’ BI INDIVIDUAL IIMIEB sine:- Mean 0'3 0.2 f (sec.) (sec.) (sec.) 1 " . 1095 . 0055 . 0030 . 055 B " e 1373 e 0083 e 0%9 e 083 G - .1361 .0108 .0116 .108 D - e 0773 e 0082 e 0067 e 082 I v . 0491 . 0105 . 0110 e 105 'lrror refers to difference between true time and stop watch times. Minus sign indicates stop watch time is less than true time. l'rom these data. the significance of the difference of the means and variances was determined for each combination of the five timers by the critical ratio and the '1' ratio tests respectively. The correlations 15 between '1' and '3' and between '6' and 'D' were plotted. From the extreme scatter it was apparent that no significant correlation was present. Therefore. in computing the 't' values. the large sample formula was used without taking into consideration correlation. The 't' and '1' values may be fouzfl in Table II. Co arisen of Using the times of the three timers designated as figfiates o True Time 'official timers'. an estimate of true time for each trial was determined employing the man. method.1 has the same three times. an arithmetic mean was computed as a second estimate of true time. A third estimate was computed by taking the average of all five times for each trial. Each of the estimates was compared with the true time for each trial and deviations computed. Irom these deviations were computed the mean. standard error of the mean. standard deviation. and the variance for each method of estimating true time. The values computed for each spear in Table 111. To determine whether or not the differences in the means of the errors and variability of the errors were significant among the various methods of estimating true time. critical ratio and '1' ratio tests were applied. To find the 't' values in this case. since correlation was present. it was taken into consideration. The large sample formula was employed. These ratios. in addition to other necessary statistical values for computing these ratios. are given in Table IV. 1g; ante.. p. 2. .213 means no». can 25» echo seeraep 0393300 on uneven Page 00.0 as: 88 00.0 50.0 00.0 0000. 0000. n 2.. n 00.0 as: 0.8: 00.0 0000.0 00.0 008. 2.00. a up 0 00.0 300 0.3: 00.0 0000.0 00.0 0000. 0000. n .F 0 00.0 g» 88 00.0 0000.0 00.0 0000. 0000. a a» a 00.0 55 0.3.. 00.0 0000.0 5.0 020. 0000. n I n 00.0 an: 0.3... 00. 000.0 00.0 0000. 0000. 0 up a 00.0 35 :00 00.0 0000.0 00.0 0.30. 0000. a up 4 00.0 as: .80 00.0 0000.0 00.0 0000. 0000. n a» 4 00.0 as: :3 00.0 80.0 00.0 0000. 0000. 0 B 4 00.0 2a. :00 00.0 000.0 00.0 0000. 0000. a up 4 flees-v .00 a 00 , a finale 300: 5 00.30.80 080.8003 0.350 mafia mug moan gbunflu ho smug Ea ha macadab a an: ho mzomamzoo HH g .030» some no 0e00a0000 use 930» can» aeoraep 00:0000000 00 Honey enchane 0000. 0000. 0000. 0000. 005.0 a»: 000 no emmaehd eea0n memo. Rec. 0000. 0000. 000000.00 00.3.0 No awaken! .2009 00000000 0000. 300. 0000. 0000. 8.3.0 05.5 0300: 5.4.4 Aeooev Aeoenv Aeoouv Anus-v e309 cyan Ihu Nnhv jrhv use: ua0usa00en no convex . mfizaa No.04: moan 28h 839 Home Engnamfi ho magnum! an nnHHOANEfl emmommfl h6.MOnaDmHmamHn nun ha mouaanmnaodmdmo HHH Huge .200» 093 00 00030000 and 0300. 0.9.0» 0000.500 030000000. 0» 0000.0 0.0050 00. as 00. 82.20 00.0 000.0 00.0 i. 0000. 0000. 35.0 .5.— 00a 00 000.804 50» .800 00000000 8.2.0 0008 0000.: 5.4.4 00. 50» 0.08 00.0 0.3.0 000.0 00. 0000. 0000. .300. 00000000 8.30 00 000034 5.0» :50 0003000 8.30 000.5 0233.. 5.0.0 0.00.0.0— no hm h on a .0 000g 300: «0 0.0020800 088.0000 .0050: madman: Ea Hm ago”... 3009 E .3 gnamn ho Homagoo bu g9 CW IV DISCUSSION 0! RESULTS Comparisons g_f_ Apparently there is a significant difference Igividual Step latch Times among the mean errors of the five timers used in this experiment as was indicated by the large 't' values found. .A differ- ence among the standard deviation of the five timers was also obvious. It seems that there is considerable variability among individuals in.their ability to time track events. The sum total of all factors operating under the conditions of this experiment tend to cause an error in.step'watch timing that is con- sistently in one direction. namely. faster than true time. Of the 505 times marked by stop watch timers in this experiment. #43 were faster than true times. The effects of these factors can.a1se be seen in the mean errors of the five timers which ranged from - 0.0h9l to - O.l#61 seconds. This confirms the earlier work of Curaten and Gee1 who found that each of the 6b timers'used in their experiment marked times faster than true time. In the remainder of this discussion. the factors causing these errors and the errors are referred to as constant factors and errors. It is pointed out that they are not constant in the strict interpretation.of the term but in the sense that they tend to cause step watch times to be consistently faster than true times. Curaten and Gee2 offer a logical explanation for these constant 1Oureton and Gee. 10c. cit. aLecz cit. 20 errors. Since there is an initial reaction time delay in starting the watches and a.genmral tendency for timers to anticipate the finish. the resulting marked times are faster than true times. It is possible that other factors may account in.part for this error but the effects of the two factors mentioned above are apparently greatest. Though a full err planatien is lacking. it is knewn.that the sum total of the factors operating in timing track situations cause the marked times to be faster than.true times in most instances. These constant errors are predominant in timing actual races. Neither Rumbenger3 nor Henry” made mention of such errors in their respective studies. The conditions under which their experiments were conducted apparently caused only variable or chance errors to affect the times. Though it was not stated by either author. it is assumed that step*watch times both faster and slower than true time were recorded and the errors varied about zero. In the present study. the presence of the comparatively lange mean errors cannot possibly be attributed solely to the errors in the timing device. The maximum error of the entire timing device was deter- .mined to be less than.l/h5th of a second. The smallest mean error of the five timers was much larger than this error. The constant errors are undoubtedly the greatest source of inac- curacies. In determining the accuracy of a stop watch time. it would normally be compared with true time. The relative accuracy of the five timers employed in.this study is roughly indicated by the means of their errors. The influence of the factors causing the constant errors may 3Rumberger. lec. cit. “Henry. loc. cit. 21 vary among individuals and within-individuals. Timers do not anticipate finishes to the same degree. nor do several different timers anticipate the same finish to the same degree. This variance may be due to fatigue. lack of attention. or any number of factors. It has been demonstrated that these and other variable errors cause the errors of individual timers to vary about the mean of their errors. this mean consistently being in the same direction from true time. The extent of these variable errors is indicated by the standard deviations. The standard deviations for the five timers used in this study ranged from .055 to .108. The extent of these variable errors determines how consistent or reliable the timer is in.marking times. A timer with a small standard deviation. despite the size of this mean error. would be considered a reliable timer. Apparently accuracy and reliability are not positively corre- lated. In this study. timer '1' had the smallest mean error. .Oh9l. and the second largest standard deviation. .105. {Although quite accurate. 'E"was not a consistent timer. Timer 'A' bad a.mean error of .1095 and a standard deviation of .055. Although slightly less accurate than.'l'. he was considerably more reliable. Timer 'C"was neither accurate nor reliable. His mean error was .1h61 and his standard deviation..108. These respective values are the langest of any of the five timers. .Altheugh it would be of great value to have this sort of infor- matien.abeut timers. in the average situation. it is not available. If the information were available. there would be some question as to the type of timer that should be used in timing track events. If accuracy. as defined above. was desired without regard for reliability. timers who marked times as did timer '1' would be selected. If reliability was con- sidered the important factor. although less accurate than timer '3'. men 22 who marked times as did timer '1' would be chosen. Of course the most desirable timer would be one who was both accurate and reliable. Since this information is not usually known. it is probable that a group of timers employed to time a tracl: most would be similar to the group chosen to mark times in this ezqaeriment. The problem then be- comes one of using a method of estimating true time from the stop watch times that will reduce the errors. both variable and constant. The prin- cipal problem of this study is to show the comparisons of several of these methods. gemparisppg pf Meth- Since the times used to estimate true times 92; 91 Estimatig 23112 Time are influenced by both variable and constant errors. the estimation would similarly be affected. The method could re- duce either or both types of errors. and the ideal method would effectively reduce both. Using the method required by the A.A.U.. times comparable to the individual times marked by timer '1' were estimated. The mean error of this method of estimating true time was relatively small. .0753. but the standard deviation was relatively large. .0663. Since the mean error of the estimations using the LAM. method was smallest of thethree methods, used. it may be said to be slightly more accurate. Conversely. since the standard deviation was larger than the standard deviation of either ef the other two methods. it may be said that the A.A.U. method was slightly less reliable than the other two methods. This is further discussed below. It so happened that the three official timers chosen at random had the smallest mean errors. Since the other two timers had larger mean errors. it was anticipated that the average of the five times would be less accurate. Had the three timers with the largest mean errors been 23 designated as official timers. when the five times were averaged. the estimate would probably have been more accurate than either of the other methods. But with the three original official timers having the smallest mean errors. when the times of the other two timers were averaged in with the three. the mean error became larger and significantly different from the estimation using the A.A.U. methods. The mean error of the average of all five times was .1013. The standard deviation of the average of five times was .0168. which is significantly smaller than the standard deviation of the A.A.U. method. The average of the three official times was slightly less as- curate than the A.A.U. method. but not significantly so. The standard deviation was not significantly different from that of the A.A.U. method. but was slightly smaller which is in the same direction as that of the average of five from the 1.1.0. method. The problem of choosing the method of estimating true time would be similar to the problem of choosing which timers to use. In order to insure consistency throughout the country or'even throughout a single meet. it would seem that an estimate computed by averaging all of the times marked would be most satisfactory. This sort of estimate would be particularly desirable in meets where qualifying heats are necessary. Even though the A.A.U. method of estimating true time was found to be the most accurate of the three methods used in this experiment (and umier the above mentioned conditions). the average of five times was founl to be a more desirable method on the basis of being fairest. The implications of this study are not in complete agreement 21; with the results of Henry's.5 The lack of agreement is probably due to the constant errors discussed above. Under the conditions of his experi- ment. apparently no constant errors were present. The stop watch times varied about true time. Therefore. a reduction in standard deviation was equivalent to a closer approximation to true time. He foumi that the average of three times was a closer estimate of true time than that com- puted using several other methods involving the same three times. He also found that the average of five times gave a closer approximation to true time that any other method involving five times. These results are not confirmed by this study. The studies are in agreement at one point. however. Smaller standard deviations were found when the three or five times were averaged than were fouml when the £4.11. method was used. This is also in agree- ment with statistical theory. As was expected, the correlation between the estimates of the average of five times and those by the bid]. method was quite high. r a .7“. Since the LLB. method and the method using the average of three times are quite similar. and since the three times used in each method were the same. an even higher correlation was found. r a .85. These correlations were used in computing the critical ratios. SBenry. loc. cit, CHAPTER 7 WILEY. CONCLUSIONS. AND RECOMMENDATIONS 8mg; The primary purpose of this investigation was to compare the validity of several methods of estimating true time from stop watch times marked on runners. Subordinate problems were the investigations of the relationships existing among times marked by individual timers and between true time and step watch times marked by the individual timers. l'or purposes of collecting data. actual race conditions were reproduced. An outdoor. 50 yard straightaway lane was marked off using an official starting line and finish line. Runners who ran one at a time were started with a starting gun and timed by five experienced timers ed an electric timing device. A total of 101 trials was taken using the same five timers and watches each trial. The true time and each of the five stop watch times were recorded for each trial. The data obtained were analysed using conventional statistical techniques. for each of the five timers. a mean error’ and a standard deviation were computed. Times marked by individual timers were then compared. Considerable variability was found to exist among timers. Two types of errors seemed to affect the times: (1) Errors that tended to cause stop watch times to be consistently faster’than true times; and. (2) Variable errors that caused a variation around the mean error for “Error refers to difference between true times and stop ntch thCe 26 each timer. Some of the timers had large mean errors but small standard deviations while others had small mean errors but large staxdard devia- tions. Using the size of the mean error as an indication of accuracy and the sise of the standard deviation as an indication of reliability. it is apparent that there was no correlation between accuracy and reliability in stop watch timing in this study. for each trial. three methods of estimating true time were used: (1) The 14.11. method using three official times: (2) The average of the three official times: and. (3) The average of all five times. A mean error' and standard deviation were computed for each method. The 1.1.0. method was significantly more accurate (having a smaller mean error) than the average of five'times but was significantly less reliable (having a larger standard deviation). Had a different combination of timers been designated official timers. it is probable that the difference in mean errors would have been much smaller. The A.A.U. method was found to be slightly less reliable and only slightly more accurate than the average of the three official times. It is important to note that in neither case were these differences sig- nificant. Conclusiog 0n the basis of evidence presented in previous chap- ters. the following conclusions seem Justified: 1. There is considerable variability among stop watch timers both in regard to mean error (difference between true time and marked times) and standard deviation (chance errors). °Irror refers to difference between true time and estimate of true time. 27 2. In addition to causing random errors. the sum total of factors involved in timing track races cause stop watch times to be con- sistently faster than true times. The major factors contributing to this 'constant' error appear to be initial reaction delay starting the watch and the anticipation of the finish. 3. There does not seem to be any correlation between the ex- tent and the consistency of the effects of these factors. A timer may be consistent and inaccurate or accurate and inconsistent. 1». The L.A.U. method was not demonstrated to be significantly more reliable or accurate than the average of the same three times used in computing the L.A.U. estimate. 5. The average of all five watches as an estimate of true time was found to be significantly more reliable (having a smaller standard deviation) than the A.A.U. method. Recomendations The following recomendations are made for additional studies in stop watch timing. 1. If a photo-electric cell unit is used as a part of the timing device. a shielding tube extending for several feet from the cell (receiving unit) would minimise the interference of the sunlight. 2. m apparatus used at the finish line as a part of the timing device should be at the same height as the yarn at the finish line. 3. The data collected for this study could be used in deter- mining the relative validity of other methods of estimating true time or in applying the same methods with different combinations of timers. 1*. It would be of value to compare the true times and stop watch times recorded in actual meets where the men reputed to be the best stop watch timers are employed. The results of such an investigation 28 could then be compared with the results of this study. BIBLIOGRAPHY m BIBLIOGRAPHY Curaton. T. I. and D. I. Use. 'An Analysis of the Irrors in Step Watch Timing.' geeeereh My, luau-109. Ray. 1933. rotter. C. 8.. 'A How Iay of Splitting Seconds.' gell Telmne m. 11:293-300. October. 1932. Henry. Franklin. 'The Loss of Precision from Discarding Discrepant Data... 20803011 my. 21:1“5-152. “3y. 195°e mmberger. l. L. “The Accuracy of Timing with a Stop Uatch.' M 2; merinental W. 10:60-61. rebruary. 1927. The Official Track and Iield Handbook. low York: The Mateur Athletic Union of the United States. 1555. 198 pp. . mania. 39b 3 .932. o: :5. ENE .. Q. $595539 ghhskhc (a: _ Hanan 3H2“; egg 8 333 4 Hang MICHIGAN STATE COLLEGE DEPARTMENT“OFK‘Vg‘VESAIgIAéNEEgEA’IEION, HEALTH . APPEMIX B GRADUAYE STUDIES AND RESEARCH . > TABU LATION SH E ET —’ TOPIC DATA. 3% 01‘ TRUE AND STOP WATCH ‘1‘ mpg TABULATED BY _E_Q’»/<____——-——~—— 300M “ ‘t‘ "e '1'- M- a 525% W: , in»; ‘* IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IllIIillfll\MlfllflkfljflIllfljwflvfllllfllflllljflrlHI!i