SIMPLE REACTION TIME AS A FUNCTION OF TIME UNCERTAINTY 1

Transcription

1 Journal of Expermental Vol. 5, No. 3, 1957 Psychology SIMPLE REACTION TIME AS A FUNCTION OF TIME UNCERTAINTY 1 EDMUND T. KLEMMER Operatonal Applcatons Laboratory, Ar Force Cambrdge Research Center An earler study (3) showed that smple reacton tme (RT) vares 'wth S's uncertanty about tme of stmulus occurrence. Ths tme uncertanty s a functon of both the mean duraton of the tme (foreperod) between a warnng sgnal and the stmulus and the varablty wthn the seres of foreperods. Foreperod varablty adds uncertanty drectly and mean foreperod s mportant snce S's ablty to predct tme of stmulus occurrence s very much a functon of the length of tme he must predct. In the prevous report the two sources of tme uncertanty were consdered separately because no sngle measure was avalable. The present experment llustrates wth new data, a method by whch all of S's tme uncertanty can be expressed as a sngle number and reacton tme plotted as a sngle-valued functon of tme uncertanty. In addton, tme uncertanty s expressed n terms of the nformaton measure. In order to estmate the amount of tme uncertanty due to S's mperfect tme-keepng ablty, t s necessary to run tme-nterval predcton tests wth ntervals equal to the mean foreperods of the reacton tme tests. The varance of the dstrbuton of each S's tmes of response n the tme predcton test s taken as a measure of hs "subjectve" tme uncertanty 1 Ths research was performed at the Operatonal Applcatons Laboratory, Ar Force Cambrdge Research Center, Bolng Ar Force Base, Washngton 5, D. C., n support of Project 768. Ths s AFCRC TR for ntervals equal to the predcted nterval. Total tme uncertanty s obtaned by addng ths measure of subjectve tme uncertanty to the varance of the dstrbuton of foreperods n the RT test havng a mean foreperod equal to the tme nterval used n the predcton test. Ths total varance can be converted to a nondmensonal nformatonal measure of uncertanty whch makes possble a comparson of the present results wth RT tests nvolvng a choce reacton. The present study, then, conssts of two separate tests seres, one RT and one tme predcton, gven to the same Ss. The results of the two seres are combned n such a way that a sngle valued plot of RT as a functon of tme uncertanty s derved for each S. METHOD RT apparatus. The apparatus conssted of an NE 51 neon stmulus bulb, a response key, and a warnng clck devce. The.-sec. stmulus was clearly vsble n the dmly lghted room. In another room a teletype tape programmer presented 11 dfferent lengths of foreperod n a random order as descrbed below. The warnng clck occurred regularly every 1 sec. Each RT was measured to the nearest mllsecond by a Berkeley Unversal counter and tmer, Model 551, and prnted out automatcally. RT procedure. Ten dfferent RT tests were used, each wth a dfferent mean foreperod and/ or foreperod varablty. These tests are descrbed n Table 1. Each S took sngle runs on each of the 1 tests n reversng order 1»1, 1 > 1 untl he had taken one practce run and fve expermental runs on each test. Three Ss began wth Test 1 and two began wth Test 1. Each run conssted of 51 stmulus presentatons.

2 196 EDMUND T. KLEMMER TABLE 1 DESCRIPTION OF REACTION TIME TESTS Test Foreperod Characterstcs (Sec.) Mean SD Range Note. The varable foreperods were chosen randomly from controlled frequences n the shape of a normal dstrbuton havng a range of rfc. SD. The Ss were always nformed of the range of foreperods before each run, and n addton, the frst three trals n the test demonstrated the range. The frst foreperod of the test was alwavs the longest for that test, the second foreperod the shortest, and the thrd foreperod the mean foreperod for that test. These frst three RT's were omtted from the analyss. The remanng 8 foreperods were randomly ordered from the normal dstrbuton of foreperods descrbed n Table 1. Note that ths s a change from the prevous study n whch the frequency dstrbuton of foreperods was rectangular. In the constant foreperod tests, 51 constant foreperods were used n each run and the frst 3 RT's were omtted from the analyss. In all tests, S was nstructed to respond as soon as possble after the stmulus lght, but never before. If a response occurred before the stmulus n any run, the run was halted and started over. Ths method produced consderably less than 1% antcpatons, none of whch occur n the runs reported here. Predcton apparatus. The predcton apparatus used a warnng clck every 1 sec. and a response key smlar to the RT apparatus. No stmulus lght was used, however. Instead, a small lght would flash at the nstant S pressed the key. Ths lght vared n poston accordng to how long after the warnng clck the key was pressed. If the key was pressed at exactly the nstructed nterval after the clck, the lght would appear on an ndex mark; f pressed too soon, the lght appeared to the left of ths mark; f pressed too late, to the rght. The dstance n each case was proportonal to the error and so S receved mmedate knowledge of drecton and magntude of error after each response. The nterval between each clck and predcton response was recorded from a Standard Electrc tmer. Predcton procedure. Tests were gven usng fve predcton ntervals:, 1,,, and 8 sec. Each S took sngle runs of 5 stmul each on each test n reversng order J > 8, 8 *, untl he had completed one practce and fve expermental runs on each test. Three Ss began wth the 8-sec. test and two began wth the -sec. test. The Ss were always nformed of the correct nterval before each test and gven at least four "warm-up" predctons followed wthout nterrupton by the 5 clcks, 1 sec. apart for the test run. In all tests, S was nstructed to make a predcton after each clck and attempt to make the lght appear as close as possble to the ndex mark. Subjects. The Ss were two unversty students and three laboratory personnel. Subjects K, B, and C had prevous RT tranng; subjects G and W dd not. All Ss took the RT tests before the tme predcton tests. RESULTS AND DISCUSSION The total uncertanty of tme of stmulus occurrence was computed for each S separately for each of the 1 RT tests. The assumpton made s that Ss uncertanty about the tme of stmulus occurrence n any test may be estmated by addng the varance of the dstrbuton of actual foreperods to the varance of hs own predctons of tme ntervals equal to the mean foreperod. Reacton-tme Tests 1 5 have no foreperod varablty so that all of the tme uncertanty s accounted for by ths estmate. Tests 6-1 have contrbutons from both foreperod varablty and S's subjectve tme uncertanty. Test 1 uses a mean foreperod of S sec. for whch predcton data was not taken but the SD of predcton s a nearly lnear functon of predcton nterval n ths regon, and so the varance for S-sec. predcton s obtaned by nterpolatng SD's between and 8 sec. The total tme uncertantes were converted to SD's and these SD's used

3 SIMPLE REACTION TIME 197.3c (bts) »> "J3 o; (sec} K. (T.1 n 3. J3 Subj.., o; W, [ +j * "T I- o:.1 3.O ' L ^^^ o; +3 G o:. O.I // 5/A/.3 O.I...I.. I IX) 3X> FIG. 1. Reacton tme as a functon of tme uncertanty of the stmulus. CT s S's tme uncertanty, gven as an SD, and found by addng foreperod varance to the varance of S's estmates of ntervals equal to the mean foreperod. HT s tme uncertanty n bts relatve to a constant 1-sec. foreperod. Straght lnes are ftted by least squares. as the tme uncertanty dmenson of the plots n Fg. 1. Tme uncertanty (or) appears on a log scale along the abscssa. Mean RT s plotted on a lnear scale along the ordnate. The flled dots represent RT Tests 1-5, readng from left to rght, and the open dots represent Tests 6-1, also readng from left to rght. Each pont represents the mean of S runs of 8 stmul each. Tme uncertanty s expressed n terms of the nformatonal measure (bts) along the upper ordnate scale of Fg. 1. Snce tme s a contnuous varable, the stmulus uncertanty measure must be relatve to some standard dstrbuton (). Shan- Informaton transmsson values are absolute rather than relatve, even when based upon contnuous dstrbutons. Transmsson s dscussed later.

4 198 EDMUND T. KLEMMER non's formulas () assume that the standard dstrbuton s a unform dstrbuton over one unt of the varable, but for the present data t has seemed better to take as the standard each S's own tme uncertanty for a constant foreperod of 1 sec. Thus the zero value of nformatonal uncertanty s placed drectly over the second flled dot correspondng to Test whch uses a constant foreperod of 1 sec. The other ponts along the scale of presented nformaton are found n the followng manner. The SD, ffr, whch s taken as the measure of total tme uncertanty s assumed to be based on a normal dstrbuton snce t s the result of addng varances from foreperod and tme-predcton dstrbutons whch are approxmately normal n shape. The uncertanty n bts to be assocated wth a normally dstrbuted random varable s gven by Shannon (). H(x) = (1) If the Shannon formula were used drectly wth or n seconds, the uncertanty values obtaned would be relatve to a unform dstrbuton over 1 sec. In order to make the nformatonal uncertanty measure relatve to the dstrbuton of estmates of a 1-sec. nterval, t s necessary to use an arbtrary unt of tme for measurng <r. These new tme unts wll be a lnear functon of or, so that we may wrte: HT = \Ogk<TT " logv7t(? () n whch <TT s stll n seconds, but HT s relatve to the desred standard dstrbuton f HT = when a-f = cr, where <n s the SD of S's estmates of a 1-sec. nterval. By substtuton: = logger j + log^lve, (3) HT = logcrt log<r. For uncertanty n bts relatve to a constant 1-sec. foreperod: HT = logaor logao-. () Ths equaton s used to compute the upper abscssa scale n Fg. 1. The negatve nformatonal uncertantes to the left of zero represent less tme uncertanty than the standard onesecond foreperod. The straght lnes n Fg. 1 are ftted to the ponts by the least mean square method. The lne for the "All Subj." plot s ftted to the total array of ponts as plotted n the ndvdual graphs. For the sake of clarty, the ndvdual S ponts are not repeated n the combned plot. The zero pont of the nformatonal scale on the combned plot s based on the average varance of response tmes n the one-second predcton tests. Product-moment correlaton between mean RT and tme uncertanty n bts (or n log or) vares from.956 to.983 among the fve Ss. When the data from all Ss are pooled, the correlaton drops to.9s because of the large dfference n slope of regresson lne among the Ss. Ths slope vares from 1 msec, per bt to msec, per bt over Ss. The pooled data shows a slope of 18 msec, per bt wth an equaton n terms of tme uncertanty gven as an SD of: RT =.18 lo glo cr r +.35, (5) where or = <r,s + o>, <rp s foreperod varance, and ov s varance of S's own estmates of nterval equal to mean foreperod, wth all values n seconds. An analyss of varance of the data from each S separately showed no sgnfcant varance due to devatons from lnear regresson between RT and tme uncertanty. Ths fndng, together wth the hgh lnear cor-

5 SIMPLE REACTION TIME 199 relatons, suggest that RT s a lnear functon of tme uncertanty n the range of ths study. Several nvestgators have studed the relaton between RT and stmulus uncertanty n stuatons n whch there was uncertanty about whch of several stmul wll be presented. In general, they have also found a lnear relaton between RT and stmulus uncertanty n bts, but the slopes have vared wdely (1). No slope, however, has been as small as the 1- msec, per bt found n the present study. The dfference n slope are due to such thngs as stmulusresponse compatblty and dmensonalty. More work needs to be done n these areas. The next queston that arses concernng tme uncertanty n nformatonal terms s how much nformaton about tme of stmulus occurrence S actually transmts. 3 Transmtted nformaton may be approxmated by the dfference between 5's prestmulus uncertanty about when the stmulus wll occur and the resdual uncertanty about tme of occurrence as estmated from hs response. If we neglect the slght relaton between foreperod and RT, and assume normal dstrbutons, ths calculaton nvolves only takng the logarthm of the rato of the tme uncertanty expressed as an SD (or) and the SD of the correspondng RT dstrbuton. The constant factor whch makes the nformaton measure relatve, drops out n ths rato so that transmtted nformaton s an absolute score. The equatons for ths approxmaton are gven below. As before, S's average nformatonal uncertanty about when each stmulus wll occur s gven by: HT (6) By the method shown above, the average nformatonal uncertanty about tme of 8 Tests 1-5 present no nformaton n clock tme to be transmtted but do nvolve consderable subjectve tme uncertanty whch s reduced by stmulus occurrence. Transmsson has been measured n terms of ths reducton n uncertanty. stmulus occurrence based upon knowledge of the response tme s gven by: Iog <7. (7) Transmtted nformaton s gven by: T = HT HRT = - (8) The above method of measurng transmtted nformaton s dfferent from a straghtforward applcaton of the usual transmsson formulas whch would consder uncertantes n clock tme only. For tests wth consderable clock-tme uncertanty n the stmulus, the two methods gve essentally the same results, but for any test wth constant foreperod, the drect applcaton of transmsson formulas would show zero transmsson. The ncluson of subjectve tme uncertanty n the present study gves a more accurate pcture of the actual nformatonal demands on the human operator. In the present data <TT vares over a -to-l range over tests whle the SD of the RT dstrbutons vares wthn only a -to-l range. Ths means that tme uncertanty of the stmulus determnes the slope of the RT versus nformaton transmtted functons whch, therefore, are very smlar to the RT vs. log OT functons as plotted n Fg. 1. Of more nterest s the absolute value of nformaton transmtted. The peak transmsson occurred n Test 1 and vares very lttle over 5s: 5.37 to 5.6 bts per stmulus. The hghest rato between nformaton transmsson and RT results from a transmsson of 5.9 bts wth a RT of msec, n Test 1. The lowest transmsson occurs n Test 1 where S has lttle uncertanty about tme of stmulus onset. The smallest rato here nvolves a transmsson of.86 bts wth a 157-msec. RT. Interestngly, the lowest and hghest ratos were both acheved by the same S. Note that the nformaton transmsson values cannot be compared to the stmulus tme uncertanty measured n bts. The transmsson scores are absolute, but the stmulus uncertanty meas-

6 EDMUND T. KLEMMER ure s relatve to an arbtrary standard dstrbuton. SUMMARY Fve Ss were gven a set of smple RT tests specfcally desgned to test the hypothess that a sngle-valued relaton could be obtaned between RT and the tme uncertanty of the stmulus. Ths relaton was shown to be approxmately lnear when tme uncertanty s plotted as an nformatonal measure. The slope of the RT-tme uncertanty functon averaged 18 msec, per bt of stmulus uncertanty whch s less than the slope arsng from RT experments nvolvng choce among several stmul prevously reported. Informaton transmtted n the tme doman vared from less than one to more than fve bts per stmulus over the 1 tests. REFERENCES 1. BRICKER, P. D. Informaton measurement and reacton tme: a revew. Henry Quastler (Ed.). Informaton theory n psychology. Glencoe, 111.: Free Press, 19SS.. KLEMMER, E. T. The nformaton content of polar coordnates. Cambrdge, Mass.: Ar Force Cambrdge Res. Center Tech. Rep. 5-5, KLEMMER, E. T. Tme uncertanty n smple reacton tme. /. exp. Psycho!., 1956, 51, SHANNON, C. E. A mathematcal theory of communcaton. Sell System Tech. J., 198, 7, (Receved August 3, 1956)