test of markov chain models for double contingent reinforcement

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388 THEMA 9 were pooled for a set of ten problems (after reversal performance had stabilized), and the proportion of MFP responses was determined for each ordinal trial. The empirical curve derived by this method was compared with the theoretical curve generated by the model after alpha had been estimated from the data. Goodness of fit was tested by means of a "runs test" described by Bush and MosteUer. In genera/, fit was satisfactory for most animals. A parallel analysis was performed by pooling the data of ten subjects fer a number of seperate problems, and the proportion of subjects making an MFP response on each ordinal trial was determined. Goodness of fit in this latter case was less satisfac- tory, presumably because of indivi&~! differences. R~I~RENCE BUSH, R. R. and MOSTELLER~ F,, Stochastic Models for Learning. New York: Wiley, 1955. TEST OF MARKOV CHAIN MODELS FOR DOUBLE CONTINGENT REINFORCU~ ~NT P. SUPPES, Slanford(U.L ',.) t~t~ M. SCHLAG-REY, Bruxelles (Belgique) An experiment was conducted in order to provide an empirical test of the adequacy of various Markov Chain Models for the learning process in the case where the probability of reinforcement depends on the sequence of the last two responses made by the subject. Twenty students (15 female and 5 male) of a school of social work were run for 400 trials. They were provided with an apparatus which, as viewed from their side, consisted of two keys and three panel lights; one light, the signal light, being above and between the two others, reinforcing lights, each of these being directly above one of the keys. On each trial, after the onset of the signal light, the subject makes a choice between one of two alternative responses by pressing one of the keys. Immediately thereafter one of the reinforcing lights goes on. A reinforcing signal indicates a correct choice when;it occurs above the key just pressed, an incorrect choice otherwise. The subject has been instructed to press the key placed under the lamp which he expects to light up and thus to make the best prediction he can on each trial. The available responses being designated A1 and A2 and the corresponding

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388 THEMA 9

were pooled for a set of ten problems (after reversal performance had stabilized), and the proportion of MFP responses was determined for each ordinal trial. The empirical curve derived by this method was compared with the theoretical curve generated by the model after alpha had been estimated from the data. Goodness of fit was tested by means of a "runs test" described by Bush and MosteUer. In genera/, fit was satisfactory for most animals. A parallel analysis was performed by pooling the data of ten subjects fer a number of seperate problems, and the proportion of subjects making an M F P response on each ordinal trial was determined. Goodness of fit in this latter case was less satisfac- tory, presumably because of indivi&~! differences.

R~I~RENCE

BUSH, R. R. and MOSTELLER~ F,, Stochastic Models for Learning. New York: Wiley, 1955.

TEST O F M A R K O V C H A I N MODELS F O R D O U B L E C O N T I N G E N T

REINFORCU~ ~ N T

P. SUPPES, Slanford(U.L ',.) t~t~ M. SCHLAG-REY, Bruxelles (Belgique)

An experiment was conducted in order to provide an empirical test of the adequacy of various Markov Chain Models for the learning process in the case where the probability of reinforcement depends on the sequence of the last two responses made by the subject.

Twenty students (15 female and 5 male) of a school of social work were run for 400 trials. They were provided with an apparatus which, as viewed f rom their side, consisted of two keys and three panel lights; one light, the signal light, being above and between the two others, reinforcing lights, each of these being directly above one of the keys.

On each trial, after the onset of the signal light, the subject makes a choice between one of two alternative responses by pressing one of the keys. Immediately thereafter one of the reinforcing lights goes on. A reinforcing signal indicates a correct choice when;it occurs above the key just pressed, an incorrect choice otherwise. The subject has been instructed to press the key placed under the lamp which he expects to light up and thus to make the best prediction he can on each trial.

The available responses being designated A1 and A2 and the corresponding

NIATHEMATISCHE MODELLE IN DER PSYCHOLOGIE 3 8 9

reinforcing signals E1 and E2, the probability of an E 1 signal on trial n is:

P(Ex,n]A*,r~AJ,n-1)=~t~; i , j = 1,2,

For the 400 trials

nix : .4, ~1~ ~-- .9, ~z21 = .2, z~2 = .7.

The models used to analyze the data are derived from stimulus sampling theory. Emphasis is given to estimating a number of conditioning parameters in order to test the goodness of fit of various "generalizext conditioning" models.

The data are also analyzed for their Markov properties independent of any particular model. In particular the results of chi-square tests for station- arity and order of the proees6 are reported.

VISUAL REACTION TIME /N T H E TLdlLESHOLD R E G I O N

D. HOWES Cambridge, Mass. (USA)

Visual. reaction times to a wide range of target intensities were measured under each of several experimental conditions. Under each condition, the range of target intensities was fixed in relation to the su~ect 's threshold for that condition, the lowest intensity being about 0.5 log unit below threshold, the highest about 1.5 log units above threshold. The proportion of presentations at each intensity was adjusted to produce approximately 50 % detection under each condition. The conditions varied experimentally were the adaptation level and the exposure duration of the target. A total of some 12,000 observations were made by three observers.

These data are applied to two questions that must be settled before an equivalence between the reaction time and detection probability can be established:

(1) Are the reaction-time distributions identical for all stimuli that yield the same detection probability? Or, in other words, is the relation between reaction time and detection probability uniquely determined? This invariance property is tested by comparing the distributions of reaction times obtained at different adaptation levels, which require very different target intensities to attain the same detection probability. The results con- firm the invariance under changes of the adaptation level. When exposure