CONDITIONING 



85 



DATA BY HGULLIKSEN 



■ 00 200 300 



NUMBER OF TRIALS fl — 



Figure 3. — Comparison of theory with experiment: simple learning. Curves, 

 theoretical from equation (10); points experimental (Gulliksen, 1934). Abscissa, 

 number of trials; ordinate, number of errors. 



Similarly, one can obtain fl(S w , R? , t w ). Thus we should be able to 

 make predictions for data as in Figure 3, but for various strengths 

 of reward or punishment and for other variables. In this way a con- 

 siderable amount of data could be brought into a single formulation 

 and the prediction tested by experiment. 



By considering various modifications of the experimental situa- 

 tion consistent with the restrictions imposed, we can derive other re- 

 lations which could be checked by experiment (Landahl, 1941). If 

 the responses R % and R 2 are made identical but t c ¥^ t w , we have an 

 analogy to a situation in which there are two paths to a goal-response 

 requiring different times, t c and t w , to traverse. We would refer to 

 the shorter path as correct, and thus t c < t w . For constant S c and 

 S w , the coefficient b will be a function of t c or tu, only. If S c and S w 

 are not too different, e c will equal e oc + b(t c )c and s w will equal 

 Sow + b (t w )w since the final response is the same. But, as b decreases 

 with t, b(t c ) > b(t w ). Thus, at least when S c = S w initially, the 

 probability of the wrong response will decrease towards zero since, 

 for small c and w , c = w , s c — e„ = 6 (t c )c — b(t w )w > zero. Thus, 

 we could determine the number of errors as a function of the number 

 of trials for various t c and t w . If e oc < s„ w , the correct response may 

 never be learned. 



Elimination of a blind alley can be accounted for since, the cor- 

 rect path being entered last, the time between S c and the reward is 

 less than the time between S w and the reward. Hence on later trials 

 there is a tendency to turn away from the wrong stimulus. An equa- 



