The effect of intertrial dependence on some sensitivity and bias statistics.

Abstract

An investigation of the intertrial dependencies in detection and recognition tasks was undertaken at different levels of a priori stimulus probability, intertrial interval, feedback, and task difficulty in a number of experiments. The effects of these experimental variables on the data are reported. After preliminary tests for stationarity the dependences were characterised using 0 , 1st and 2nd order manifest Markov processes, an autoregressive process and a latent Markov process. Although none of the models described all the data it appeared that the autoregressive process was the least helpful and that to obtain a reasonable fit of the latent Markov model a numerical minimum X2 estimation procedure had to be employed. Estimates of the parameters of various detection and recognition models were found based on all the data and based on data which was preceded by a particular type of trial. From such evidence it appeared that the value of these estimates depended on the state on the last trial. In particular the bias statistics were dependent on the immediately preceding response and the sensitivity statistics appeared dependent on whether the immediately preceding trial was correct or wrong. Neither Atkinsonfs (196 5) model nor the model proposed by Tanner Rauk & Atkinson (1971) was found to adequately describe the observed dependences. Statistical tests have been developed for a number of the detection and recognition models used in the above study. These tests assume intertrial dependence. Simulations of the Markov process estimated from the experiments were used to examine the robustness of such tests against violations of the independence assumption. The tests were found to be relatively robust but large biases were found when the test statistics were based on small samples. This effect was shown to be able to account for some of the earlier findings.