A Comparison of Six Statistical Tests for Evaluating Presolution Stationarity in Gradual and All-or-none Learning

The hypothesis that a process is either all-or-none or gradual is usually tested with χ² tests based on a partitioning of the presolution trials or on the individual backward presolution curves. Both methods are to some extent biased towards null hypothesis acceptance. It is argued that techniques based on a correlation measure provide a better test of the two hypotheses. By means of Monte Carlo samples six tests for deciding whether a process is stationary are compared: the nonparametric correlation measures r_Tukey and r_Spearman and the product-moment correlation coefficient tested against a bootstrap sampling distribution, the t test associated with the product-moment correlation coefficient and the χ² tests based on trial partitioning and on the backward learning curve. Within each cell of a completely factorial design based on sample size (5 vs. 20), sample homogeneity (homogeneous vs. heterogeneous), learning speed (slow or fast) and trial blocking, 40 Monte Carlo samples were used. In general, the test statistics were only moderately sensitive, except for the χ² trial partitioning technique in large samples. The χ² backward learning curve technique was very unsensitive under all conditions. In small samples, the test of the product-moment correlation coefficient against the bootstrap distribution, appears to be the most appropriate test.