Estimating inspection time: response probabilities, the BRAT IT algorithm, and IQ correlations

Abstract

Bates and Eysenck (1993), used a 3rd-order cubic polynomial curve fitting procedure on correct-response probabilities computed from the trial record of individual research participants ( N = 70) in an inspection time (IT) task. They demonstrated that this methodology produced estimates of IT that, when correlated with full-scale IQ scores (assessed by Jackson's Multidimensional Aptitude Battery), provided a measure of agreement that exceeded that given by the Barrett BRAT IT algorithm. The correlation between IT computed via the BRAT algorithm and full-scale IQ in this sample was −0.35, that between IQ and the cubic polynomial estimate was −0.35. When removing one outlier observation from the polynomial estimate data, this correlation increased to −0.47. Further, Bates and Eysenck also removed a further 5 cases from the dataset on the basis of “bad fit” of the data by the polynomial function, this had the effect of increasing the correlation to −0.62. However, it is demonstrated in this paper that when systematic, explicit, and quantified, criteria are applied to the outlier analysis, and replication of the results is sought across a further four IT datasets, the correlations between the BRAT algorithm parameters and those produced from 3 curve equation functions are actually equivalent. The average systematic outlier-corrected correlation between IT and IQ for both the BRAT and cubic polynomial estimates is −0.34. Further, the unadjusted correlations between BRAT IT estimates and cubic polynomial estimates all exceed 0.95, across all 5 datasets. It is concluded that given the relative difficulty of producing exact polynomial estimates at 0.76 response probability, the inappropriate use of a cubic polynomial for a function bounded by (0,1), and the perhaps inappropriate data produced by the BRAT algorithm for this type of approach to IT estimation, the use of the curve-fit procedure is sub-optimal with regard to this particular form of IT estimation algorithm.