Autocorrelation Analysis of Gross Learning Scores

Abstract

This study applies autocorrelation methods to the analysis of gross learning scores on the rotary pursuit task. Autocorrelation analysis is one method of time series analysis, and an excellent discussion of autocorrelation and spectral analysis is given by Abelson (1) who includes an adequate bibliography. The term autocorrelation is used to designate the method and theoretical functions, while the term serial correlation is used for the autocorrelation function that is computed from a sample of data. The serial correlation function is a plot of r, the correlation coefficient, against T, the degree of separation of correlated scores in the time series. For example, in the time series 1, 4, 3, 8, 7, 3, 2, 5, 9, 8, 9, 4, 2, . . . , the serial correlation for T = 0 would be obtained by correlating the following pairs of measures: 1-1, 4-4, 3-3, 8-8, etc. For T = 1, the correlation would be computed for 1-4,4-3, 3-8, 8-7, etc.; for T = 2, the pairs would be 1-3, 4-8, 3-7, 8-3, 7-2, etc.; for T = 3, the pairs would be 1-8, 4-7, 3-3, 8-2, 7-5, etc.; and for T = 4, the pairs would be 1-7, 4-3, 3-2, etc. The course of learning is described by a series of measures of performance, and like any time series, the learning series may be described in terms of autocorrelation analysis, Fourier analysis, or other standard time series techniques. If a time series consists of random variations in a stationary state, the time averages are the same as the statistical averages, and a detailed analysis is possible. Learning, of course, is not a stationary process but shows progressive changes in performance measures. It is not easy to handle progressive changes in a time series, but there are many standard procedures for handling constant drifts, secular, and seasonal trends in time data that have been developed in the analysis of economic statistics. Although the autocorrelation and spectral analysis of learning data may turn out to be complicated by absence of stationary