Wilks’s Lambda is a statistical measure used to compare the relative strengths of different groups. It is a measure of the variance between two or more groups, with larger values indicating greater variance. It was first proposed by Robert Wilks in 1938 and has become a popular statistic in many scientific and educational fields.
Wilks’s Lambda is typically used in multivariate analysis to compare the relative strength of different groups, often in the context of assessing the effect of an intervention or manipulation. For example, it can be used to compare the relative strength of a control group to a treatment group, or to compare the relative strength of different treatments. The higher the value of Wilks’s Lambda, the greater the variance between the groups.
The formula for Wilks’s Lambda is as follows:
Lambda = (detA)/n
where A is the matrix of group means, and n is the number of groups. Wilks’s Lambda can be computed using a variety of statistical software packages, such as SPSS and SAS.
Wilks’s Lambda has been used in many research studies to compare the relative strengths of different groups. For example, it has been used to compare the treatment effects of different types of psychotherapy, the relative strength of different sports teams, and the strength of different academic programs. In addition, Wilks’s Lambda is often used in the analysis of educational and psychological tests, to compare the relative strength of different test items.
Wilks’s Lambda is a useful statistic for comparing the relative strengths of different groups. It is important to note, however, that Wilks’s Lambda is only one measure of group differences, and should be used in combination with other measures, such as effect size measures, in order to draw meaningful conclusions.
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics, 9(1), 60-62.
Horn, J. L., & Rubin, D. B. (1974). A method for determining the relative strength of two sets of tests. Applied Psychological Measurement, 8(4), 433-438.
Kirk, R. E. (1982). Experimental design: Procedures for the behavioral sciences (2nd ed.). Belmont, CA: Wadsworth.