**Contrast analysis** is a way to provide more precise conclusions than a traditional analysis of variance for tests with factorial designs.

While an F-Test will give you an idea of whether your independent variables have an effect on the study, a contrast test will tell you exactly where these differences appear. The result of contrast analysis is *contrast coefficients* — a set of numbers that give you information about the pattern of results [1].

The contrast test weighs several means and combines them into one or two sets. These combined means can then be tested with t-tests. The resulting effect size is the difference between means [2].

## On the Unpopularity of Contrast Analysis

Although contrast analysis has the benefit of being relatively simple and effective, it isn’t a popular tool and most statistical software doesn’t include it as a convenient point-and-click option. Most researchers use factorial ANOVA instead [3].

According to Abelson (1964; cited in [3]), the unpopularity of contrast analysis may be explained by its simplicity:

“One compelling line of explanation is that the statisticians do not regard the idea as mathematically very interesting (it is based on quite elementary statistical concepts) …”

Another reason for the test’s unpopularity may be that any interpretation in terms of likelihood or precision or likelihood requires Bayesian likelihood intervals or credible intervals. However, these intervals and Bayesian t-tests can be performed with free software [4].

## References

[1] Abdi, H. & Williams, L. Contrast Analysis. Retrieved June 25, 2022 from: https://personal.utdallas.edu/~Herve/abdi-contrasts2010-pretty.pdf

[2] Haans, Antal (2018) “Contrast Analysis: A Tutorial,” Practical Assessment, Research, and Evaluation: Vol. 23, Article 9.

DOI: https://doi.org/10.7275/7dey-zd62

Available at: https://scholarworks.umass.edu/pare/vol23/iss1/9

[3] Rosenthal, R., Rosnow, R. L., & Rubin, D. R. (2000).

Contrast and effect sizes in behavioral research: A

correlational approach. Cambridge, UK: Cambridge

University Press.

[4] Wiens, S. & Nilsson, M. Performing Contrast Analysis in Factorial Designs: From NHST to Confidence Intervals and Beyond. Educ Psychol Meas. 2017 Aug; 77(4): 690–715. Published online 2016 Oct 6. doi: 10.1177/0013164416668950.