Mixed-design analysis of variance

In statistics, a mixed-design analysis of variance model, also known as a split-plot ANOVA, is used to test for differences between two or more independent groups whilst subjecting participants to repeated measures.

[1]: 506 Andy Field (2009)[1] provided an example of a mixed-design ANOVA in which he wants to investigate whether personality or attractiveness is the most important quality for individuals seeking a partner.

The random factors, or so-called repeated measures, are looks, which consists of three levels (very attractive, moderately attractive, and highly unattractive) and the personality, which again has three levels (highly charismatic, moderately charismatic, and extremely dull).

The looks and personality have an overall random character because the precise level of each cannot be controlled by the experimenter (and indeed may be difficult to quantify[2]); the 'blocking' into discrete categories is for convenience, and does not guarantee precisely the same level of looks or personality within a given block;[3] and the experimenter is interested in making inferences on the general population of daters, not just the 18 'stooges'[4] The fixed-effect factor, or so-called between-subjects measure, is gender because the participants making the ratings were either female or male, and precisely these statuses were designed by the experimenter.

When there is homogeneity of variance, sphericity of the covariance matrix will occur, because for between-subjects independence has been maintained.

[5][page needed] For the within-subject effects, it is important to ensure normality and homogeneity of variance are not being violated.

[5] It is as if you are running two separate ANOVAs with the same data set, except that it is possible to examine the interaction of the two effects in a mixed design.

As can be seen in the source table provided below, the between-subject variables can be partitioned into the main effect of the first factor and into the error term.

When following up interactions for terms that are both between-subjects or both within-subjects variables, the method is identical to follow-up tests in ANOVA.