mixeddesign

Mixed design, in statistics and experimental research, refers to designs that combine within-subjects and between-subjects factors. In a mixed design, some factors are manipulated between subjects (levels differ across participants), while others are manipulated within subjects (the same participants experience multiple levels). A common example is a split-plot design, where one factor such as treatment is assigned to groups, and another factor such as time or condition is repeated within each participant.

Analysis of mixed designs typically uses a mixed-design analysis of variance (ANOVA), also known as a split-plot ANOVA, or more flexibly, linear mixed-effects models. These methods include fixed effects for the factors and random effects for subjects, which accounts for correlations among repeated measurements and can handle unbalanced data. A typical scenario is a drug vs placebo between-subjects factor with multiple follow-up time points as a within-subjects factor, allowing testing of main effects and their interaction.

Assumptions depend on the method: ANOVA assumes normality and sphericity or homogeneity of variance, while mixed-effects models assume normally distributed random effects and residuals, offering more flexibility for missing data and complex designs. Advantages of mixed designs include efficient use of participants, the ability to test interactions between between- and within-subjects factors, and often improved statistical power. Limitations involve greater analytical complexity, potential sensitivity to mis-specification of the random effects structure, and challenges in interpreting interactions. Mixed designs are common in psychology, education, and social sciences.