Question

9) Please provide an example of a mixed ANOVA design and explain why you consider it a mixed ANOVA design.

10) If we have homogeneity of variances and equal group sizes, why might we decide to use a R-E-G-W-Q post hoc instead of a Bonferroni post hoc? (Note: Think Type I/Type II error)

Answer 1

Ans-9.

A mixed ANOVA compares the mean differences between groups that have been split on two "factors" (also known as independent variables), where one factor is a "within-subjects" factor and the other factor is a "between-subjects" factor.

For example, a mixed ANOVA is often used in studies where you have measured a dependent variable (e.g., "back pain" or "salary") over two or more time points or when all subjects have undergone two or more conditions (i.e., where "time" or "conditions" are your "within-subjects" factor), but also when your subjects have been assigned into two or more separate groups (e.g., based on some characteristic, such as subjects' "gender" or "educational level", or when they have undergone different interventions). These groups form your "between-subjects" factor.

The primary purpose of a mixed ANOVA is to understand if there is an interaction between these two factors on the dependent variable.

EXAMPLE:-

Your within-subjects factor is time.
Your between-subjects factor consists of conditions (also known as treatments).

• INTRODUCTION

Imagine that a health researcher wants to help suffers of chronic back pain reduce their pain levels. The researcher wants to find out whether one of two different treatments is more effective at reducing pain levels over time. Therefore, the dependent variable is "back pain", whilst the within-subjects factor is "time" and the between-subjects factor is "conditions". More specifically, the two different treatments, which are known as "conditions", are a "massage programme" (treatment A) and "acupuncture programme" (treatment B). These two treatments reflect the two groups of the "between-subjects" factor.

• PROCESS

In total, 60 participants take part in the experiment. Of these 60 participants, 30 are randomly assigned to undergo treatment A (the massage programme) and the other 30 receive treatment B (the acupuncture programme). Both treatment programmes last 8 weeks. Over this 8 week period, back pain is measured at three time points, which represents the three groups of the "within-subjects" factor, "time" (i.e., back pain is measured "at the beginning of the programme" [time point #1], "midway through the programme" [time point #2] and "at the end of the programme" [time point #3]).

• WHY MIXED ANOVA

At the end of the experiment, the researcher uses a mixed ANOVA to determine whether any change in back pain (i.e., the dependent variable) is the result of the interaction between the type of treatment (i.e., the massage programme or acupuncture programme; that is, the "conditions", which is the "between-subjects" factor) and "time" (i.e., the within-subjects factor, consisting of three time points).