21/05/2023
It has been a while since anyone updated this page. I would like to refresh this Page with a topic on Repeated measures ANOVA using answers from ChatGPT
Prompt: Explain the different type of repeated measures anova available. Highlight their key differences.
Repeated Measures ANOVA is a statistical technique used to analyze data where the same individuals are measured multiple times. It is often used in experimental and clinical research to examine the effects of an intervention or treatment over time or under different conditions. There are several types of repeated measures ANOVA available, each with its own unique features:
1. One-Way Repeated Measures ANOVA: This type of ANOVA is used when there is only one independent variable, and each participant is measured multiple times under different levels or conditions of the independent variable. For example, if a study measures the effect of a drug at different time points, the time points would be the levels of the independent variable.
2. Two-Way Repeated Measures ANOVA: This type of ANOVA is used when there are two independent variables, and each participant is measured multiple times under different levels or conditions of both independent variables. For example, if a study measures the effect of a drug and a psychological intervention on a particular outcome variable, then the drug and the psychological intervention would be the two independent variables.
3. Mixed Design Repeated Measures ANOVA: This type of ANOVA is used when there are both within-subjects and between-subjects factors. For example, if a study measures the effect of a drug on a particular outcome variable, with some participants receiving the drug and others receiving a placebo, then the drug would be the between-subjects factor, and the time points at which the outcome variable is measured would be the within-subjects factor.
The key differences between these types of repeated measures ANOVA lie in the number of independent variables and the way they are measured. One-Way Repeated Measures ANOVA involves only one independent variable, while Two-Way Repeated Measures ANOVA involves two independent variables. Mixed Design Repeated Measures ANOVA involves both within-subjects and between-subjects factors. Therefore, the choice of which type of repeated measures ANOVA to use depends on the specific research question and the nature of the data being analyzed.
Prompt: Explain the above answer using nested versus crossed factorial terminology.
The terms "nested" and "crossed" refer to the way in which the levels of the independent variables are organized in a factorial design.
In a crossed design, each level of one independent variable is paired with every level of the other independent variable. For example, if we have two independent variables, A and B, each with three levels, a crossed design would involve measuring each participant in all nine possible conditions (A1B1, A1B2, A1B3, A2B1, A2B2, A2B3, A3B1, A3B2, A3B3).
In a nested design, the levels of one independent variable are nested within the levels of the other independent variable. For example, if we have two independent variables, A and B, where A has two levels and B has three levels, a nested design might involve measuring participants in all three levels of B, but only in one level of A (B1A1, B2A1, B3A1, B1A2, B2A2, B3A2).
Using this terminology, we can see that the One-Way Repeated Measures ANOVA is a nested design, because each level of the independent variable is nested within each participant. The Two-Way Repeated Measures ANOVA is a crossed design because each level of each independent variable is crossed with each level of the other independent variable. And the Mixed Design Repeated Measures ANOVA is a combination of nested and crossed designs, as it involves both within- and between-subjects factors.
It is important to consider the organization of the levels of the independent variables when selecting an appropriate ANOVA model, as this will affect the way in which the sources of variation are accounted for in the analysis.