Repeated measures ANOVA is a statistical method used to analyze the effects of one or more within-subjects factors on a continuous dependent variable measured repeatedly over time or under different conditions. It is particularly useful in research designs where the same participants are measured multiple times, allowing researchers to assess changes within subjects across various levels of the independent variable.
When to Use Repeated Measures ANOVA:
Repeated measures ANOVA is appropriate when:
The same participants are measured on the same dependent variable multiple times.
There are two or more levels of a within-subjects factor (independent variable), representing different conditions or time points.
The dependent variable is continuous and approximately normally distributed.
Assumptions and Data Requirements:
Before conducting repeated measures ANOVA, several assumptions must be met:
Sphericity: The variances of the differences between all possible pairs of conditions should be equal.
Normality: The dependent variable should be approximately normally distributed within each level of the within-subjects factor.
Homogeneity of Covariance: The covariances between pairs of repeated measures should be equal across all levels of the within-subjects factor.
Additionally, the data required for repeated measures ANOVA should consist of a continuous dependent variable measured on the same participants across multiple levels or conditions of the within-subjects factor.
Writing the Hypothesis:
The null hypothesis (H0) for repeated measures ANOVA states that there are no significant differences in the means of the dependent variable across different levels of the within-subjects factor. The alternative hypothesis (H1) suggests that there is at least one significant difference in the means of the dependent variable across the levels of the within-subjects factor.
For example:
H0: There are no significant differences in mean reaction times across different experimental conditions.
H1: There is a significant difference in mean reaction times across different experimental conditions.
Sample Situation with Sample Data:
Suppose a researcher wants to investigate the effect of three different teaching methods (Traditional, Blended, Online) on students' performance in a mathematics test. The same group of students is exposed to all three teaching methods, and their test scores are measured after each method.
In this scenario, repeated measures ANOVA can be conducted to determine whether there are significant differences in the mean test scores across the three teaching methods.
Reporting the Results in a Research Paper:
The results of repeated measures ANOVA are typically reported with the following information:
The F-value (test statistic) and the corresponding degrees of freedom for both the numerator and denominator.
The p-value indicating the significance level.
A conclusion regarding the rejection or non-rejection of the null hypothesis.
Post-hoc tests (if applicable) to determine which specific conditions or levels differ significantly from each other.
For example:
"A repeated measures ANOVA was conducted to examine the effect of three teaching methods (Traditional, Blended, Online) on students' performance in a mathematics test. The results revealed a significant effect of teaching method on test scores (F(2, 87) = 6.12, p < 0.05), indicating that there were significant differences in mean test scores across the three teaching methods. Post-hoc tests using the Bonferroni correction indicated that the mean test score for the Online teaching method was significantly higher than both the Traditional and Blended teaching methods (p < 0.05)."
NOTE:
The main difference between one-way ANOVA and repeated measures ANOVA lies in the design and the type of data being analyzed.
One-Way ANOVA:
One-way ANOVA is used to compare the means of three or more independent groups on a continuous dependent variable.
In one-way ANOVA, the independent variable (also known as the factor) has distinct, non-repeated levels or categories.
Participants are typically different individuals or subjects in each group, and they are only measured once.
One-way ANOVA assesses whether there are statistically significant differences in the means of the groups.
Repeated Measures ANOVA:
Repeated measures ANOVA is used when the same participants are measured multiple times on the same dependent variable under different conditions or time points.
Repeated measures ANOVA is also known as within-subjects ANOVA because it examines changes within the same subjects over time or across conditions.
The independent variable in repeated measures ANOVA is typically a within-subjects factor with two or more levels or conditions.
Participants serve as their control, and each participant's data is measured across all levels of the independent variable.
Repeated measures ANOVA assesses whether there are statistically significant differences in the means of the repeated measures across different levels or conditions of the within-subjects factor.
