One-Way Within-Subjects (Repeated Measures) ANOVA
One-way within-subjects ANOVA is also known as repeated measures analysis of variance, randomized-blocks one-way analysis of variance, single-factor within-subjects analysis of variance. As the subjects are exposed to each condition in turn, the measurement of the dependent (response) variable is repeated. The computed test statistic evalustes if there is a significant difference between at least two of the conditions of repeated measures in a set of k conditions.
One-Way Repeated Measures ANOVA Output
The default output includes the one-way ANOVA table. The additional output depends on selected options, and can include the mean table, a mean bar plot, the results for sphericity test and correction, and table reports for selected multiple comparisons tests.
The Default Output: One-Way ANOVA Table
- The source of variability: The between-subjects variability (the amount of variability between the mean scores of n subjects); the between-conditions variability (a measure of the variance of the means of the k conditions); the residual (i.e., chance factor or experimental error beyond the control of a researcher)
- The sum of the squared deviations from the mean (Sum of Squares); the degrees of freedom (df); the Mean Square for each of the variability components
- The test statistics (F) and the p value
- The partial omega squared test result (testing strength of association)
This table displays:
Sphericity Evaluation (Locally Best Invariant Test)
Sphericity implies that the variances of the differences between the repeated measurements should be approximately the same. However, within subjects analysis of variance is very sensitive to violations of the sphericity assumption. Therefore, sphericity tests and corrections are always provided with the repeated measures ANOVA.
Greenhouse & Geisser and Huynd & Feldt Corrections
Mean Bar Plot
The error bars displayed on the mean bar plot can represent:
Multiple Comparisons/Post-Hoc Tests
Simple comparisons (also know as pair-wise comparisons) accompanying one-way within-subjects ANOVA include:
- Tukey's HSD test (see the example above)
- Tukey B test on ordered means
- Fisher's LSD test
- The Newman-Keuls (Neuman-Keuls) test on ordered means
- Tukey Kramer test
- Scheffé test
- Bonferroni-Dunn test
The example below is the Tukey's HSD test result for the one-way within-subjects ANOVA example illustrated above. For more information regarding multiple comparisons, click here.
Supported Worksheet Layout
For this ANOVA design, Aabel supports two different worksheet layouts.
- The layout I allows storing the design experimental scores (response data) from all of the k >= 3 conditions of repeated measures in a single numeric column, and uses the levels of the design single factor (A) to split the data accordingly. In this layout, a subject occurs in multiple worksheet rows: hence, it is required to have a data column (numeric or categorical) with the subject ID.
- The layout II requires storing the design experimental scores (response data) from each condition of repeated measures in a separate numeric column, i.e., each column represents one of the levels of the design (within-subjects) single factor.