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The test is also called one-way ANOVA with dependent groups.
The one-way repeated measures ANOVA checks if the difference between the averages of two or more dependent groups is significant.
While on one-way ANOVA each subject appears only in one group, on one-way repeated measures ANOVA each subject appears in every group. A one-way repeated measures ANOVA contains only one categorical variable, each group/treatment is one value of the categorical variable.
For two categorical variables, use the two-way ANOVA calculator. The paired t-test is a special case of repeated measures ANOVA with two groups.
If you use a two-way mix model ANOVA with no repeat, with the subject as a random factor, and the group as a fixed factor you will get the same results.
The repeated measures ANOVA test checks if the difference between the averages of two or more dependent groups is significant when every subject appears in each group.When performing the repeated measures ANOVA test, we try to determine if the difference between the averages reflects a real difference between the groups, or is due to the random noise inside each group.
Sample data from all compared groups
|Sum of Squares (SS)||Mean Square (MS)||F statistic||p-value|
| A - Subjects (rows)|
Between the subjects
|DFA = a - 1||SSA = Σiab(Ȳi-Ȳ)2||MSA = SSA / DFA||FA = MSA / MSE||P(x > FA)|
| B - Treatments (Columns)|
Between the treatments
|DFB = b - 1||SSB = Σjba(Ȳj-Ȳ)2||MSB = SSB / DFB||FB = MSB / MSE||P(x > FB)|
Within the cells
|DFE = n - a - b + 1||SSE=ΣiaΣjb(Yi,j - Ȳi - Ȳj + Ȳ)2||MSE = SSE / DFE|
All the deviations from the average
|DFT = n - 1||SST=ΣiaΣjb(Yi,j - Ȳ)2|
|MSE = S2 = SST / (n - 1)|