Degrees of freedom (df) and the F value, at the output of repeated measures ANOVA (within-subject and between subject), are used with p value when reporting this result. But, what do they mean? How should we interpret these values?
F and df are used to calculate the p-value. You actually only want to see if the p-value is small, as this tells you that your data are informative about the response w.r.t. the ANOVA factors. Knowing F and df in addition to the p-value is typically not required but if can help statisticians to spot pseudo-replication.
The F-value is a statistic calculated from the sample data. If the response has a normal distribution and is entirely unaffected by the experimental factors, then this value can be interpreted as a realization of a random variable with an F-distribution. The density of the F-distribution is strongly right-skewed, its concrete shape depends on the df. Large values are unexpected.
Often, the ANOVA F-test is not of particular interest scientifically. Often, test about mean differences are more intersting.
There are 1001 more things to say, about sums-of-squares, within-, between-, total- and residual variance, nominator and denominator degrees of freedom, the equivalence of t-tests and F-tests with 1 denominator df, multiple testing and protective F-tests, and so on.
Hello Emre Uysal. You said that you have both a between-Ss and a within-Ss variable in your model. In some fields, then, your model would be described as mixed design ANOVA. And the conventional model will have three F-tests, one for each main effect, and one for the interaction. If you carry out a search on , you should find lots of online resources that explain how to interpret the results. E.g., see this chapter from Andy Field's popular textbook:
- https://edge.sagepub.com/system/files/chapter15_1.pdf
HTH.
What people, who think they need mixed-design repeated measures ANOVA and p-values, often really need is multi-level factorial models and coefficient tables.
When reporting the results of a repeated measures ANOVA, you should include the following information:
Here is an example of how to report the results:
"A repeated measures ANOVA was conducted to examine the effect of [within-subjects factor] on [dependent variable]. The main effect of [within-subjects factor] was significant, F(df1, df2) = F-value, p < .05, partial eta-squared = [effect size]. There was also a significant interaction between [within-subjects factor] and [between-subjects factor], F(df1, df2) = F-value, p < .05, partial eta-squared = effect size. Post-hoc tests revealed that [specific effects or comparisons]."
The F-value in a repeated measures ANOVA represents the ratio of the variance between the groups to the variance within the groups. It tests the null hypothesis that there is no significant difference between the means of the groups, and a larger F-value indicates that the difference between the means is more likely to be significant. The p-value associated with the F-value represents the probability of observing such an extreme F-value by chance if the null hypothesis were true. Therefore, a smaller p-value indicates that the result is more statistically significant.
Kind regards,
Wadie
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