How do you report F statistics in APA format? I am working on PHD and am not certain that I am reporting the F statistics in the proper manner.

I have been reporting it as F (_,_). The second space I am unclear as to what number gets placed there.

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    $\begingroup$ This arguably belongs on CrossValidated. $\endgroup$ – jona Jun 9 '14 at 16:05
  • $\begingroup$ I agree with @jona, in that APA format is not unique to cognitive sciences, whereas the question is explicitly statistical. However, there may be a duplicate on CV already, so I'd recommend checking before migrating. I don't see any harm in leaving it here in any case. $\endgroup$ – Nick Stauner Jun 10 '14 at 0:56
  • $\begingroup$ I think the title focuses on APA style and in general I think that APA style (i.e., psychology) is on topic for cogsci (see this meta discussion). However, the body of this question is mostly a general statistical question that would be very much at home on CrossValidated. On balance, I think it would be fine on either site. $\endgroup$ – Jeromy Anglim Jun 10 '14 at 8:09

The F ratio statistic has a numerator and denominator degrees of freedom. Thus, you report:

F (numerator_df, denominator_df) = F_value, p = ..., effect size = ...

The numerator degrees of freedom relates to the factor of interest; the denominator degrees of freedom corresponds to the degrees of freedom for the error variance.

The exact way that these degrees of freedom are calculated depends on the statistical test you are using. Standard textbooks will describe these approaches. For example, in a standard one-way between subjects ANOVA with $k$ groups and $n$ participants per group, you would have $k-1$ numerator degrees of freedom and $kn-k$.

Generally, you will be able to read off these numbers from the output of your statistics package.


Here is an example with k=3 groups and n=5 participants. See the df in the "group" row and the "error" row.

F(2, 12) = 24.667, p < .001.


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The numbers inside the parentheses are the degrees of freedom for the F-statistic.

The second number is the within-group degrees of freedom. When you have the same number of subjects in all conditions, then the second number will be the number of subjects - the number of cells (conditions) in your design.

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