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Please I have a thesis defense and I wrote from this article this number f(1, 78) but I don't know what it refers to Can anyone clear it up for ME?

THANK YOU

Sycorax
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Razan Najee
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    It's an [F-distribution](https://en.wikipedia.org/wiki/F-distribution). The 1 and 78 are the degrees of freedom. – ralph Jun 04 '21 at 23:54
  • Some related threads: https://stats.stackexchange.com/questions/67543/why-do-we-use-a-one-tailed-test-f-test-in-analysis-of-variance-anova and https://stats.stackexchange.com/questions/258461/proof-that-f-statistic-follows-f-distribution – Sycorax Jun 05 '21 at 00:36
  • Thank u soooooo much – Razan Najee Jun 05 '21 at 05:44

1 Answers1

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As posted in the comments, this refers to an $F$ distribution with $1$ and $78$ degrees of freedom. In the derivation of the $F$ distribution, we divide a $\chi^2$ variable by another $\chi^2$ variable:

$$F(a, b) = \dfrac{\chi^2_a/a}{\chi^2_b/b}$$

Here, $a$ and $b$ are the degrees of freedom of the $\chi^2$ variables, and those values make their way to the $F$ distribution.

In your case, you have $F(1, 78) = F(a, b) = \dfrac{\chi^2_1/1}{\chi^2_{78}/78}$.

There are variations of this notation, such as $F_{1, 78}$, which has the same meaning.

Dave
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  • Thank u sooo much – Razan Najee Jun 05 '21 at 05:46
  • @RazanNajee I’m glad to hear it! Perhaps consider upvoting and accepting this answer so future readers with similar confusion about $F$ distribution notation will know to read this. – Dave Jun 05 '21 at 12:20