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I'm trying to do F-test (ratio of the variances) for two samples with 92 data points each. I look at several links for the critical value for degrees of freedom equal to 91 but most of them are skipping values in between. For example, from the link below, the df for the numerator skipped: 40,60,120 and the same as the denominator.

sample critical table

Is there a way to estimate the critical value for an F-test(the easiest way possible)?

I am comparing daily temperatures from 1979-1993 and 1994-2008. I got "daily variance" for both epochs for July-August-September. So I now have 92 values for each epoch.I want to do F-test from this.

I'll appreciate any help.

Lyndz
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  • Which kind of F are you doing? Is this a ratio-of-variances test (where both numerator and denominator df will be very large) or an ANOVA (where it looks like the numerator df will be 1 but the denominator df will be large)? – Glen_b Apr 13 '17 at 05:33
  • I'm comparing the variances of the two samples. The ratio of the variances. – Lyndz Apr 13 '17 at 05:35
  • How does this problem arise? Is it for a course for example? – Glen_b Apr 13 '17 at 05:51
  • Since your modification greatly reduces the df (now to below 120), besides using a computer package to do it for you, you can use interpolation. See the discussion and examples here: [How do I find values not given in (interpolate in) statistical tables?](https://stats.stackexchange.com/questions/64538/how-do-i-find-values-not-given-in-interpolate-in-statistical-tables) (if your df were very large like your original post, my advice would be different). There's an explicit F example. For your case, with such a big numerator df you can probably get away with linear interpolation – Glen_b Apr 13 '17 at 05:58
  • Sorry, I just editted my previous question. I added some details based from your comments. Many thanks – Lyndz Apr 13 '17 at 06:02
  • My comment above yours is relevant to your current question, but please update your title as well. Also the information that it's a ratio of variances test should be in the question. A pity about the 15-fold decrease, I was almost ready to post the 1379 df answer – Glen_b Apr 13 '17 at 06:03
  • Note two issues: 1. The F test for variances is *very* sensitive to non-normality. 2. daily figures are likely not independent (and this, too can have a substantial effect on tests). As a result your F test for variances may not have the desired properties (e.g. the desired type I error rate may differ substantially from what you think you're getting) – Glen_b Apr 13 '17 at 06:42
  • Some upper tail F quantiles for 91,91 df (obtained easily from R): \begin{array}{c|c} \text{p} & \text{F}_\text{crit}\\ \hline 0.900 & 1.309744\\ 0.950 & 1.414341\\ 0.975 & 1.512109\\ 0.990 & 1.634784\\ 0.995 & 1.724317 \end{array} – Glen_b Apr 13 '17 at 06:48

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