I have a fairly simple question regarding the interpretation of the F-test in Microsoft Excel.

Let't say these are the results of my F-test:

enter image description here

I am now wondering how to interpret it in order to choose the correct t-test (assuming equal or unequal variances) for my data-set.

I have found guides telling me if F critical > F, then use unequal variances. However, some of the guides tell you to use only the p value, so I am unsure which parameters to look at when interpreting the results.


Several things:

1) When doing hypothesis tests, the decision is the same whether you use p-values or critical values (if it isn't, you did something wrong, or at least inconsistent).

2) When sample sizes are equal, the t-test (or ANOVA) is less sensitive to differences in variance.

3) You shouldn't do a formal equality of variance test to work out whether or not to assume equal variances; the resulting procedure for testing equality of means doesn't have the properties you'd likely wish it did. If you're not reasonably comfortable with the equal variance assumption, don't make it (if you like, assume the variances are always different unless you have some reason to think they're going to be fairly close). The t-test (and ANOVA) procedures aren't highly sensitive to small to moderate differences in population variance, so with equal (or nearly equal) sample sizes you should be safe whenever you're confident they're not highly different.

4) The "usual" F-test for equality of variance is extremely sensitive to non-normality. If you must test equality of variance, using that test wouldn't be my advice.

Which is to say, if you're able to do a Welch-type test or similar, you may be better off just to do so. It will never cost you much, it may save a lot. (In your particular situation in this case, you are probably safe enough without it - but there's no particular reason not to do it.)

I'll note that R by default uses the Welch test when you try to do a two-sample t-test; it only does the equal-variance version when you tell it to. I think this is the right way to do it (to do the safer thing by default), if only to save us from ourselves.

  • 1
    $\begingroup$ Thanks for your reply, Glen_b. However, in i.imgur.com/evP3NPh.jpg the F critical is larger than the F value, which would prompt me to use the t-test assuming unequal variances, but the p value is larger then 0,05, which would prompt me to use the t-test assuming equal variances. This is why I am curious how to interpret the results. $\endgroup$ – praznin Apr 9 '13 at 4:21
  • 2
    $\begingroup$ You're mistaken. Having the F smaller than the critical value isn't suggesting the variances are more different that could have happened by chance. You have that exactly backward (can you point to the guides that say so?). Hence my earlier comment: "the decision is the same whether you use p-values or critical values (if it isn't, you did something wrong...)". The direct implication is that you had done something wrong. But given my other comments, it's entirely moot. The exercise is a bad idea in any case. $\endgroup$ – Glen_b -Reinstate Monica Apr 9 '13 at 4:25
  • 1
    $\begingroup$ No problem, here is one of the sources: chemistry.depaul.edu/wwolbach/390_490/Excel/… $\endgroup$ – praznin Apr 9 '13 at 4:31
  • 1
    $\begingroup$ Ok, I think I udnerstand now. This F critical > F thing works only when p < 0.05, otherwise we can say that the samples have equal variances? $\endgroup$ – praznin Apr 9 '13 at 4:36
  • 3
    $\begingroup$ I think you don't understand it. If $F < F_{\mathrm{crit}}$ then automatically $p> 0.05$. Correspondingly, if $F \geq F_{\mathrm{crit}}$ then automatically $p\leq 0.05$. Alternatively, if $p\leq 0.05$ then $F \geq F_{\mathrm{crit}}$ and if $p> 0.05$ then $F < F_{\mathrm{crit}}$. Further, under no circumstances can you say the two populations the samples were drawn from have equal variances. Whether the samples themselves have equal variances you can tell just by looking at the numbers - you don't need a test for that, but when they differ it doesn't tell you much of interest. $\endgroup$ – Glen_b -Reinstate Monica Apr 9 '13 at 5:50

If you want to know more about the meaning and calculation of the F test when used as a criterion for the analysis of variance (ANOVA) with examples in Excel, I recommend this series of four articles. The final formula is able to take into account the size of alpha, the number of degrees of freedom for the F ratio's numerator and denominator, and the noncentrality parameter.

  1. The Concept of Statistical Power - http://www.informit.com/articles/article.aspx?p=2036566
  2. The Statistical Power of t-Tests - http://www.informit.com/articles/article.aspx?p=2036565
  3. The Noncentrality Parameter in the F Distribution - http://www.informit.com/articles/article.aspx?p=2036567
  4. Calculating the Power of the F Test - http://www.informit.com/articles/article.aspx?p=2036568

Important: be sure that the variance of Variable 1 is higher than the variance of Variable 2. If not, swap your data. As a result, Excel calculates the correct F value, which is the ratio of Variance 1 to Variance 2 (F = Var1 / Var 2).

Conclusion: if F > F Critical one-tail, we reject the null hypothesis. That means the variances of the two populations are unequal.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.