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I am performing the test to see if there is any differences between the preferences of chocolate for male and female students. My null hypothesis is that there is no difference.

My data is not normally distributed and data transformations failed to 'squash' the data. Therefore I performed the F test on the unchanged data:

var.test(dframeA$Chocolate,dframeB$Chocolate) 

        F test to compare two variances

data:  dframeA$Chocolate and dframeB$Chocolate
F = 0.9539, num df = 238, denom df = 138, p-value = 0.7447
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.7041521 1.2768820
sample estimates:
ratio of variances 
         0.9538888

The above shows the result.

I am very new to R (and statistics for the matter). Please would you help me understand what the results mean? I am assuming that this test is 2-tailed..

user3069564
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1 Answers1

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One quick remark: I assume that you want to know if the variances of the two population are equal (if you want to compare population means an F-test is not the correct choice). The ratio of the variance estimations is F-distributed (given normality of the data) and we are interested if the variance in one population is bigger or smaller than in the other, i.e. a two-sided test. Notice however, that the F-Test is sensible to non-normality and other tests are more suitable in this case (see the Levene-Test or Brown-Forsyth Test for more robust approaches; see Why Levene test of equality of variances rather than F ratio? and When to use (non)parametric test of homoscedasticity assumption?).

Said that, the results suggest that the null hypothesis of equal variances is not rejected, as p=0.7447, i.e. >.05 or >.10, depending on your alpha level. This is equivalent to saying that the null hypothesis of F=1 (same variances) is included in the confidence interval [0.7041521, 1.2768820] and thus not rejected.

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Mark Heckmann
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  • Thank you for the response Mark Heckmann. I tried to transform the data as it is not normally distributed and then apply the F test. However even transformations of y^3 result in a left skew so I have now moved on to a Wilcox test...I am a bit confused though, as I have been asked to provide the degrees of freedom for this.. – user3069564 Dec 08 '13 at 00:27