Lesson 6 of 7 · 14 min

Testing variances: chi-square and F

A claim about one variance is tested with chi-square; a comparison of two variances is tested with the F-ratio of the sample variances.

In short

One variance, normal population: $\chi^2 = (n-1)s^2/\sigma_0^2$ with $n - 1$ df.
Chi-square is never negative and is skewed to the right, so its lower and upper critical values are not mirror images.
Two variances, independent samples from normal populations: $F = s_1^2/s_2^2$ with $n_1 - 1$ (numerator) and $n_2 - 1$ (denominator) df.
F is also never negative. An F near 1 means similar variances.
Always work in variances: square every standard deviation first, including the hypothesised one.

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