Tests of Variances
Until now we have confined ourselves to hypothesis testing of means. Both z- and t-testing involved the usage of distributions which possessed similar traits: the symmetrical shape and the central point equivalent to zero. However, when testing variance and standard deviation, one requires a strikingly different distribution, the Chi-Square distribution.
Properties of the Chi-Square Distribution:
- The graph is assymetrical, skewed to the right.
- All values are nonnegative.
- Tests of the variance requires us to assume that the population has normally distributed values.
As you might expect, the relevant statistics S 2 and 2 are present in the chi-square equation.