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.