Analysis of Variance

   The z and t tests should not be used when three orb more means are compared, instead, F-test can be used to compare three or more means. This technique is called analysis of variance or ANOVA .For three groups, the F-test can only show whether or not a difference exists among the three means. It cannot reveal where the difference lies. If the F test indicates that there is a difference among the means, other statistical test are used to find where the difference exists. The most commonly used tests are the Scheffe test and the Tukey test.

One-Way Analysis of Variance
- Analysis of variance used to compare three or more means which contains only one variable.

Two-Way Analysis of Variance
-ANOVA that involves two variables.

Reasons why the t test should not be used on three or more populations:
1. When one is comparing two means at a time, the rest of the means under study are ignored. With the f test, all the means are compared simultaneously.
2. When one is comparing two means at a time, the probability of rejecting the null hypothesis when it is true increased, since more t test are conducted, the greater is the likelihood of getting significant differences by chance alone.
3. The more means there are to compare, 3 the more t tests are needed.

Assumptions for the F test for comparing Three or more means
1. The populations from which the samples were obtained must be normally or approximately normally distributed.
2. The samples must be independent for each.
3. The variances of the population must be equal.


J.Santillan