Analysis of Variance

1-way ANOVA

-          Analysis of variance is used to compare 3 0r more means w/c contains only 1 variable.

2-way ANOVA

-          ANOVA that involves 2 variables.

Reasons why the T-test should not be used on 3 or more populations

1.       When 1 is comparing 2 means at a time, the means of the rest of the study are ignored. W/ F-test, all the means are tested simultaneously.

2.       When 1 is comparing 2 means at a time, the probability of rejecting the null hypothesis when it is true increased, since more T-tests are conducted, the greater is the likelihood of getting significant differences by chance alone.

3.       The more means are to compare, 3 the mote T-tests are needed.

Assumptions for the F-test in comparing three of more means

1.       The populations in w/c the samples were obtained must be normally distributed or approximately normally distributed.

2.       The sample must be independent for each.

3.       Te variances of the population must be equal.

With the f-test, 2 different estimates of the population variances are made. The 1^st estimate is called the between group variance or mean square of the between group that involves finding the variance of the means. The 2^nd estimate, the w/in group variance or mean square of the w/in group. This is made by computing all the variances using the data and is not affected by the difference of the means.

No difference in the means.

·         The between group variance estimate is approximately equal to the w/in group variance.

·         F-test value will be approximately equal to 1.

·         The null hypothesis will not be rejected.

Means differ significantly.

·         The between group variance is much larger than the w/in group variance.

·         F-test will be significantly greater then 1.

·         The null hypothesis will be rejected.