Question

You wish to compare the population means between three categories. Compare and contrast using ANOVA vs. three separate t-tests.

In what ways are ANOVA and three separate t-tests the same?

In what ways are ANOVA and three separate t-tests different?

Answer 1

(a)

Model for three separate t tests and ANOVA are the same. Three separate t tests are just a special case of ANOVA Each of the three separate t tests is equivalent to ANOVA of analyzing the means of two groups.

(b)

The results of ANOVA will be to find out whether there is significant difference exists between means of 3 categories. Three separate t tests will find out which mean among the three categories is different in case such a difference exists as per ANOVA test.

ANOVA and three separate t tests are different in the value of Type I error as follows. Every time we conduct a t test, there is a chance that we will make a Type I Error: = 0.05. By running3 t tests on the same data, we have increased our chance of making a mistake to a larger quantity. ANOVA controls for these errors so that Type I error remains at = 0.05.