Question

When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?

Answer 1

Because it increases the risk of Type 1 error

Explanation:

ANOVA is the analysis of the variance .

When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error .

For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test. Similarly to test 10 population mean would require 45 separate two sample t test.

This has two disadvantages .

First the procedure is too lengthy and tediuos.

Second the overall level of significance greatly increases as the number of t- tests increases.

The analysis of the variance compares two different estimates of variance using the F distributionto determine whether the population means are equal.