One-way Analysis of Variance

ANOVA 

• is used to test the significance of different between means of three or more sets of data simultaneously
• method of dividing the variation of served in experimental data into different parts
• a technique using an F test to test the hypotheses concerning the means of three or more population
• procedure of comparing variances

Reasons Why Multiple T Test Cannot be Used to Compare Three or More Means:

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 and making all pair wise comparison, the probability of rejecting the null hypotheses when it is true is increased, since the more T Test are conducted, the greater is the likelihood of getting the significant differences of chance alone. 
3. The more means there to compare, the more T Test are needed.

Assumptions for the F Test for Comparing Three or More Means:

1. The populations from which samples were obtained, must be normally or approximately normally distributed.
2. The samples must be independent of each other.
3. The variances of populations must be equal.

By: Andrea Beatrice A Pechueco