ANOVA

The Analysis Of Variance can be used in cases where there are more than two groups for comparison. (ANOVA) simultaneously compares the differences among sample means of more than two groups for a one-factor experiment.

Example:

• Hypothesis 1 : μ1 = μ2= μ3 (there is no difference between the three means)
• Hypothesis 2: μ1 ≠ μ2 ≠ μ3 (there is a difference between the three means)

Example: You might use ANOVA to compare mean morphine consumption between total knee replacement patients that received a femoral nerve block, those that received a femoral and a popliteal nerve block, and those that did not receive a nerve block of any kind.

Why Not Multiple T-Tests?

t-test can only be used to test differences between two means. When there are more than two means conducting such multiple t-tests makes the study complicated especially if there are large number of population groups and in such circumstances we use ANOVA.

Assumptions

There are four basic assumptions used in ANOVA.

1. the expected values of the errors are zero
2. the variances of all errors are equal to each other
3. the errors are independent
4. they are normally distributed