Question

Discuss two methods for checking the assumptions of normal populations and equal standard deviations for a one-way ANOVA.

Short answer

The condition of normality and equal standard deviations is met if the large sample deviation to small sample deviation ratio is less than two.

Step-by-step solution

Given Information

Consider ANOVA in one direction.

Take the residual analysis method into consideration.

Explanation

The residual is computed for each value in a one-way ANOVA. The difference between the actual and expected values is known as the residual.

The normal probability plot of the residual is approximately linear if normality and equal standard deviations are met. The residuals plot should be horizontal band centered and symmetric about the horizontal axis when compared to the sample means.

Consider a normal probability plot of the sample data, which is useful for detecting normality variations.

It's tough to check for equal standard deviations when the sample size is tiny. The condition of normality and equal standard deviations is satisfied if the large sample deviation to small sample deviation ratio is less than two.