What statistical assumptions need to be validated for ANOVA results to be valid?
a. observations are from an F-distribution
b. Observations are from a Chi square distribution
c. Observations are normally distributes, independent, a variances are equal
d. Observations are selected, not randomized
e. No assumptions are required to be met
a. observations are from an F-distribution
c. Observations are normally distributes, independent, a variances are equal
The correct answer is c. Observations are normally distributed, independent, and variances are equal.
ANOVA (Analysis of Variance) is a statistical test used to compare means between three or more groups. In order to obtain valid results from ANOVA, certain assumptions need to be validated. These assumptions are as follows:
1. Normality - The data within each group or treatment should follow a normal distribution. This assumption is important because ANOVA assumes that the population distributions of each group are normal.
2. Independence - The observations within each group should be independent of each other. In other words, the value of one observation should not be influenced by or related to the value of another observation in the same group.
3. Equal Variances - The variances (levels of variability) within each group should be approximately equal. This assumption is called homogeneity of variances. It is important because ANOVA assumes that the population variances of the groups being compared are equal.
Therefore, options a, b, and d are incorrect because they do not reflect the necessary assumptions for ANOVA. Option e is also incorrect because ANOVA does have assumptions that need to be met for the results to be valid.