Which of the following is NOT assumed before starting an $ANOVA$ test?

• A. The populations are normally distributed.
• B. The samples are independent of each other.
• C. The population means are equal.
• D. The populations have equal variances.

Answer: (C)

Verified step by step guidance

1. Understand that ANOVA (Analysis of Variance) is used to compare the means of three or more populations to see if at least one mean is different.
2. Recall the key assumptions required before performing an ANOVA test: (1) The populations from which samples are drawn are normally distributed, (2) The samples are independent of each other, and (3) The populations have equal variances (homogeneity of variance).
3. Recognize that the assumption about population means being equal is actually the null hypothesis of the ANOVA test, not a precondition or assumption.
4. Therefore, the statement 'The population means are equal' is not an assumption made before starting the ANOVA test; it is what the test aims to evaluate.
5. Summarize that all other options listed are assumptions, but the equality of population means is the hypothesis tested by ANOVA.