Question

For an ANOVA comparing three treatment conditions, rejecting the null hypothesis is equivalent to concluding that all three treatment means are different.
True / False.

Answer 1

Answer: False.

Explanation:

ANOVA is an acronym that stands for analysis of variance.

We use ANOVA to test whether there is significant difference between the means.

For an ANOVA comparing three treatment conditions,  

Null hypothesis: The mean is the same for all groups.

= $H_0:\mu_1=\mu_2=\mu_3$

Alternative hypothesis: There is a significant difference between the means.

$H_a:\mu_1\neq\mu_2\neq\mu_3$

By rejecting the null hypothesis is equivalent to " not all of the means are equal."

Then we find which treatment is the most important among the pairwise comparison using t-distribution.

Hence, the given statement is False.