In a one-way ANOVA for a completely randomized design, $q _ { \alpha }$
is always less than $t _ { \alpha / 2 }$
.

Question

In a one-way ANOVA for a completely randomized design, $q _ { \alpha }$ 
is always less than $t _ { \alpha / 2 }$ 
.

Quizplus · Accepted Answer

In a one-way ANOVA for a completely randomized design, $q _ { \alpha }$ (the critical value from the Tukey's range test) and $t _ { \alpha / 2 }$ (the critical value from the Student's t-test) are not directly comparable in this manner. The value of $q _ { \alpha }$ depends on the number of groups and the total number of observations, while $t _ { \alpha / 2 }$ depends on the degrees of freedom for the error term and the chosen level of significance. Their relative sizes can vary depending on these parameters.

In a One-Way ANOVA for a Completely Randomized Design qαq _ { \alpha }qα​

In a One-Way ANOVA for a Completely Randomized Design $q _ { \alpha }$