If 95% Tukey confidence intervals tell us to reject H_{0}:μ_{1}=μ_{2} and H_{0}:μ_{1}=μ_{3}, will we necessarily reject H_{0}:μ_{2}=μ_{3}?

emancipezN

emancipezN

Answered question

2021-05-26

If 95% Tukey confidence intervals tell us to reject H0:μ1=μ2 and H0:μ1=μ3, will we necessarily reject H0:μ2=μ3?

Answer & Explanation

Dora

Dora

Skilled2021-05-27Added 98 answers

If we have 3 groups and we calculate the Tukey confidence interval for each pair of means difference and we reject H0:μ1=μ2 and H0:μ1=μ3,We necessarily reject hypotheses H0:μ2=μ3. We had in a, previous task this situation.
For example, if μ2 is very close to μ3 this means that μ2μ3μ. So, since it would be almost the same value for both means, they will be different from ja1. But, also it can be that all three means are very different one from another.

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