The 95% individual confidence interval for $\mu _ { 1 } - \mu _ { 2 }$
will always be narrower than the Tukey 95% simultaneous confidence interval for $\mu _ { 1 } - \mu _ { 2 }$
.

Question

The 95% individual confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ 
will always be narrower than the Tukey 95% simultaneous confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ 
.

Quizplus · Accepted Answer

The Tukey 95% simultaneous confidence interval accounts for multiple comparisons and thus is wider to maintain the overall confidence level across all comparisons, whereas the 95% individual confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ is calculated for a single comparison and does not adjust for multiple comparisons, making it narrower.

The 95% Individual Confidence Interval For μ1−μ2\mu _ { 1 } - \mu _ { 2 }μ1​−μ2​

The 95% Individual Confidence Interval For $\mu _ { 1 } - \mu _ { 2 }$