Question

We like to test the effect of design (design1, 2, 3 and 4) on distance with 0.05 alpha.

This is the Tukey outputs.

diff       lwr upr p adj

design2-design1 11.902 6.679545 17.124455   0.0000027

design3-design1 19.974 14.751545 25.196455 0.0000000

design4-design1 22.008 16.785545 27.230455 0.0000000

design3-design2 8.072 2.849545 13.294455 0.0010308

design4-design2 10.106 4.883545 15.328455 0.0000451

design4-design3 2.034 -3.188455 7.256455 0.7221072

Which one is the correct conclusion of Tukey test?

	a.	Design 3 and 4 are not different. But rest pairs are different.
	b.	Design 3 and 4 are different. But rest pairs are not different.
	c.	All pairs are different.
	d.	All pairs are not different.

Answer 1

In Tukey test we make a pair wise comparession to see if there are significant difference between two groups. Here you have four design and also you have conducted the Tukey test and given the value of test statistics and corresponding p value. Let us the p-value for each pairs. Here if p values are less than alpha then it shows that there is significant difference between designs. By observing it one can easily see that all the p values are less than 0.05 (significance level alpha) except last one which is for pairs design 4 and design 3. Thus Design 3 and 4 are not different. But rest pairs are different. That is option a is correct.