Question

The pairwise post hoc tests indicate which quality groups' means are statistically significantly different for the others. Using the results of the Tukey HSD post hoc test, what two quality rating groups had significantly different mean alcohol by volume levels? How do you know?

Post Hoc Tests

Multiple Comparisons
Dependent Variable:   Alcohol by Volume (in %) for brand
Tukey HSD
(I) Rated Quality of Brand	(J) Rated Quality of Brand	Mean Difference (I-J)	Std. Error	Sig.
VeryGood	Good	.30000	.12995	.069
	Fair	.39000*	.14093	.025
Good	VeryGood	-.30000	.12995	.069
	Fair	.09000	.13354	.780
Fair	VeryGood	-.39000*	.14093	.025
	Good	-.09000	.13354	.780

Multiple Comparisons
Dependent Variable:   Alcohol by Volume (in %) for brand
Tukey HSD
(I) Rated Quality of Brand	(J) Rated Quality of Brand	95% Confidence Interval
		Lower Bound	Upper Bound
VeryGood	Good	-.0193	.6193
	Fair	.0437*	.7363
Good	VeryGood	-.6193	.0193
	Fair	-.2382	.4182
Fair	VeryGood	-.7363*	-.0437
	Good	-.4182	.2382

*. The mean difference is significant at the 0.05 level.

Homogeneous Subsets

Alcohol by Volume (in %) for brand
Tukey HSDa,b
Rated Quality of Brand	N	Subset for alpha = 0.05
		1	2
Fair	10	4.5100
Good	14	4.6000	4.6000
VeryGood	11		4.9000
Sig.		.784	.082

Means for groups in homogeneous subsets are displayed.

a. Uses Harmonic Mean Sample Size = 11.436.

b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.

Answer 1

From Tukey Post hoc test we see that from simultaneous confidence intervals of Very Good-Good and Good-Fair contain zero hence Vary Good and Good are not significantly different and Good and Fair are also not significantly different. Whereas confidence interval of Very Good-Fair does not contain zero hence Vary Good and fair are significantly different.This is also seen from p-value approach. Since p-value corresponding Very Good-Good=0.069>0.05, p-value corresponding Good-Fair=0.780>0.05 and p-value corresponding Very Good-Fair=0.025<0.05 so we get same conclusion. Hence Very Good and Fair rating groups had significantly different mean alcohol by volume levels.