Question

Q2. Researchers were interested in which of the following diets were more effective in weight loss: 1) Weight Watchers; 2) Nutrisystem; 3) Atkins. After a 6-month program the amount of weight loss was compared and there were significant differences.  Using the information provided below, interpret the post hoc analysis. See page 335 in your textbook.

Multiple Comparisons
Dependent Variable: Weight lost (kg)
	(I) Diet	(J) Diet	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
						Lower Bound	Upper Bound
Tukey HSD	1	2	.2741	.67188	.912	-1.3325	1.8806
		3	-1.8481*	.67188	.020	-3.4547	-.2416
	2	1	-.2741	.67188	.912	-1.8806	1.3325
		3	-2.1222*	.65182	.005	-3.6808	-.5636
	3	1	1.8481*	.67188	.020	.2416	3.4547
		2	2.1222*	.65182	.005	.5636	3.6808
LSD	1	2	.2741	.67188	.684	-1.0644	1.6125
		3	-1.8481*	.67188	.007	-3.1866	-.5097
	2	1	-.2741	.67188	.684	-1.6125	1.0644
		3	-2.1222*	.65182	.002	-3.4207	-.8237
	3	1	1.8481*	.67188	.007	.5097	3.1866
		2	2.1222*	.65182	.002	.8237	3.4207

Answer 1

Solution

Back-up Theory

The mean difference is significant, implying the two means are significantly different, if the p-value [given under the column ‘Sig’ is less than 0.05 or equivalently, if the confidence interval does not contain zero.]

Now to work out the solution,

Based on the above theory, both HSD and LSD bring out consistent results.

µ₁ and µ₃ are significantly different,

µ₂ and µ₃ are significantly different, but

µ₁ and µ₂ are NOT significantly different.

Further, referring to ‘Mean Difference’ column,

µ₁ - µ₃ = - 1.8481 or µ₃ = µ₁ + 1.8481

µ₂ - µ₃ = - 2.1222 or µ₃ = µ₂ + 2.1222

Above => µ₃ > µ₁ > µ₂

Or, in the context of the given scenario,

In terms of effectiveness in reducing weight,

Atkins is most effective, followed by Weight Watchers and Nutrisystem is least effective. Answer

DONE