Question

exercise and the tukey hsd test: in how it works 11.1, we conducted a one-way between-groups anova on an abbreviated data set from research by irwin and colleagues (2004) on adherence to an exercise regimen. Participants were asked to attend a monthly group education program to help them change their exercise behavior. Attendance was taken and participants were divided into three categories: those who attended fewer than 5 sessions, those who attended between 5 and 8 sessions, and those who attended between 9 and 12 sessions. The dependent variable was number of minutes of exercise per week. Here are the data once again:

<5 sessions: 155, 120, 130,

5-8 sessions: 199, 160, 184,

9-12 sessions: 230, 214, 195, 209.

a) What conclusion did we draw in step 6 of the ANOVA? Why could you not be more be more specific in your conclusion? That is, why is an additional test necessary when the ANOVA is statistically significant?

b) Conduct a Tukey HSB test for this example. State your conclusions based on this test. Show all calculations.

c) If we did not reject the null hypothesis for a particular pair of means, then why cant we conclude that the two means are the same?

Answer 1

(a) The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are equal

<5 sessions	5-8 sessions	9-12 sessions
155	199	230
120	160	214
130	184	195
		209
	Mean	n	Std. Dev
	135.0	3	18.03	<5 sessions
	181.0	3	19.67	5-8 sessions
	212.0	4	14.45	9-12 sessions
	179.6	10	36.85	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	10,172.4	2	5,086.2	17.37	.0019
Error	2,050.00	7	292.857
Total	12,222.4	9

The p-value is 0.0019.

Since the p-value (0.0019) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a significant difference between the group means.

(b) Using the Tukey Method and 95% Confidence

Factor	N	Mean	Grouping
9-12 sessions	4	212.00	A
5-8 sessions	3	181.0	A
<5 sessions	3	135.0		B

Means that do not share a letter are significantly different.

There is a significant difference between the means of 9-12 sessions and <5 sessions.

There is a significant difference between the means of 5-8 sessions and <5 sessions.

(c) There is no significant difference between the means of 9-12 sessions and 5-8 sessions between their confidence intervals overlap.

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