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Statistical Analysis Techniques: ANOVA and Post-Hoc Tests

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A market researcher is interested in knowing the type of training that works best for DVD users. Thirty consumers are randomly selected from a population of known DVD owners (i.e., users). Ten users are trained by giving them the DVD user's manual and allowing them to read it. Another ten users are trained from a 30 minute DVD user training video. Another ten users are trained from a self-paced computer tutorial. The users are then timed in their ability to setup and program the DVD by performing a series of operations. Which statistical analysis technique should be used? What is the null hypothesis? Can the market researcher get an answer? Why or why not?

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Since there are 3 groups with 10 users in each group, we can use Analysis of Variance (abbreviation: ANOVA) as the statistical analysis technique. We usually use ANOVA to test the means of three groups. Using this analysis, it would help us figure out which type of ...

Solution Summary

The solution discusses the statistical analysis technique such as ANOVA and post-hoc tests and all detailes involved in the test such as null hypothesis, p-value and so on.

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3 ANOVA Problems: Identify hypothesis, conduct analysis, accept or reject

WEB CALCULATOR EXERCISE 5

ANOVAs

1. A researcher is interested in comparing the effectiveness of three different kinds of therapy for anger problems. Eight participants are randomly assigned to three treatment conditions: Cognitive Therapy (CT), Cognitive-Behavioral Therapy (CBT), and Interpersonal Therapy (IT). All participants complete the weekly treatment for 8 weeks. Participants take an anger test before and after the 8-week treatments. Each participant's difference score (= anger score after the treatment minus (-) anger score before the treatment) is shown in the following table. The three therapists in this experiment have equal educational levels and clinical experiences.

CT CBT IT
3 5 7
4 4 8
4 6 9
4 6 10
3 5 6
8 4 7
6 9 11
2 7 10

a. What statistical test should be used to analyze the data?
b. Identify H0 and Ha for this study.
c. Conduct the appropriate analysis.
d. Should H0 be rejected? What should the researcher conclude?

2. A teacher is interested in comparing the effects of three different types of rehearsal methods (Rote rehearsal, Imagery, and Story) on number of words recalled. Participants are randomly assigned into three different groups. In each group, participants are asked to study a list of words using the assigned method. The following table shows the result.

Rote rehearsal Imagery Story
5 5 7
5 4 6
4 6 8
6 7 9
5 7 6
4 6 9
3 8 8
5 5 10
6 7 9

a. What statistical test should be used to analyze the data?
b. Identify H0 and Ha for this study.
c. Conduct the appropriate analysis.
d. Should H0 be rejected? What should the researcher conclude?
e. If there is a significant difference, conduct the post hoc test.

3. A professor is interested in whether there is a difference in counseling students' statistics competency scores among 1) those who have never taken any statistics course, 2) those who have only taken an undergraduate statistics course, 3) those who have taken COUN 503, and 4) those who have taken an advanced statistic course while working on a Ph. D. The professor gathers information from a random sample of students and obtains the statistics competency scores. The scores are normally distributed.

1) 2) 3) 4)
7 11 13 15
6 11 14 14
8 10 15 15
5 12 12 15
4 13 13 10
4 15 13 15

a. What statistical test should be used to analyze these data?
b. Identify H0 and Ha for this study.
c. Conduct the appropriate analysis.
d. Should H0 be rejected? What should the researcher conclude?

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