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# Statistics: Conducting a One-Way ANOVA

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A psychologist believes that the kind of feedback a person receives about their work affects the quality of the work. You randomly assign 12 widget makers to one of three groups: positive feedback only, corrective feedback only, and no feedback. You track the number of widgets that each person makes correctly (out of 10) and obtain the following data:

Positive Feedback Only Corrective Feedback Only No Feedback
5 4 5
4 5 4
4 3 6
7 6 2

Use an analysis of variance (alpha = 0.05) to determine whether this data is sufficient to conclude that there are significant differences between the feedback conditions.

Make sure you include a complete ANOVA summary table. Also, report the appropriate null and research hypotheses and the critical value (alpha = 0.05). In addition, provide your statistical conclusion, including a calculation of the test statistic, in the APA format and a conceptual conclusion in one to two sentences.

https://brainmass.com/statistics/analysis-of-variance/statistics-conducting-a-one-way-anova-415714

#### Solution Preview

Null Hypothesis: There is no difference between the mean numbers of widgets among the three groups based on feedback conditions.

Alternate Hypothesis: There is a significant difference between the mean numbers of widgets among the three groups based on feedback conditions.

Analysis Plan:
We shall use significance ...

#### Solution Summary

This solution is comprised of a detailed explanation of the various aspects of Analysis of Variance as it pertains to the given problem and provides students with a clear perspective of the calculations and underlying concepts required. Two files are attached, an Excel spreadsheet and a Word document which contain material pertaining to this solution.

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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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