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# One way ANOVA

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Problem 1: A researcher wants to see if 4 different therapy approaches lead to different scores on a depression inventory. She conducts a study whereby individuals seeking therapy for depression are randomly assigned to 1 of the 4 therapy approaches. At the end of six months of therapy, each subject completes a depression inventory. She finds the mean depression score for the individuals in each of the 4 therapy approaches. Let us assume that the variance of the depression scores within each therapy approach is the same. Below are three possible scenarios of the resulting 4 group means. For which scenario would you expect F to be the highest? For which scenario below would you expect F to be the lowest? Why?

Scenario 1:
M1 = 98.62 M2 = 64.51 M3 = 71.88 M4 = 92.18
Scenario 2:
M1 = 62.45 M2 = 14.18 M3 = 36.21 M4 = 99.98
Scenario 3:
M1 = 71.28 M2 = 69.88 M3 = 67.45 M4 = 73.24

Problem 2: Suppose a researcher wants to determine if the level of alexithymia (an inability to express feelings and emotions with words) is different for individuals in three different occupations: (a) accountants, (b) therapists, and (c) medical doctors. To answer this question, the researcher obtains a random sample of 4 accountants, 4 therapists, and 4 medical doctors, and obtains an alexithymia score using an alexithymia inventory. The data are shown below. Based on these data, answer the researcher's question. Be certain to clearly specify the statistical test you used in answering this question, and show all of the computations you used in answering this question.

Accountants Therapists Medical Doctors
4 6 2
4 7 4
3 7 3
5 8 3

https://brainmass.com/statistics/analysis-of-variance/one-way-anova-test-depression-scores-groups-419841

#### Solution Preview

Computational details are given in the Excel file.

Statistics
Please provide detailed solutions to the following problems:

Problem 1: A researcher wants to see if 4 different therapy approaches lead to different scores on a depression inventory. She conducts a study whereby individuals seeking therapy for depression are randomly assigned to 1 of the 4 therapy approaches. At the end of six months of therapy, each subject completes a depression inventory. She finds the mean depression score for the individuals in each of the 4 therapy approaches. Let us assume that the variance of the depression scores within each therapy approach is the same. Below are three possible scenarios of the resulting 4 group means. For which scenario would you expect F to be the highest? For which scenario below would ...

#### Solution Summary

Step by step method for computing test statistic for One way ANOVA is given in the answer.

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