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?

The between subjects one-way randomized ANOVA should be used to analyze the data. Although the total number of participants is not indicated it would not make sense to have each participant in the three different therapies either concurrently or consecutively. The data are on an interval/ratio scale. The following assumptions are met: ● The underlying distribution is normally distributed.

● The variances among the populations being compared are

homogeneous.

● The observations are all independent of one another.

b. Identify H0 and Ha for this study.

H0 there is no significant difference between the mean values of the treatment therapies Ha there is a significant difference between the mean values of the treatment therapies H0: There will be no difference in the statistics competency scores among the four groups of counseling students. OR µ1= µ2 =µ3

Ha: There will be a difference in the statistics competency scores among the four groups of counseling students. OR at least one µ ≠another µ

c. Conduct the appropriate analysis.

In order for Anova (F-test) used for the analysis to be done the following steps will need to take place: 1 - Arrange the collected data in their respective cells

2 - Determine the mean for each cell

3 - Sum the means together and then divide by the number of cells to obtain the Grand mean 4 - For each value calculate the squared deviation from the grand mean and sum them together to determine the SSTotal 5 - Using the mean for each group, calculate the squared value for each scores deviation from the mean of its group/cell 6 – Sum these values for each group/cell to determine SSWithin 7 - For each group subtract the grand mean from the group mean, square this value and multiply by the number of participants in the group to determine the between group score for each group. Add these values together to obtain the between group sum of squares SSBetween . As a check add SSWithin and SSBetween which should equal SSTotal 8 - Next the mean square scores need to be calculated for each group, SSWithin, SSBetween ,and SSTotal by their respective degrees of freedom. The calculations are: dfTotal = total number of scores (N) – 1, dfWithin = N - number of groups (k, and dfBetween = number of groups (k) – 1. As a check sum, dfWithin plus dfBetween = dfTotal 9 - Now perform the calculations for the mean squares MSBetween = SSBetween / dfBetween 10 - Next perform the calculation for mean squares MSWithin = SSWithin / dfWithin 11 - The F –ratio must be calculated F = MSBetween / MSWithin 12 - To determine Fcritical consult the Table A.8 in the text using the degrees of freedom within on the left side of the table and the degrees of freedom between across the top of the table and use the value where these intersect. If there number of degrees of freedom with is not found in the table round down to the nearest value. 13 - If FObtain is greater than Fcritical the results are statistically significant and the null hypothesis should be rejected 14 - Effect size will need to be...