Tests of Significance

1. Researches are interested in whether depressed people undergoing group therapy will perform a different number of activities of daily living after group therapy. The researchers randomly selected 12 depressed clients to undergo a 6-week group therapy program.

Use the five steps of hypothesis testing to determine whether the average number of activities of daily living (shown below in the table) obtained after therapy is significantly different from a mean number of activities of 17 that is typical for depressed people. (Clearly list each step).

Test the difference at both the .05 and .01 levels of significance.

As part of Step 5, indicate whether the behavioral scientists should recommend group therapy for all depressed people based on evaluation of the null hypothesis at both levels of significance (.05 and .01).

Data to be entered in SPSS (instructions below)

CLIENT AFTER THERAPY
A 18
B 14
C 11
D 25
E 24
F 17
G 14
H 10
I 23
J 11
K 22
L 19

Step 1: Data managing

1. Open a blank SPSS data file: File New Data
2. In the blank SPSS data file, create your SPSS data set by entering the number of activities of daily living performed by the depressed clients (see above) in the Data View window.
3. In the Variable View window, change the variable name to “ADL.” Set the decimals to zero.

Step 2: SPSS execution

a. Click: Analyze  Compare Means  One-Sample T test  use the arrow to move “ADL” to the Variable(s) window on the right.
b. Enter the population mean (17) in “Test Value”
c. Click OK.

Mock Study 2: t- Test for Dependent Means (20 points)

2. Researchers are interested in whether depressed people undergoing group therapy will perform a different number of activities of daily living before and after group therapy. The researchers randomly selected 8 depressed clients in a 6-week group therapy program.

Use the five steps of hypothesis testing to determine whether the observed differences in the numbers of activities of daily living obtained before and after therapy are statistically significant at .05 level of significance. (Clearly list each step).

As part of Step 5, indicate whether the researchers should recommend group therapy for all depressed people based on evaluation of the null hypothesis.

Data to be entered in SPSS (instructions below)

CLIENT BEFORE THERAPY AFTER THERAPY
A 11 17
B 7 12
C 10 12
D 13 21
E 9 16
F 8 17
G 13 17
H 12 8

3. Six months after an industrial accident, a researcher has been asked to compare the job satisfaction of employees who participated in counseling sessions with those who chose not to participate. The job satisfaction scores for both groups are reported in the table below.

Use the five steps of hypothesis testing to determine whether the job satisfaction scores of the group that participated in counseling session are statistically different from the scores of employees who chose not to participate in counseling sessions at .01 level of significance. (Clearly list each step).

As part of Step 5, indicate whether the researcher should recommend counseling as a method to improve job satisfaction following industrial accidents based on evaluation of the null hypothesis.

Data to be entered in SPSS (instructions below)

PARTICIPATED IN COUNSELING DID NOT PARTICIPATE IN COUNSELING
36 38
39 36
41 36
36 32
37 30
35 39
37 41
39 35
42 33

Step 1: Data managing

1. Open a blank SPSS data file: File New Data
2. In the blank SPSS data file, create your SPSS data set by entering the number of activities of daily living performed by those who participated/did not participated in the counseling sessions (reported on previous page). Please create two columns. Column one is the test variable, where you enter ALL the 18 scores in the table. Column 2 is the grouping variable, where you use “1” to indicate if a score is from someone who participated in the counseling sessions; and “0” to indicate if a score is from someone who chose not to participate in the counseling sessions. The data set will look like this in SPSS Data View window:

36 1
49 1
……….
39 0
36 0
……….

3. After data entry, go to Variable View window, change the name of the first variable (test variable) to “ADL” and the second variable (grouping variable) as “group.” Set decimals for both variables to zero.

4. 15 clients are placed in three different groups. Clients in Group 1 receives 1 hour of therapy every 2 weeks; clients in Group 2 receives 1 hour of therapy every week; and clients in Group 3 receives 2 hours of therapy every week. Their number of daily activities are recorded in the table on the next page.

Use the five steps of hypothesis testing to determine whether the observed differences in the number of activities across three groups are statistically significant at .05 level of significance. (Clearly list each step).
As part of Step 5, indicate whether the researcher should recommend counseling based on evaluation of the null hypothesis.

Data to be entered in SPSS (instructions below)

GROUP 1 GROUP 2 GROUP 3
16 21 24
15 20 21
18 17 25
21 23 20
19 19 22

Step 1: Data managing

1. Open a blank SPSS data file: File New Data
2. In the blank SPSS data file, create your SPSS data set by entering the number of activities performed by the 15 clients. Please create two columns. Column one is the test variable where you enter ALL 15 scores in above table. Column 2 is the grouping variable, where you use “1” for “GROUP 1,” “2” for “GROUP 2,” and “3” for “GROUP 3.” The data set will look like this in SPSS Data View window:

16 1
15 1
……….
21 2
36 2
……….
24 3
21 3
……….

3. After data entry, go to Variable View window, change the name of the first variable (test variable) to “ADL” and the second variable (grouping variable) to “THERAPY.” Set decimals for both variables to zero.

6. The following table includes the primary method of conflict resolution used by 20 students.

Method Aggressive Manipulative Passive Assertive
N of Students 8 2 2 8

Following the five steps of hypothesis testing, conduct “goodness of fit” chi-square test to determine whether the observed frequencies in the four cells are significantly different from the expected frequencies at the .05 level of significance. (Clearly list each step).

As part of Step 5, indicate whether the observed frequency is significantly different from the expected frequency when equal number of students in each conflict resolution style (20/4=5) is assumed; and what does this mean in regard to this mock study.

Step 1: Data managing

1. Open a blank SPSS data file: File New Data
2. In the blank SPSS data file, please create just ONE column. This column stands for frequencies of different types of conflict resolutions. We’ll use “1” for “Aggressive,” “2” for “Manipulative,” 3 for “Passive,” and 4 for “Assertive.” The data set will look like this in SPSS Data View window:

1
1 (enter “1” for 8 times, since there are 8 observations)

2
2
3
3
4
4

3. After data entry, go to Variable View window, change the name of this variable to “STYLE.” Set decimal to zero.

Step 2: SPSS execution

a. Click: Analyze  Non-Parametric Tests  Legacy Dialogs  Chi-Square  use the arrow to move STYLE to “Test Variable list.”
• This procedure instruct SPSS that the chi-square for goodness of fit should be performed on the conflict-resolution style variable. Note that “All categories equal” is the default selection in the “Expected Values” box, which means that SPSS will conduct the goodness of fit test using equal expected frequencies for each of the four styles, in other words, SPSS will assume that the proportions of students each style are equal.
b. Click OK.

Mock study 5-2: Chi-Square Test for Independence

7. Next, researchers categorized the same group students in the previous study based on the primary method of conflict resolution used and whether that student had been suspended from school for misbehavior. These data are presented below.

Conflict Resolution Method
Suspended Aggressive Manipulative Passive Assertive Total
Yes 7 1 1 1 10
No 1 1 1 7 10
Total 8 2 2 8 20

Following the five steps of hypothesis testing, conduct chi-square test for independence at the .05 level of significance. . (Clearly list each step).

As part of Step 5, indicate whether the observed frequency is significantly different from the expected frequency; and what that means in regard to this mock study.

Step 1: Data managing
1. Continue to work on the data set created in Mock Study 5-1: goodness of fit Chi-square test
2. Add a second column to the data set. This column stands for whether or not a student was suspended from school due to misbehavior. We’ll use “1” for “Yes” and “2” for “No.” The data set will look like this in SPSS data view:

1 1
1 1

2 1
2 2
3 1
3 2
4 1
4 2

3. After data entry, go to Variable View window, change the name of this new variable to “SUSPEND.” Set decimal to zero.

8. Use SPSS to calculate the measure of association for variable “STYLE” and “SUSPEND.” Insert your SPSS output here. Use the concept of“Proportional Reduction of Error” to interpret your output.

 

 

 

Sample Solution

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