Assignment 2: Tests of Significance

Throughout this assignment you will review mock studies. You will needs to follow the directions outlined in the section using SPSS and decide whether there is significance between the variables. You will need to list the five steps of hypothesis testing (as covered in the lesson for Week 6) to see how every question should be formatted. You will complete all of the problems. Be sure to cut and past the appropriate test result boxes from SPSS under each problem and explain what you will do with your research hypotheses. All calculations should be coming from your SPSS. You will need to submit the SPSS output file to get credit for this assignment. This file will save as a .spv file and will need to be in a single file. In other words, you are not allowed to submit more than one output file for this assignment.

The five steps of hypothesis testing when using SPSS are as follows:

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State your research hypothesis (H1) and null hypothesis (H0).

Identify your significance level (.05 or .01)

Conduct your analysis using SPSS.

Look for the valid score for comparison. This score is usually under ‘Sig 2-tail’ or ‘Sig. 2’. We will call this “p”.

Compare the two and apply the following rule:

If “p” is < or = significance level, than you reject the null.

Be sure to explain to the reader what this means in regards to your study. (Ex: will you recommend counseling services?)

* Be sure that your answers are clearly distinguishable. Perhaps you bold your font or use a different color.

t Tests

t Test for a Single Sample (20 points)

Open SPSS

Enter the number of activities of daily living performed by the depressed clients studied in #1 in the Data View window.

In the Variable View window, change the variable name to “ADL” and set the decimals to zero.

Click Analyze à Compare Means à One-Sample T test à the arrow to move “ADL” to the Variable(s) window.

Enter the population mean (17) in the “Test Value” box.

Click OK.

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 have 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) obtained after therapy is significantly different from a mean number of activities of 17 that is typical for depressed people. (Clearly indicate each step).

Test the difference at the .05 level of significance and at the .01 level (in SPSS this means you change the “confidence level” from 95% to 99%).

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.

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

t Test for Dependent Means (20 points)

Open SPSS

Enter the number of activities of daily living performed by the depressed clients studied in Problem 2 in the Data View window. Be sure to enter the “before therapy” scores in the first column and the “after therapy” scores in the second column.

In the Variable View window, change the variable name for the first variable to “ADLPRE” and the variable name for the second variable to “ADLPOST”. Set the decimals for both variables to zero.

Click Analyze à Compare Means àPaired-Samples T Test àthe arrow to move “ADLPRE” to the Paired Variable(s) window à “ADLPOST” and then click the arrow to move the variable to the Paired Variable(s) window.

Click OK.

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 have 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 numbers of activities of daily living (shown below) obtained before and after therapy are statistically significant at the .05 level of. (Clearly indicate 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 at the .05 level of significance and calculate the measure of association.

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

The t Test for Independent Samples (20 points)

Once you have entered the data, click on Analyze, then on Compare Means, and then click on Independent-Samples T Test…

A dialog box will appear, with your variables (student, condition, score) on the left. Your options are (a) move one or more variables into the “Test Variable(s)” box to select your dependent variables(s) and (b) move one of your variables into the “Grouping Variable” box to select the independent variables (or identify the groups to be compared).

Make “?” the dependent variable by moving it to the “Test Variable(s)” box. Then make “?” your independent variable by moving it to the “Grouping Variable” box. Now, the “Define Groups” button is functioning, click on Define Groups and another dialog box appears. Here you must specify the two values of the condition variable that represent the two groups you are comparing. Click in the box next to Group 1 and type the number 1, then click in the box next to Group 2 and type the number 2. Now you can click Continue to return to the “Independent-Samples T Test” dialog box, and click onOK to run the analysis.

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 the satisfaction of employees who chose not to participate.

The scores on a job satisfaction inventory for both groups are listed 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 are statistically higher than the scores of employees who did not participate in counseling at the .01 level of significance.

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 and calculate the measure of association. NOTE: Do not forget to give a numeric value for those who participated in counseling (e.g. 0) and those who did not participate in counseling (e.g. 1).

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

ANOVA (20 points)

Open SPSS

Analyze the data for #1. Remember that SPSS assumes that all the scores in a row are from the same participant. In this study, there are 15 participants divided into three groups of five. Therefore, each of the 15 participants will be described by two variables, type of therapy and the number of activities of daily living performed.

If “1” represents the group receiving individual therapy for 1 hour every 2 weeks, “2” represents the group receiving 1 hour of individual therapy each week, and “3” indicates the group receiving 2 hours of individual therapy each week, the first participant will be described by entering “1” in the top cell of the first column in the Data View window and “16” in the top cell of the second column to indicate that the participant underwent 1 hour of therapy every 2 weeks and performed 16 activities of daily living. The second participant will be described by “1” and “15”, and the third by “1” and “18”.

When the two variables have been entered for the five participants in this group, repeat the process for participants who underwent 1 hour of individual therapy each week, using “2” to describe their therapy group. When the two variables for the five participants in this group have been entered, repeat the process for Group 3, entering “3” in the first column. In the Variable View window, change the first variable name to “THERAPY” and the second to “ADL” and set the decimals for both to zero.

Click Analyze à Compare Means à One-Way ANOVA àSince “THERAPY” is already selected, you can click the arrow to move the variable to the Factor window. Select “ADL” and click the arrow to move the variable to the Dependent List window, which instruct SPSS to conduct the analysis of variance on the number of activities performed.

Click “Options” and click the box labeled “Descriptive” to obtain descriptive statistics.

Click Continue.

Click OK.

4. Keep in mind that the clients in Group 1 will receive 1 hour of therapy every 2 weeks, the clients in Group 2 will receive 1 hour of therapy every week, and the clients in Group 3 will receive 2 hours of therapy every week.

Use the five steps of hypothesis testing to determine whether the observed differences in the number of activities in the following table performed by the three groups are statistically significant at the .05 level of significance. Clearly indicate each of the five steps.

CLIENT

GROUP 1

GROUP 2

GROUP 3

1

16

21

24

2

15

20

21

3

18

17

25

4

21

23

20

5

19

19

22

5. Describe the circumstances under which you should use ANOVA instead of t tests, and explain why t tests are inappropriate in these circumstances.

Chi-Square (20 points)

Chi-Square

SPSS instructions:

Chi-Square Test for Goodness of Fit:

Open SPSS

Remember that SPSS assumes that all the scores in a row are from the same participant. In the study presented in #1, there are 20 students, some of whom have been suspended for misbehavior. The primary conflict-resolution style used by each student is also entered. [Ignore the first variable in this analysis.]

When you have entered the data for all 20 students, move to the Variable View window and change the first variable name to “SUSPEND” and the second to “STYLE”. Set the number of decimals for both variables to zero.

Click Analyze à Non-Parametric Tests à Chi-Square

Click the variable “STYLE” and then the arrow next to the box labeled “Test Variable List” to indicate that the chi-square for goodness of fit should be conducted 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.

Click OK.

Chi-Square Test for Independence:

Open SPSS

For #2, you need to add the variable “SUSPEND” to the analysis. Remember that in this problem, we are interested in whether there was an association between conflict-resolution style and having been suspended from school for misbehavior. Since the analysis will involve two nominal variables, the appropriate test is a chi-square test for independence.

Click Analyze à Descriptive Statistics à Crosstabs

Since “SUSPEND” is already selected, click the arrow next to the box labeled “Rows.”

Click the variable “STYLE” and click the arrow next to the box labeled “Columns.”

Click “Statistics” and click the box labeled “Chi-Square.”

Click Continue.

Click “Cells” and click the box labeled “Expected.”

Click Continue.

Click OK.

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

a. Following the five steps of hypothesis testing, conduct the appropriate chi-square test to determine whether the observed frequencies are significantly different from the frequencies expected by change at the .05 level of significance. Clearly identify each of the five steps.

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

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

a. Following the five steps of hypothesis testing, conduct the appropriate chi-square test to determine whether the observed frequencies are significantly different from the frequencies expected by change at the .05 level of significance. Clearly identify each of the five steps.

b. Calculate the measure of association.

8. Believing that assertiveness is the most effective method of conflict resolution, the researchers categorized students so that the aggressive, manipulative, and passive categories were combined. These data are presented in the table below.

Conflict Resolution

Suspension from School

Assertive

Other

Total

Yes

1

9

10

No

6

4

10

Total

7

13

20

a. Following the five steps of hypothesis testing, conduct the appropriate chi-square test to determine whether the observed frequencies are significantly different from the frequencies expected by change at the .05 level of significance. Clearly identify each of the five steps.

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