Statistical Analyses
Research Scenario
A psychologist was interested in evaluating the effectiveness of a domestic violence prevention program in changing attitudes towards domestic violence in a sample of high school students. The psychologist recruited male and female high school students between the ages of 16 and 17 years from nine high schools in the Greater Brisbane Region. The students received a sixweek domestic violence prevention program and the psychologist recorded their attitudes to domestic violence on Day 1 (baseline), Day 30, and Day 90. Based on the following data, determine whether the domestic violence prevention program had an influence on the attitudes towards domestic violence in high school students (higher scores indicate greater acceptance of domestic violence). If the ANOVA result is significant, conduct and report Bonferroni post hoc analyses to determine exactly which time points differed from one another.
Dependent: attitude
Independent: sex and age.
Day 1  Day 30  Day 90 
31  27  15 
34  16  8 
35  14  10 
45  10  4 
37  25  26 
49  18  20 
39  7  18 
32  26  8 
35  20  21 
42  10  26 
50  28  15 
47  34  26 
36  11  20 
18  8  25 
46  20  11 
43  12  11 
29  17  4 
44  11  20 
Which of the following statistical analyses should be performed for this scenario? Note that you may need to select more than one analysis depending upon the specifications of the scenario.
To indicate a selection choose ‘Yes’ otherwise choose ‘No’:
One way independent measures ANOVA: 


One way repeated measures ANOVA: 


Kruskal Wallis test: 


Friedman test: 


Bonferroniadjusted pairwise comparisons: 


Wilcoxon pairwise comparisons: 


Tukey’s HSD: 


Mann Whitney U: 

Now run the appropriate analysis or analyses using SPSS and enter all relevant values into the fields provided.
Important Notes:
 Be careful to select the correct statistical test.
 It is strongly recommended that you copy and paste the data into SPSS to avoid transcription errors.
 Paste from Moodle into Microsoft Excel first and then from Excel into SPSS or you could experience layout issues.
 There may be more value answer fields than are required.
 Report only those values that correspond to the statistical test you have chosen (i.e., the values you will need for your results write up).
 g., if the scenario requires a ttest and there is an answer field for an F ratio then you would leave that field blank.
 You must present values exactlyaccording to correct APA format.
 Refer to the module materials for instructions on how to do this.
 Ensure you do not include any extraneous characters (e.g., spaces) in your answers.
 In most cases you will enter just a numerical value, however when reporting very small p values you may need to include the < sign in your answer, where appropriate, to demonstrate correct APA formatting.
Statistic  Value  
Day 1  Mean (SD)  Answer (Answer ) 
Mean Rank  Answer  
Day 30  Mean (SD)  Answer (Answer ) 
Mean Rank  Answer  
Day 90  Mean (SD)  Answer (Answer ) 
Mean Rank  Answer  
Homogeneity of variance assumption  F  Answer 
F_{max}  Answer  
df OR
(df1, df2) 
Answer
(Answer , Answer ) 

p  Answer  
Primary analysis  F  Answer 
Χ2  Answer  
df OR
(df1, df2) 
Answer
(Answer , Answer ) 

N  Answer  
p  Answer  
η^{2} or η^{2}_{p}  Answer  
Day 1 vs Day 30 comparison  T  Answer 
U  Answer  
p  Answer  
d  Answer  
r  Answer  
Negative Ranks: n  Answer  
Negative Ranks: Sum of ranks 
Answer  
Positive Ranks: n  Answer  
Positive Ranks: Sum of ranks 
Answer  
Ties: n  Answer  
Day 1 vs Day 90 comparison  T  Answer 
U  Answer  
p  Answer  
d  Answer  
r  Answer  
Negative Ranks: n  Answer  
Negative Ranks: Sum of ranks 
Answer  
Positive Ranks: n  Answer  
Positive Ranks: Sum of ranks 
Answer  
Ties: n  Answer  
Day 30 vs Day 90 comparison  T  Answer 
U  Answer  
p  Answer  
d  Answer  
r  Answer  
Negative Ranks: n  Answer  
Negative Ranks: Sum of ranks 
Answer  
Positive Ranks: n  Answer  
Positive Ranks: Sum of ranks 
Answer  
Ties: n  Answer 
Question 2.
Indicate whether a onetailed or twotailed analysis would be most appropriate, providing a justification for your choice, and report the null and alternative hypotheses for the primary statistical analysis.
Should a onetailed or twotailed test be used? Provide a justification for your choice.
Enter your answer here
Enter the null hypothesis (H_{0}) for the primary statistical test in words not symbols:
Enter your answer here
Enter the alternative hypothesis (H_{A}) for the primary statistical test in words not symbols:
Enter your answer here
Question 3.
Report the results of the analyses in APA (6th edition) format, as they should be presented in a journal article, including all appropriate statistical notation.
Important notes:
 You can type your report directly into the response box.

 Select the ‘Toolbar Toggle’ icon in the top left corner of the editing toolbar to reveal more editing options (such as the Ωbutton for inserting symbols).

 Alternatively, you can type up your report in Microsoft Word and then paste it into the response box.

 Just be sure to check that all of your formatting (e.g., italics, symbols, etc.) is retained if you paste your answer in from somewhere else.

 If APA formatted tables or figures should be included within your report, insert these into the pdf document that you submit with your SPSS output to retain the formatting.
Question 4.
Enter your effect size calculations (i.e., workings) into the response box below if effect size is not provided in the SPSS output, and attach a single pdf file with the relevant SPSS output to support your results writeup.
Question 5.
Research Scenario
A social psychologist wanted to determine whether stereotype threat (the fear that one’s performance on a task will confirm a negative stereotype about one’s group) was associated with job satisfaction in a sample of mature age workers. Furthermore, the researcher wanted to determine if levels of job satisfaction could be predicted based on the level of stereotype threat. The social psychologist recruited a sample of mature age employees from the Melbourne metro region and asked them to complete selfreport questionnaires of stereotype threat (higher scores indicate higher levels of stereotype threat) and job satisfaction (higher scores indicate greater job satisfaction). These questionnaire scores involve summation across multiple Likert items, so you can assume at least an interval scale of measurement for this data. Determine: (1) whether there is a negative relationship between stereotype threat and job satisfaction; and (2) if stereotype threat significantly predicts job satisfaction.
Stereotype Threat 
Job Satisfaction 
55  25 
52  25 
54  27 
49  39 
53  32 
51  41 
50  34 
50  43 
50  42 
51  25 
47  45 
55  35 
47  50 
46  36 
52  15 
50  46 
59  18 
54  22 
50  44 
52  15 
60  40 
45  40 
58  36 
56  22 
51  37 
56  37 
54  40 
49  29 
53  43 
49  26 
50  37 
Which of the following statistical analyses should be performed for this scenario? Note that you may need to select more than one analysis depending upon the specifications of the scenario.
To indicate a selection choose ‘Yes’ otherwise choose ‘No’:
Paired samples ttest: 


Friedman test: 


Pearson correlation: 


Spearman correlation: 


Linear regression: 


Wilcoxon pairwise comparisons: 

Now run the appropriate analysis or analyses using SPSS and enter all relevant values into the fields provided.
Important Notes:
 Be careful to select the correct statistical test.
 It is strongly recommended that you copy and paste the data into SPSS to avoid transcription errors.
 Paste from Moodle into Microsoft Excel first and then from Excel into SPSS or you could experience layout issues.
 There may be more value answer fields than are required.
 Report only those values that correspond to the statistical test you have chosen (i.e., the values you will need for your results write up).
 g., if the scenario requires a ttest and there is an answer field for an F ratio then you would leave that field blank.
 You must present values exactlyaccording to correct APA format.
 Refer to the module materials for instructions on how to do this.
 Ensure you do not include any extraneous characters (e.g., spaces) in your answers.
 In most cases you will enter just a numerical value, however when reporting very small p values you may need to include the < sign in your answer, where appropriate, to demonstrate correct APA formatting.
Statistic  Value  
Stereotype threat  Mean (SD)  Answer (Answer ) 
Mean Rank  Answer  
Job satisfaction  Mean (SD)  Answer (Answer ) 
Mean Rank  Answer  
Primary analysis  Mean difference  Answer 
t  Answer  
Χ2  Answer  
r  Answer  
r_{s}  Answer  
df  Answer  
N  Answer  
p  Answer  
d  Answer  
η^{2}  Answer  
Secondary (prediction) analysis  F  Answer 
df OR (df1, df2) 
Answer (Answer , Answer ) 

p  Answer  
R^{2} (in %)  Answer %  
Adjusted R^{2}  Answer  
B  Answer  
SE B  Answer  
β  Answer  
p  Answer  
95% confidence intervals [low, high] 
[Answer , Answer ]  
Stereotype threat vs Job satisfaction comparison  T  Answer 
p  Answer  
r  Answer  
Negative Ranks: n  Answer  
Negative Ranks: Sum of ranks 
Answer  
Positive Ranks: n  Answer  
Positive Ranks: Sum of ranks 
Answer  
Ties: n  Answer 
Note: You may be prompted to answer all parts of this question. This does not apply to the value answer fields. Leave value answer fields blank if they are not required for the statistical test you have selected.
Question 6.Indicate whether a onetailed or twotailed analysis would be most appropriate, providing a justification for your choice, and report the null and alternative hypotheses for the primary statistical analysis.
Should a onetailed or twotailed test be used? Provide a justification for your choice.
Enter your answer here
Enter the null hypothesis (H_{0}) for the primary statistical test in words not symbols:
Enter your answer here
Enter the alternative hypothesis (H_{A}) for the primary statistical test in words not symbols:
Enter your answer here
Question 7.
Report the results of the analyses in APA (6th edition) format, as they should be presented in a journal article, including all appropriate statistical notation.
Question 8.
Enter your effect size calculations (i.e., workings) into the response box below if effect size is not provided in the SPSS output, and attach a single pdf file with the relevant SPSS output to support your results writeup.
Solution
Research Scenario
A psychologist was interested in evaluating the effectiveness of a domestic violence prevention program in changing attitudes towards domestic violence in a sample of high school students. The psychologist recruited male and female high school students between the ages of 16 and 17 years from nine high schools in the Greater Brisbane Region. The students received a sixweek domestic violence prevention program and the psychologist recorded their attitudes to domestic violence on Day 1 (baseline), Day 30, and Day 90. Based on the following data, determine whether the domestic violence prevention program had an influence on the attitudes towards domestic violence in high school students (higher scores indicate greater acceptance of domestic violence). If the ANOVA result is significant, conduct and report Bonferroni post hoc analyses to determine exactly which time points differed from one another.
Dependent: attitude
Independent: sex and age.
Day 1  Day 30  Day 90 
31  27  15 
34  16  8 
35  14  10 
45  10  4 
37  25  26 
49  18  20 
39  7  18 
32  26  8 
35  20  21 
42  10  26 
50  28  15 
47  34  26 
36  11  20 
18  8  25 
46  20  11 
43  12  11 
29  17  4 
44  11  20 
Which of the following statistical analyses should be performed for this scenario? Note that you may need to select more than one analysis depending upon the specifications of the scenario.
To indicate a selection choose ‘Yes’ otherwise choose ‘No’:
One way independent measures ANOVA: 


One way repeated measures ANOVA: 


Kruskal Wallis test: 


Friedman test: 


Bonferroniadjusted pairwise comparisons: 


Wilcoxon pairwise comparisons: 


Tukey’s HSD: 


Mann Whitney U: 

Now run the appropriate analysis or analyses using SPSS and enter all relevant values into the fields provided.
Important Notes:
 Be careful to select the correct statistical test.
 It is strongly recommended that you copy and paste the data into SPSS to avoid transcription errors.
 Paste from Moodle into Microsoft Excel first and then from Excel into SPSS or you could experience layout issues.
 There may be more value answer fields than are required.
 Report only those values that correspond to the statistical test you have chosen (i.e., the values you will need for your results write up).
 g., if the scenario requires a ttest and there is an answer field for an F ratio then you would leave that field blank.
 You must present values exactlyaccording to correct APA format.
 Refer to the module materials for instructions on how to do this.
 Ensure you do not include any extraneous characters (e.g., spaces) in your answers.
 In most cases you will enter just a numerical value, however when reporting very small p values you may need to include the < sign in your answer, where appropriate, to demonstrate correct APA formatting.
Statistic  Value  
Day 1  Mean (SD)  Answer (Answer ) 
Mean Rank  Answer  
Day 30  Mean (SD)  Answer (Answer ) 
Mean Rank  Answer  
Day 90  Mean (SD)  Answer (Answer ) 
Mean Rank  Answer  
Homogeneity of variance assumption  F  Answer 
F_{max}  Answer  
df OR
(df1, df2) 
Answer
(Answer , Answer ) 

p  Answer  
Primary analysis  F  Answer 
Χ2  Answer  
df OR
(df1, df2) 
Answer
(Answer , Answer ) 

N  Answer  
p  Answer  
η^{2} or η^{2}_{p}  Answer  
Day 1 vs Day 30 comparison  T  Answer 
U  Answer  
p  Answer  
d  Answer  
r  Answer  
Negative Ranks: n  Answer  
Negative Ranks: Sum of ranks 
Answer  
Positive Ranks: n  Answer  
Positive Ranks: Sum of ranks 
Answer  
Ties: n  Answer  
Day 1 vs Day 90 comparison  T  Answer 
U  Answer  
p  Answer  
d  Answer  
r  Answer  
Negative Ranks: n  Answer  
Negative Ranks: Sum of ranks 
Answer  
Positive Ranks: n  Answer  
Positive Ranks: Sum of ranks 
Answer  
Ties: n  Answer  
Day 30 vs Day 90 comparison  T  Answer 
U  Answer  
p  Answer  
d  Answer  
r  Answer  
Negative Ranks: n  Answer  
Negative Ranks: Sum of ranks 
Answer  
Positive Ranks: n  Answer  
Positive Ranks: Sum of ranks 
Answer  
Ties: n  Answer 
Note: You may be prompted to answer all parts of this question. This does not apply to the value answer fields. Leave value answer fields blank if they are not required for the statistical test you have selected.
Question 2.
Indicate whether a onetailed or twotailed analysis would be most appropriate, providing a justification for your choice, and report the null and alternative hypotheses for the primary statistical analysis.
Should a onetailed or twotailed test be used? Provide a justification for your choice.
We are to test whether the domestic violence prevention program had an influence on the attitudes towards domestic violence in high school students. Also, we need to determine exactly which time points differed from one another. This clearly indicates that twotailed test should be used to examine which time points differed from one another. In particular, the Mauchly’s test was used to test the hypothesis that the variances of the differences between conditions are equal, which is a twotailed test.
Enter the null hypothesis (H_{0}) for the primary statistical test in words not symbols:
H_{0}: The domestic violence prevention program had no significant influence on the attitudes towards domestic violence in high school students (i.e., the variances of the differences between conditions are equal)
Enter the alternative hypothesis (H_{A}) for the primary statistical test in words not symbols:
H_{A}: The domestic violence prevention program had significant influence on the attitudes towards domestic violence in high school students (i.e., the variances of the differences between conditions are not equal)
Question 3.
Report the results of the analyses in APA (6th edition) format, as they should be presented in a journal article, including all appropriate statistical notation.
Result:
In repeated measures anova, it is important to consider the result of Sphericity since the effect of violating Sphericity assumption is a loss of power, leads to an increased probability of a Type II error. In this case, the Mauchly’s Test of Sphericity was found to be insignificant (W = .992, p = .937), indicating that the variances of differences are not significantly different. This suggests that the assumption of Sphericity has been met.
From the ANOVA table of Tests of WithinSubjects Effects, it can be clearly seen that there is significant difference in the score of attitudes towards domestic violence in high school students due to the domestic violence prevention program.
Since the result of ANOVA is significant, the posthoc test has been conducted and the corresponding result showed that there is significant improvement in the score from Day1 to Day30 (p < .05) and from Day1 to Day90 (p < .05), while the difference is not statistically significant from Day30 to Day90 (p = 1).
On the whole, we conclude that the score of attitudes towards domestic violence in high school students has significantly increased from Day1 through Day90 due to the domestic violence prevention program.
Question 4.
Enter your effect size calculations (i.e., workings) into the response box below if effect size is not provided in the SPSS output, and attach a single pdf file with the relevant SPSS output to support your results writeup.
Effect Size: From the result of Multivariate Tests, the value of Partial Eta Squared is .858, which is more than 0.50, indicating that the effect is large.
Note: Include ONLY the essential output (i.e., output that displays the test results and assumption checks referred to in your results writeup). Marks will be deducted for including nonessential information.
Question 5.
Research Scenario
A social psychologist wanted to determine whether stereotype threat (the fear that one’s performance on a task will confirm a negative stereotype about one’s group) was associated with job satisfaction in a sample of mature age workers. Furthermore, the researcher wanted to determine if levels of job satisfaction could be predicted based on the level of stereotype threat. The social psychologist recruited a sample of mature age employees from the Melbourne metro region and asked them to complete selfreport questionnaires of stereotype threat (higher scores indicate higher levels of stereotype threat) and job satisfaction (higher scores indicate greater job satisfaction). These questionnaire scores involve summation across multiple Likert items, so you can assume at least an interval scale of measurement for this data. Determine: (1) whether there is a negative relationship between stereotype threat and job satisfaction; and (2) if stereotype threat significantly predicts job satisfaction.
Stereotype Threat 
Job Satisfaction 
55  25 
52  25 
54  27 
49  39 
53  32 
51  41 
50  34 
50  43 
50  42 
51  25 
47  45 
55  35 
47  50 
46  36 
52  15 
50  46 
59  18 
54  22 
50  44 
52  15 
60  40 
45  40 
58  36 
56  22 
51  37 
56  37 
54  40 
49  29 
53  43 
49  26 
50  37 
Which of the following statistical analyses should be performed for this scenario? Note that you may need to select more than one analysis depending upon the specifications of the scenario.
To indicate a selection choose ‘Yes’ otherwise choose ‘No’:
Paired samples ttest: 


Friedman test: 


Pearson correlation: 


Spearman correlation: 


Linear regression: 


Wilcoxon pairwise comparisons: 

Now run the appropriate analysis or analyses using SPSS and enter all relevant values into the fields provided.
Important Notes:
 Be careful to select the correct statistical test.
 It is strongly recommended that you copy and paste the data into SPSS to avoid transcription errors.
 Paste from Moodle into Microsoft Excel first and then from Excel into SPSS or you could experience layout issues.
 There may be more value answer fields than are required.
 Report only those values that correspond to the statistical test you have chosen (i.e., the values you will need for your results write up).
 g., if the scenario requires a ttest and there is an answer field for an F ratio then you would leave that field blank.
 You must present values exactlyaccording to correct APA format.
 Refer to the module materials for instructions on how to do this.
 Ensure you do not include any extraneous characters (e.g., spaces) in your answers.
 In most cases you will enter just a numerical value, however when reporting very small p values you may need to include the < sign in your answer, where appropriate, to demonstrate correct APA formatting.
Statistic  Value  
Stereotype threat  Mean (SD)  Answer51.87 (Answer 3.658 ) 
Mean Rank  Answer  
Job satisfaction  Mean (SD)  Answer (Answer ) 
Mean Rank  Answer  
Primary analysis  Mean difference  Answer 
t  Answer  
Χ2  Answer  
r  Answer  
r_{s}  Answer  
df  Answer  
N  Answer  
p  Answer 0.0215  
d  Answer  
η^{2}  Answer  
Secondary (prediction) analysis  F  Answer 
df OR (df1, df2) 
Answer (Answer , Answer ) 

p  Answer  
R^{2} (in %)  Answer %  
Adjusted R^{2}  Answer %  
B  Answer  
SE B  Answer  
β  Answer  
p  Answer  
95% confidence intervals [low, high] 
[Answer ,
Answer ] 

Stereotype threat vs Job satisfaction comparison  T  Answer 
p  Answer 0.0215  
r  Answer  
Negative Ranks:  Answer  
Negative Ranks: Sum of ranks 
Answer  
Positive Ranks: n  Answer  
Positive Ranks: Sum of ranks 
Answer  
Ties: n  Answer 
Question 6.
Indicate whether a onetailed or twotailed analysis would be most appropriate, providing a justification for your choice, and report the null and alternative hypotheses for the primary statistical analysis.
Should a onetailed or twotailed test be used? Provide a justification for your choice.
Since we need to test whether there is a negative relationship between stereotype threat and job satisfaction, it is appropriate to use onetailed test. In this case, the alternate hypothesis to test would be H_{1}: ρ< 0 (onetailed or lefttailed test), which indicates that onetailed test should be used to test whether there is a negative relationship between stereotype threat and job satisfaction.
Enter the null hypothesis (H_{0}) for the primary statistical test in words not symbols:
H_{0}: There is no significant relationship between Stereotype Threat and Job Satisfaction
Enter the alternative hypothesis (H_{A}) for the primary statistical test in words not symbols:
H_{A}: There is significant negative relationship between Stereotype Threat and Job Satisfaction
Question 7.
Report the results of the analyses in APA (6th edition) format, as they should be presented in a journal article, including all appropriate statistical notation.
Results:
The correlation between stereotype threat and job satisfaction is .366, which indicates that there is a weak negative relationship between stereotype threat and job satisfaction. This correlation was found to be statistically significant at 5% level (p < .05). The regression coefficient was found to be .95, which indicates that job satisfaction will decrease by .95 for one unit increase in stereotype threat. In addition, the regression result showed that stereotype threat is significantly predicts job satisfaction, F(1, 29)=4.49, p<.05. The residual plots showed that the assumptions of normality and homogeneity of variances are satisfied for this regression model.
Question 8.
Enter your effect size calculations (i.e., workings) into the response box below if effect size is not provided in the SPSS output, and attach a single pdf file with the relevant SPSS output to support your results writeup.
The related effect size is Rsquare, the coefficient of determination calculated as the square of the correlation coefficient, r. In this case, the value of Rsquare is .134, indicating that there is 13.4% of the variation in the dependent variable ‘Job Satisfaction’ is explained by the independent variable ‘Stereotype threat’. Since this value is below 30%, the effect size is said to be medium or below medium.
Cohen’s fsquare is another effect size measure used in the context of regression. The value of Cohen’s fsquare = R2/(1R2) = 0.134/(10.134) = 0.1547. This value is less than 0.30, indicating that the effect of the test is medium or below.