Statistical Analyses

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 six-week 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:
 Yes  No
One way repeated measures ANOVA:
 Yes
Kruskal Wallis test:
 Yes  No
Friedman test:
 Yes  No
Bonferroni-adjusted pairwise comparisons:
 Yes  No
Wilcoxon pairwise comparisons:
 Yes  No
Tukey’s HSD:
 Yes  No
Mann Whitney U:
 Yes  No

Now run the appropriate analysis or analyses using SPSS and enter all relevant values into the fields provided.

Important Notes:

  1. Be careful to select the correct statistical test.
  2. 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.
  3. 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 t-test and there is an answer field for an F ratio then you would leave that field blank.
  4. 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.
  5. 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
Fmax 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
η2 or η2p 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 one-tailed or two-tailed 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 one-tailed or two-tailed test be used? Provide a justification for your choice.

Enter your answer here

Enter the null hypothesis (H0) for the primary statistical test in words not symbols

Enter your answer here

Enter the alternative hypothesis (HA) 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:

  1. 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).
  1. 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.
  1. 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 write-up.

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 self-report 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 t-test:
 Yes  No
Friedman test:
 Yes  No
Pearson correlation:
 Yes  No
Spearman correlation:
 Yes  No
Linear regression:
 Yes  No
Wilcoxon pairwise comparisons:
 Yes  No

Now run the appropriate analysis or analyses using SPSS and enter all relevant values into the fields provided.

Important Notes:

  1. Be careful to select the correct statistical test.
  2. 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.
  3. 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 t-test and there is an answer field for an F ratio then you would leave that field blank.
  4. 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.
  5. 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
rs Answer
df Answer
N Answer
p Answer
d Answer
η2 Answer
Secondary (prediction) analysis F Answer
df OR
(df1, df2)
Answer
(Answer , Answer )
p Answer
R2 (in %) Answer %
Adjusted R2 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 one-tailed or two-tailed 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 one-tailed or two-tailed test be used? Provide a justification for your choice.

Enter your answer here

Enter the null hypothesis (H0) for the primary statistical test in words not symbols

Enter your answer here

Enter the alternative hypothesis (HA) 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 write-up. 

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 six-week 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:
 Yes  No
One way repeated measures ANOVA:
Yes
Kruskal Wallis test:
 Yes No
Friedman test:
 Yes No
Bonferroni-adjusted pairwise comparisons:
 Yes  No
Wilcoxon pairwise comparisons:
 Yes  No
Tukey’s HSD:
 Yes No
Mann Whitney U:
 Yes No

Now run the appropriate analysis or analyses using SPSS and enter all relevant values into the fields provided.

Important Notes:

  1. Be careful to select the correct statistical test.
  2. 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.
  3. 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 t-test and there is an answer field for an F ratio then you would leave that field blank.
  4. 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.
  5. 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
Fmax 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
η2 or η2p 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 one-tailed or two-tailed 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 one-tailed or two-tailed 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 two-tailed 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 two-tailed test.

Enter the null hypothesis (H0) for the primary statistical test in words not symbols

H0: 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 (HA) for the primary statistical test in words not symbols:

HA: 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 Within-Subjects 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 post-hoc 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 write-up.

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 write-up). Marks will be deducted for including non-essential 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 self-report 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 t-test:
 Yes No
Friedman test:
 Yes No
Pearson correlation:
Yes  No
Spearman correlation:
 Yes No
Linear regression:
Yes  No
Wilcoxon pairwise comparisons:
 Yes No

Now run the appropriate analysis or analyses using SPSS and enter all relevant values into the fields provided.

Important Notes:

  1. Be careful to select the correct statistical test.
  2. 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.
  3. 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 t-test and there is an answer field for an F ratio then you would leave that field blank.
  4. 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.
  5. 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
rs Answer
df Answer
N Answer
p Answer  0.0215
d Answer
η2 Answer
Secondary (prediction) analysis F Answer
df OR
(df1, df2)
Answer
(Answer , Answer )
p Answer
R2 (in %) Answer   %
Adjusted R2 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 one-tailed or two-tailed 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 one-tailed or two-tailed 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 one-tailed test. In this case, the alternate hypothesis to test would be H1: ρ< 0 (one-tailed or left-tailed test), which indicates that one-tailed test should be used to test whether there is a negative relationship between stereotype threat and job satisfaction.

Enter the null hypothesis (H0) for the primary statistical test in words not symbols

H0: There is no significant relationship between Stereotype Threat and Job Satisfaction

Enter the alternative hypothesis (HA) for the primary statistical test in words not symbols:

HA: 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 write-up.

The related effect size is R-square, the coefficient of determination calculated as the square of the correlation coefficient, r. In this case, the value of R-square 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 f-square is another effect size measure used in the context of regression. The value of Cohen’s f-square = R2/(1-R2) = 0.134/(1-0.134) = 0.1547. This value is less than 0.30, indicating that the effect of the test is medium or below.