THE UNIVERSITY OF SUSSEX. BSc Second Year Examination DISCOVERING STATISTICS SAMPLE PAPER INSTRUCTIONS

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1 C8552 THE UNIVERSITY OF SUSSEX BSc Second Year Examination DISCOVERING STATISTICS SAMPLE PAPER INSTRUCTIONS Do not, under any circumstances, remove the question paper, used or unused, from the examination room; they will be collected before you may leave. Time allowed: 2 Hours Answer ALL questions in the answer book provided /Turn over

2 1. A record company executive was interested in the effects of subliminal messages on records having had many of his artists sued for allegedly having evil messages on their records (e.g. Ozzy Osbourne) that incited daft people to do stupid things like kill themselves. So, he took a record by Westlife and inserted different types of subliminal message onto different versions: (1) a control record didn t have any message (no message); (2) a second record had a friendly message that said Be happy and at one with your being (Friendly); (3) the third had the satanic message surrender your soul to beelzibub (Satan); (4) the fourth had another satanic message that instructed them to do a violent act Surrender your soul to the dark lord and sacrifice some goats while you re at it (Goats); and (5) a final record had the same satanic message about goats but it was played backwards (Backwards). He played the different types of record to different groups of teenagers. The outcome that the executive measured was the number of goats that each listener sacrificed. The SPSS Output is reproduced after the question. (a) What does Cohen s d represent? Compute and interpret Cohen s d for the difference in the number of goat s sacrificed in the Satan group and the No Message group [5 marks] (b) There are some numbers missing from the ANOVA summary table. Calculate these three values (residual sum of squares and mean squares and the F-ratio). [3 marks]. (c) Is the assumption of homogeneity of variance met? [3 marks] (d) What conclusions could we make about the effects of subliminal messages on records? [2 marks] (e) The executive made 3 predictions: (1) having no message, or a friendly message, would have less effect than having some kind of satanic message; (2) the backward satanic message would have more impact than the two non-backward messages; (3) the satanic message that specifically told people to kill goats would have more effect than the satanic message that did not. Suggest some planned contrasts (with the appropriate group codings) that could be done to test these hypotheses. [4 marks] (f) What do you understand by the term mean squares (i.e. conceptually speaking what does the mean squares in an ANOVA table represent)? [3 marks] 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound No Message Friendly Satan Goats Backward Total /Turn over

3 Number of Goats Sacrificed Levene Statistic df1 df2 Sig Number of Goats Sacrificed ANOVA Sum of Squares df Mean Square F Sig. Between Groups Within Groups 31 Total Robust Tests of Equality of Means Number of Goats Sacrificed Statistic a df1 df2 Sig. Welch Brown-Forsythe a. Asymptotically F distributed. 2. An experiment was done to look at the positive arousing effects of imagery on different people. A sample of statistics lecturers was compared against a group of students. Both groups received presentations of positive images (e.g. cats and bunnies), neutral images (e.g. duvets and lightbulbs), and negative images (e.g. corpses and vivisection photographs). Positive arousal was measured physiologically (high values indicate positive arousal) both before and after each batch of images. The order in which participants saw the batches of positive, neutral and negative images was randomised to avoid order effects. It was hypothesised that positive images would increase positive arousal, negative images would reduce positive arousal and that neutral images would have no effect. Differences between the participant groups (lecturers and students) were not expected. The SPSS Output is reproduced after the question. (a) What type of analysis has been carried out (briefly describe the design in answering this question)? [2 marks] (b) With reference to the current experiment, what are the relative pros and cons of repeated measures experimental designs compared to independent (aka between-group) ones? [5 marks] (c) Are any assumptions broken and if so what impact does that have? [3 marks] (d) Interpret the output in full: do students and statistics lecturers differ in the type of stimuli that arouse them? Are statistics lecturers more aroused than 3 /Turn over

4 students in general? Do the images vary in the degree to which they affect physiological arousal? [10 marks] Descriptive Statistics Arousal Before Positive Imagery Arousal Before Neutral Imagery Arousal Before Negative Imagery Arousal After Positive Imagery Arousal After Neutral Imagery Arousal After Negative Imagery Group Statistics Lecturers Total Statistics Lecturers Total Statistics Lecturers Total Statistics Lecturers Total Statistics Lecturers Total Statistics Lecturers Total Mean Std. Deviation N Mauchly's Test of Sphericity b Measure: MEASURE_1 Within Subjects Effect TIME IMAGERY TIME * IMAGERY Epsilon a Approx. Greenhous Mauchly's W Chi-Square df Sig. e-geisser Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. a. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table. b. Design: Intercept+GROUP Within Subjects Design: TIME+IMAGERY+TIME*IMAGERY 4 /Turn over

5 Tests of Within-Subjects Effects Measure: MEASURE_1 Source TIME TIME * GROUP Error(TIME) IMAGERY IMAGERY * GROUP Error(IMAGERY) TIME * IMAGERY TIME * IMAGERY * GROUP Error(TIME*IMAGERY) Type III Sum of Squares df Mean Square F Sig Arousal Before Positive Imagery Arousal Before Neutral Imagery Arousal Before Negative Imagery Arousal After Positive Imagery Arousal After Neutral Imagery Arousal After Negative Imagery Levene's Test of Equality of Error Variances a F df1 df2 Sig Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept+GROUP Within Subjects Design: TIME+IMAGERY+TIME*IMAGERY 5 /Turn over

6 Measure: MEASURE_1 Transformed Variable: Average Source Intercept GROUP Error Tests of Between-Subjects Effects Type III Sum of Squares df Mean Square F Sig Mean Arousal Before Imagery Figure 1: Mean arousal before and after imagery Time After Imagery 6 /Turn over

7 Mean Arousal Statistics Lecturers Group Figure 2: Mean arousal for statistics lecturers and students 8 Mean Arousal Negative Neutral Positive Type of Imagery Figure 3: Mean arousal for different types of imagery 7 /Turn over

8 10 Mean Arousal Group Statistics Lecturers 2 Before Imagery After Imagery Time Figure 4: Mean arousal before and after imagery in statistics lecturers and students Mean Arousal 5 0 Group Statistics Lecturers Negative Neutral Positive Time Figure 5: Mean arousal after different types of imagery in statistics lecturers and students 8 /Turn over

9 14 12 Mean Arousal Imagery Negative Neutral Positive 4 2 Before Imagery Time After Imagery Figure 6: Mean arousal before and after different types of imagery 15 Statistics Lecturers 10 Mean Arousal 5 0 Imagery Negative Neutral Positive 5 10 Before Imagery After Imagery Time Before Imagery After Imagery Figure 7: Mean arousal before and after different types of imagery in statistics lecturers and students 9 /Turn over

10 3. A study was carried out to explore the relationship between aggression and several potential predicting factors in 300 children that had an older sibling. Variables measured were Parenting Style (high score = strict, low score = liberal), Computer Games (high score = more time spent playing computer games), Television (high score = more time spent watching television), E- numbers (high score = more e-numbers in the child s diet), and Sibling Aggression (high score = more aggression seen in their older sibling). The SPSS Output is reproduced after the question. (a) What is a bootstrap confidence interval and when would you use one? [3 marks] (b) What factors predict aggression and which do not (quote the relevant statistics)? Which is the most substantial predictor? [6 marks] (c) The R 2 statistic is the squared correlation coefficient between which two variables? How would you interpret the four values of R 2 in this output? [4 marks] (d) What assumption does the Durbin-Watson statistic help us to assess? Describe what you understand the assumption to mean and whether it has been met in these data. [3 marks] (e) What assumption does the scatterplot in this output assess? Describe what you understand the assumption to mean and whether it has been met in these data. [4 marks] Variables Entered/Removed a Model Variables Entered Variables Removed Method 1 Sibling Aggression, Parenting Style b. Enter 2 Computer Games b. Enter 3 E-Numbers b. Enter 4 Television b. Enter a. Dependent Variable: Aggression b. All requested variables entered. Model Summary e Change Statistics Model R R Square Adjusted R Square Std. Error of the Estimate R Square Change F Change df1 df2 Sig. F Change Durbin- Watson a b c d a. Predictors: (Constant), Sibling Aggression, Parenting Style b. Predictors: (Constant), Sibling Aggression, Parenting Style, Computer Games c. Predictors: (Constant), Sibling Aggression, Parenting Style, Computer Games, E-Numbers d. Predictors: (Constant), Sibling Aggression, Parenting Style, Computer Games, E-Numbers, Television e. Dependent Variable: Aggression 10 /Turn over

11 ANOVA a Model Sum of Squares df Mean Square F Sig. Regression b Residual Total Regression c Residual Total Regression d Residual Total Regression e Residual Total a. Dependent Variable: Aggression b. Predictors: (Constant), Parenting Style, Sibling Aggression c. Predictors: (Constant), Parenting Style, Sibling Aggression, Computer Games d. Predictors: (Constant), Parenting Style, Sibling Aggression, Computer Games, E-Numbers e. Predictors: (Constant), Parenting Style, Sibling Aggression, Computer Games, E-Numbers, Television 11 /Turn over

12 Coefficients a Unstandardized Coefficients Standardized Coefficients 95.0% Confidence Interval for B Collinearity Statistics Model B Std. Error Beta t Sig. Lower Bound Upper Bound Tolerance VIF (Constant) Sibling Aggression Parenting Style (Constant) Sibling Aggression Parenting Style Computer Games (Constant) Sibling Aggression Parenting Style Computer Games E-Numbers (Constant) Sibling Aggression Parenting Style Computer Games E-Numbers Television a. Dependent Variable: Aggression 12 /Turn over

13 Bootstrap for Coefficients Bootstrap a Model B Bias Std. Error Sig. (2- tailed) BCa 95% Confidence Interval Lower Upper (Constant) Sibling Aggression Parenting Style (Constant) Sibling Aggression Parenting Style Computer Games (Constant) Sibling Aggression Parenting Style Computer Games E-Numbers (Constant) Sibling Aggression E Parenting Style Computer Games E-Numbers E Television a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples Casewise Diagnostics a Case Number Std. Residual Aggression Predicted Value Residual a. Dependent Variable: Aggression 13 /Turn over

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