Practice Final (2)

STAT E-150 Practice Final Exam 1. In the sample dataset, the variable Sprint is the respondent's time (in seconds) to sprint a given distance, and Smoking is an indicator about whether or not the respondent smokes (0 = Nonsmoker, 1 = Past smoker, 2 = Current smoker). Let's use ANOVA to test if there is a statistically significant difference in sprint time with respect to smoking status. Sprint time will serve as the dependent variable, and smoking status will act as the independent variable. Please interpret the ANOVA table below, using a complete sentence and in APA format. Sum of Squares df Mean Square F Sig. Between Groups 26.788 2 13.394 9.209 .000 Within Groups 509.082 350 1.455 Total 535.870 352 2. We want to know if there are any differences between the weights of the rats after the 6-week period. We have measured the weights of different rats. There are three groups of rats: Controls: these have not received any physical exercise. Exercised: these have performed 6 weeks of physical exercise. Pill: these have been treated with a diet pill for 6 weeks. How would you interpret the following post hoc table below. Please use complete sentences and interpret the p -values. Multiple Comparisons Dependent Variable: Weight Tukey HSD (I)Group (J) Group Mean Difference (I-J) Std Error Sig. Lower Bound Upper Bound Control Exercised Pill 96.3125 46.0750 2.9910 2.9910 .000 .000 88.773 38.536 103.852 53.614 Exercised Control Pill -96.3125 -50.2375 2.9910 2.9910 .000 .000 -103.852 -57.777 -88.773 -42.698 Pill Control Exercised -46.0750 50.2375 2.9910 2.9910 .000 .000 -53.614 42.698 -38.536 57.777 3. A Psychologist was interested in the variation of ability to cope with workplace-related stress (CWWS score) across four groups with different physical activity levels. He ran an ANOVA with the predictor variable ‘group’, which had four categories, ‘sedentary’, ‘low’, ‘moderate’, and ‘high’ levels. The outcome variable was

‘coping_stress’. How would you interpret the graph below? Please respond to the following:  Based on this example and in looking at the Contrasts Coefficients table below please indicate which groups each of the following contrasts compare: Contrast 1: Contrast 2: Contrast 3: Contrast 4: Contrast Coefficients Contrast Sedentary Low Moderate High 1 3 -1 -1 -1 2 0 -2 1 1 3 0 0 1 -1 4 0 -1 1 0  Did the Contrasts Coefficients table below follow the Planned Contrasts coding rules? Why or why not? 4. Consider the following ANCOVA example: The example looks at the effects of drug A (dose à 1=control; 2=15mg; 3=30mg) on pain reduction (scale of 0-10) with the covariate being ‘nonpharmacologic pain rehabilitation’ (scale of 0-7 [based on number of days of rehab each week]). So, our model looks like the following: Pain Reduction i = b 0 + b 1 LowDose i + b 2 HighDose i + b 3 Covariate i + ε I a. What should replace the word Covariate? (an abbreviation is fine) A Psychologist was interested in the variation of ability to cope with workplace- related stress (CWWS score) across four groups with different physical activity levels. He ran an ANOVA with the predictor variable ‘group’, which had four categories, ‘sedentary’, ‘low’, ‘moderate’, and ‘high’ levels. The outcome variable was ‘coping_stress’. 5. How would you interpret the graph below?

b. The reason our model looks like this is because we can add a covariate as a predictor to the model to test the difference between group means adjusted for the covariate. Including covariates can be important, because covariates can help us to exert stricter experimental control by taking account of __________ variables to give us a ‘purer’ measure of effect of the __________ manipulation. 8. Consider the following factorial ANOVA example: A professor of a statistics course was interested in the effect of proximity to the final exam (5 weeks away, 1 week) on the stress levels of psychology and business students. He measured their level of perceived stress on a standardized questionnaire. In this scenario, stress is the dependent variable while proximity and students' field of study are independent variables. In reviewing the table below, are the main and interaction effects significant? Please indicate in the order that they are labeled and provide an interpretive statement for each using APA format and complete sentences. 9. Let’s say I’m running a one-way ANOVA in SPSS, and I decide I want to test for linear trends in the data while I’m entering my 3 contrasts above, as indicated in #22 above. In the contrasts dialogue box, I click on polynomials. Given that I have 4 groups, including one base group and three groups of smokers:  What is the highest degree of trend we can choose?  Why is this the highest degree of trend we can choose?  If that said highest degree of trend is significant in our output, does that mean that as smoking frequency increased, the outcome (let’s say it’s “frequency of colds per year”) increased proportionately?  Why or why not to your response to item “c” immediately above?

10.Let’s say that we were interested in the effects of a mindfulness intervention on individuals with a Major Depressive Disorder diagnosis and whether the effect was different for individuals who were also prompted to notice novelty (pay attention to new things about the experience) while engaging in certain daily activities vs. those who were not. Given the type of analyses we learned in class during the second half of this semester, which analysis would you use and why? Factorial ANOVA because there are two independent variables, the levels of the mindfulness interventions and whether the participants were prompted to notice novelty. 11. A Psychiatrist wants to be able to predict whether treatment outcomes for Depression can be predicted based on Therapy type. She coded the Cognitive Behavioral Therapy group as “0” and the Psychodynamic Therapy group as “1”. Please answer the following questions based on the table below:  In Table 1 below, the significance value is in for Step 1 is telling us what about this Model? The model has improved significantly by adding therapy type as predictor, x 2 (1) = 35.839, p < .001 (or p = .001). Table 1. Block 1: Method = Enter Omnibus Tests of Model Coefficients Chi- square df Sig. Step 1 Step Blo ck Model 35.839 35.839 35.839 1 1 1 .001 .001 .001  Given what you know about how Chi-square test is calculated in table 1 above, and using table 2 below as well, please determine what the -2LL was for the baseline model. 117.273 + 35.839 = 153.112 Table 2. Model Summary

There was a statistically significant difference in “memory for the assailant” for the mindfulness training group and the no training group, F(1, 16) = 16.000, p = .001. c. Is there a significant interaction effect? There was a significant interaction between film and mindfulness training on in “memory for the assailant”, F (1, 16) = 16.000, p = .001. Tests of Between-Subjects Effects Dependent Variable: Memory for Assailant Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squ. Corrected Model 120.000 3 40.000 32.000 .000 .857 Intercept 320.000 1 320.000 256.000 .000 .941 Violence 80.000 1 80.000 64.000 .000 .800 Training 20.000 1 20.000 16.000 .001 .500 Violence * Training 20.000 1 20.000 16.000 .001 .500 Error 20.000 16 1.250 Total 460.000 20 Corrected Total 140.000 19 b. R Squared = .857 (Adjusted R Squared = .830) 13. A marketeer wants to launch a new commercial and has four concept versions. She shows the four concepts to 40 participants and asks them to rate each one of them on a 10-point scale. Please use the output below to answer the following questions in complete sentences and APA format.

a. Do we meet the assumption of sphericity? Mauchly's test of sphericity indicated that the assumption of sphericity had not been violated, χ 2 (5) = 4.045, p = .543. b. Based on your answer for Part A, please provide the interpretation of the correct line of the Test of Within Subjects Effects and identify which line you used. You can use the ‘Sphericity Assumed’ row to determine that there was a significant difference between the ratings of products, F 3,117 = 15.372, p < .001, partial eta = .53