Grad Stats Final Exam Fall, 2000Question IThis problem is a reward to the one SLHS student who stuck with us. A speech researcher istrying to find ways to help people whose speech has been impaired by injuries to either theirvocal apparatus or to the brain areas responsible for speech. She suspects that one reason peoplewith such injuries have trouble being understood is that they don’t talk loudly enough, eitherbecause their injuries make it difficult to do so or because they are embarrassed by their acquiredspeech problems. Before designing an intervention, she conducts a study to examine therelationship between loudness and speech intelligibility among a group of patients with speechproblems. The following variables are available for each patient:LOUD loudness (in dB) of the patient’s typical speechINTEL intelligibility as rated on a 10-point scale by judges unaware of the purposes ofthe studyAGE age (in years) of the patientFor each substantive question below, specify MODEL A/MODEL C comparisons that could beused to answer the question.1. Are patients who speak louder easier to understand? (In this question and subsequent ones,treat INTEL as the dependent variable.)2. Age is known to affect loudness. When controlling for age, are patients who speak loudereasier to understand?3. Is it more true for younger patients than older patients that patients who speak louder areeasier to understand?4. Ignoring age for the moment and assuming there is a relationship been intelligibility andloudness, can there be too much of a good thing? That is, do effects of loudness onintelligibility decrease with increasing loudness?5. Assuming that loudness is decreasingly effective, is the optimal level intelligibility attainedwhen loudness is 80 dB?6. Does the degree to which the effectiveness of loudness decreases at higher levels depend onthe age of the patient?Question IIAlthough African-Americans (AA) as a group are economically disadvantaged compared toCaucasian-Americans as a group, there are many salient counterexamples of AA affluence in themedia (e.g., Oprah, Colin Powell). What effect do such images have on the perception of AA'splight as a whole? The enlightened racism perspective argues that successful AA individualsmay actually undermine the perception that AA as a whole are discriminated against. Thus,thinking about Colin Powell may at least temporarily decrease how much discrimination youthink exists toward AAs.Bodenhausen, Schwarz, Bless and Wanke (1995) investigated this issue by making an affluentAA temporarily salient to participants and then assessing participants' attitudes. Specifically,participants completed a survey on which the last question referred to Oprah, Michael Jordan orJulia Roberts (control condition) thus making either an AA or control target temporarilyavailable to participants. In an unrelated task participants later rated how much they believedAA continued to be discriminated against in the U.S. on a scale from 0 = not very much to 9 =very much. The average response, standard deviation and n for each condition are providedbelow.OprahMichael JordanControlMean:6.85.43.0St. Dev.:1.61.81.4n:1513121. Develop two contrast codes to analyze this data keeping in mind that one code shouldaddress the enlightened racism hypothesis. Give a brief interpretation of the substantivequestion asked by each code.2. Calculate the parameter estimate for each contrast-coded predictor you gave in question 1.3. Provide a full source table for the one-way ANOVA of this data.4. Write a one-paragraph results section that summarizes the results you have found. Make sureto address what the results imply about the viability of the enlightened racism hypothesis inthe discussion.Question IIIData are collected on a sample of 200 elderly people to examine the determinants of depressionin old age. Four variables are measured:DEP Scores on a depression inventory, ranging from 1 to 50, where higher numbersindicate greater levels of depression. This is the outcome variable in all analyses.AGE Respondent's AgeFRIENDS The number of "very close" friends reported by the respondent (from 0 to 4).EVENTS The number of traumatic life events reported by the respondent in the last 3 years.In the following analyses, two other variables are computed from the above variables:AGE2 = AGE*AGEFEINT = FRIENDS*EVENTSThe following models are estimated using the above variables:Proc reg: model dep=friends; model dep=age; model dep=events; model dep=friends age events/pcorr2 ss2 tol clb; model dep=age age2/pcorr2 ss2 tol clb; model dep=friends events feint/pcorr2 ss2 tol clb; model dep=friends age events age2 feint/pcorr2 ss2 tol clb;Following these models, a one-way analysis of variance is conducted, to examine meandifferences in DEP as a function of the five levels of FRIENDS. To do this, four contrast codes(using orthogonal polynomials) are used to code the five levels of FRIENDS (originally scoredas 0 to 4). These codes are defined by the lambda's in the following table:FRIENDS01234Contrast Coded VariableFLIN (linear code)-2-1012FQUAD (Quadratic code)2-1-2-22FCUB (Cubic code)-120-21FQUAR (Quartic code)1-46-41This analysis of variance is conducted by regressing DEP on FLIN, FQUAD, FCUB, andFQUAR. The following are the mean values of DEP (and cell n's) at each level of FRIENDS::FRIENDS01234Mean DEP39.5235.8134.0531.2430.06N1352545516Based on these analyses, answer the following questions:5. Ignoring all other variables, are older respondents more depressed than younger respondents?(Give PRE, F*, n-pa, and pa-pc)6. Are older respondents more depressed than younger respondents once FRIENDS andEVENTS are controlled? (Give PRE, F*, n-pa, and pa-pc)7. Do FRIENDS and EVENTS as a set predict depression once AGE is held constant? (GivePRE, F*, n-pa, and pa-pc).8. What would be the value of r-squared if AGE were regressed on EVENTS and FRIENDS?9. Ignoring FRIENDS and EVENTS, is there evidence that AGE has a nonlinear relationshipwith depression? (Give PRE, F*, n-pa, and pa-pc).10. Provide interpretations of all three parameter estimates in the model where DEP is regressedon AGE and AGE2.11. Ignoring AGE, is there evidence that the impact of more negative EVENTS on DEP issmaller as individuals report having more FRIENDS? (Give PRE, F*, n-pa, and pa-pc).12. Given the model where DEP is regressed on FRIENDS, EVENTS, and their interaction, whatis the simple slope for EVENTS for respondents