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Grad Stats Final Exam Fall 2000 Question I This problem is a reward to the one SLHS student who stuck with us A speech researcher is trying to find ways to help people whose speech has been impaired by injuries to either their vocal apparatus or to the brain areas responsible for speech She suspects that one reason people with such injuries have trouble being understood is that they don t talk loudly enough either because their injuries make it difficult to do so or because they are embarrassed by their acquired speech problems Before designing an intervention she conducts a study to examine the relationship between loudness and speech intelligibility among a group of patients with speech problems The following variables are available for each patient LOUD loudness in dB of the patient s typical speech INTEL intelligibility as rated on a 10 point scale by judges unaware of the purposes of the study AGE age in years of the patient For each substantive question below specify MODEL A MODEL C comparisons that could be used 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 louder easier to understand 3 Is it more true for younger patients than older patients that patients who speak louder are easier to understand 4 Ignoring age for the moment and assuming there is a relationship been intelligibility and loudness can there be too much of a good thing That is do effects of loudness on intelligibility decrease with increasing loudness 5 Assuming that loudness is decreasingly effective is the optimal level intelligibility attained when loudness is 80 dB 6 Does the degree to which the effectiveness of loudness decreases at higher levels depend on the age of the patient Question II Although African Americans AA as a group are economically disadvantaged compared to Caucasian Americans as a group there are many salient counterexamples of AA affluence in the media e g Oprah Colin Powell What effect do such images have on the perception of AA s plight as a whole The enlightened racism perspective argues that successful AA individuals may 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 you think exists toward AAs Bodenhausen Schwarz Bless and Wanke 1995 investigated this issue by making an affluent AA temporarily salient to participants and then assessing participants attitudes Specifically participants completed a survey on which the last question referred to Oprah Michael Jordan or Julia Roberts control condition thus making either an AA or control target temporarily available to participants In an unrelated task participants later rated how much they believed AA 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 provided below Mean St Dev n Oprah 6 8 1 6 15 Michael Jordan 5 4 1 8 13 Control 3 0 1 4 12 1 Develop two contrast codes to analyze this data keeping in mind that one code should address the enlightened racism hypothesis Give a brief interpretation of the substantive question 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 sure to address what the results imply about the viability of the enlightened racism hypothesis in the discussion Question III Data are collected on a sample of 200 elderly people to examine the determinants of depression in old age Four variables are measured DEP AGE Scores on a depression inventory ranging from 1 to 50 where higher numbers indicate greater levels of depression This is the outcome variable in all analyses Respondent s Age FRIENDS EVENTS The number of very close friends reported by the respondent from 0 to 4 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 FEINT AGE AGE FRIENDS EVENTS The 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 mean differences 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 scored as 0 to 4 These codes are defined by the lambda s in the following table 0 Contrast Coded Variable FLIN linear code FQUAD Quadratic code FCUB Cubic code FQUAR Quartic code 2 2 1 1 FRIENDS 1 2 3 1 1 2 4 0 2 0 6 1 2 2 4 4 2 2 1 1 This analysis of variance is conducted by regressing DEP on FLIN FQUAD FCUB and FQUAR The following are the mean values of DEP and cell n s at each level of FRIENDS Mean DEP N 0 39 52 13 FRIENDS 1 2 3 35 81 34 05 31 24 52 54 55 4 30 06 16 Based 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 and EVENTS 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 Give PRE 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 relationship with depression Give PRE F n pa and pa pc 10 Provide interpretations of all three parameter estimates in the model where DEP is regressed on AGE and AGE2 11 Ignoring AGE is there evidence that the impact of more negative EVENTS on DEP is smaller 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 what is the simple slope for EVENTS for respondents reporting the mean level of FRIENDS i e FRIENDS 2 045 13 Is there evidence that the


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