STAT 379 FINAL Examname

1

STAT 379 FINAL EXAMName:

Spring 2007

Please write all answers simply and concisely as if directed to a fellow grad student looking for explanation -- NOT as if writing a textbook chapter or encyclopedia entry. Carry out any calculations to 4 decimal places to prevent rounding error.

F(kL - kS, N - kL - 1) = [(R2L - R2S) / (kL - kS)] / [(1- RL2) / (N - kL - 1)]

1.A study of the effect of playing violent video games on aggression investigated whether anger acted as a moderating variable in 167 undergraduate students. As an index of anger, participants completed a scale measuring tendency for emotional arousal and angry outbursts (ANGER, continuous). Then they played either a nonviolent or a violent video game for 15 minutes (VIOLENCE, categorical). Subsequently they wrote conclusions to 60 brief story stems and the number of aggressive story points they produced was counted (AGGRESS, continuous).

a)List each step in the analysis. (Note that the IV of interest is a categorical variable and the proposed moderator is a continuous variable, the opposite of typical examples you've encountered. This has no implications for the analysis!)

b)What pattern of results would indicate that anger is in fact a moderator of the relationship between playing violent video games and aggressive behavior?

c)What pattern of results would make this suitable for interpretation as an Analysis Of Covariance (ANCOVA)?

d)In this study R2 increased from 0.051 to 0.082. Show the value of F (with df) that tests the significance of that increase.

e)Now imagine you leave ANGER out of the analysis and regress AGGRESS on VIOLENCE alone, but a third group is included in the analysis: a control group that plays no video games at all but simply watches recorded scenes from the non-violent game. Show the dummy-coded variables that would represent these three groups in a regression equation (that is, show how each group would be coded).

f)With this third group included as a control group, interpret the meaning of the t-test of the b-weight you would get for your first dummy variable.

2.At the end of the semester, five Intro Psych instructors compare their classes' knowledge of five areas of experimental psychology -- Neuropsychology, Learning, Human Memory, Perception, and Language -- by giving their students a set of standard test bank questions for each topic. Students are given a score for each of the areas of psychology represented.

a)Even if they're only interested in the DVs separately - e.g., was there a significant difference in performance on Neuropsychology questions, or on Learning questions, etc. - MANOVA would probably be employed here too. Why?

b)What does the value of Wilks' Lambda represent?

c)What is the name for the quantity [1 - Wilks' Lambda] and what does its value represent?

d)What would Discriminant Analysis tell you about the MANOVA results if the MANOVA is significant?

e)How many Discriminant Functions could be found in this study?

f)What does the assumption of "homogeneity of variance-covariance matrices" mean (you can give examples of something it means and something it doesn't mean, if that helps).

3.Logistic Regression

a)In Logistic Regression, coefficients are derived to produce a regression equation to predict a value Y', as usual. Rather than being a score on a continuous variable as in Linear Regression, what exactly does the numerical value of Y' represent here - that is, what is the number that's being predicted?

b)What is the difference between "odds" and an "odds ratio"?

c)If Exp(B) = 2.0, what happens to the odds of being in the predicted category when X increases by 1 point?

d)What does the Wald statistic tell you?

e)Which is more influential in predicting group membership, a predictor whose Exp(B) = 0.25 or one whose Exp(B) = 1.75?

f)Name one thing that makes logistic regression preferable to discriminant analysis for predicting dichotomous outcomes.

4.Give as brief a description as possible of each of the following:

a)scree plot: what it is, how to use it

b)oblique rotation and why it produces two kinds of loadings (pattern matrix and structure matrix)

c)homoscedasticity

d)list the three basic steps in a mediation analysis (using variable names "IV", "DV", and "Mediator")

e)meaning of incremental / sequential R-square for a variable not entered first in sequential regression

f)centering (just what it means, not why it's done)

Comparison of analyses: Write the LETTER (a, b, c, d, e) of your choice in the space. If the statement applies to multiple analyses, you must choose the option listing all the choices it applies to.

I.Sequential Regression

II.Logistic Regression

III.Factor Analysis

IV.MANOVA

V.Discriminant Analysis

5._____ assumes linearity between IVs and DV(s)

a) Ib) IIc) IVd) Ve) all of I, II, III, IV, & V

6._____ assumes normality of DV(s)

a) Ib) IIc) IVd) I & IIe) I & IV

7._____ assumes the DV's variance is same at all levels of the IV

a) Ib) IIc) IVd) I & IIe) I & IV

8._____ allows use of categorical IVs

a) Ib) IIc) IVd) I & IIe) I, II & IV

9._____ allows use of categorical DVs

a) Ib) IIc) IVd) II & Ve) IV & V

10._____ is tested using Wilks' Lambda

a) IIb) IIIc) IVd) IV & Ve) III & V

11._____ is a multivariate analysis

a) IIb) IIIc) Vd) II & Ve) III & V

12._____ can be performed with 60 participants and 2 IVs

a) Ib) IIc) IIId) I & IIe) I & III

13._____ produces more than one eigenvector in the output

a) IIb) IIIc) Vd) III & Ve) II & III

14._____ involves a linear combination of observed variables

a) Ib) IIc) IIId) IVe) all of I, II, III, IV, & V

True / False items: Write (a) for True and (b) for False in the space for each item.

a = True; b = False

15._____ The Sobel test evaluates whether partial moderation is present.

16._____ The number of factors in a factor analysis solution is strictly determined by the size of the eigenvalues.

17._____ A mediator explains the mechanism of an IV's effect on a DV, and a moderator explains under what circumstances the IV will have its effect on the DV.

18._____ Stepwise regression chooses a set of predictors without the use of theory.

19._____ Confirmatory factor analysis is theory-driven.

20._____ To minimize multicollinearity, the value of the "tolerance" should be as close to 1.0 as possible.

21._____ After factor rotation, the eigenvalues of the factors are different but the sum of the eigenvalues of the rotated factors remains the same.

22._____ "Gender" is a good candidate to be a mediating variable.

23._____ Rotation of factors is done for mathematical reasons and does not help with interpreting the factors.

24._____ The last predictor entered in a sequential regression will get the same b-weight and significance as if it were in a simultaneous regression with the same set of predictors.

25._____ Homoscedasticity and linearity can be evaluated by plotting standardized residuals against predicted Y-values.

SS = (X-Mx)2

SP = (X-Mx)(Y-My)

s2x = SS/df = (X-M)2 / (N-1)

zx = X - Mx / sx

COVxy = SP/df = (X-Mx)(Y-My) / (N-1)

rxy = COVxy/(sxsy)

b = SP / SSx

a = My - bMx

sy = bsx

SStot = SSreg + SSres

standard error of estimate = MSres = [SSres / (N - k - 1)]

F(k, N - k - 1) = (SSreg / k) / [SSres / (N - k - 1)] = (R2 / k) / [(1- R2) / (N - k - 1)]

dfreg = k and dfres = N - k - 1

t(N - k - 1) = b / SEb =  / SE

standard error of b = SEb = SEest / SSx

R2y12 = (r2y1 + r2y2 - 2ry1ry2r12) / (1-r212)

adj. R2 = 1 - [(1 - R2)*(N -1) / (N - k - 1)]

1 = (ry1 - ry2r12) / (1-r212)

ry1.2 = (ry1 - ry2r12) / [(1-r2y2)(1-r212)]

ry(1.2) = (ry1 - ry2r12) / (1-r212)

incremental R2: F(kL - kS, N - kL - 1) = [(R2L - R2S) / (kL - kS)] / [(1- RL2) / (N - kL - 1)]