Psy 40 Final Exam Fall 06 Ainsworth Key Name
Psy 40 Final A researcher is studying the effect of Yoga, Meditation, Anti-Anxiety Drugs and taking Psy 40 and the anxiety levels of the participants. Twenty participants were randomly assigned to one of four treatment groups and each participant was given a measure of anxiety before (CV) and after (DV) the treatment. T x = 9 T y = 76 ΣX = 649 ΣY = 676 ΣXY = 06 GM x =.45 GM y = 8.8. Perform a BG ANCOVA on the data above. Include a summary table of the adjusted /MS and a test of significance for the effect. (35 points) 8 + 38 + 5 + 58 76 A = = 659. 548.8 = 0.4 5 0 = 676 659. = 6.8 SP SP S / A A( x) S / A( x) ( x) S / A A S / A Yoga Meditation Drugs Psy 40 Pre Post Pre Post Pre Post Pre Post 7 0 7 0 3 0 5 8 0 3 3 6 3 8 0 5 8 0 0 5 0 7 9 4 3 Sum 5 8 55 38 59 5 63 58 Mean 0.4 5.6 7.6.8 0.4.6.6 = 676 548.8 = 7. 5 + 55 + 59 + 63 9 = = 635.8 6.05 = 3.75 5 0 = 649 635.8 = 3. = 649 6.05 = 6.95 76(9) = 06 = 06 05. = 46.8 0 5(8) + 55(38) + 59(5) + 63(58) = 06 = 06 053.6 = 8.4 5 46.8 8.4 = 0.4 = 0.4 [ 8.7 5.35] = 0.4 [ 75.9] = 34.48 6.95 3. 8.4 = 6.8 = 6.8 5.35 =.45 3. Source df MS F A 34.48 3.493 5.06 S/A.45 5 0.763 CV 45.93 9 Fcrit(3,5) =.99, since 5.09 >.99, reject h0.
. Calculate the adjusted means for each group. (5 points) B Y Y Y S / A yoga meditation drugs 8.4 = =.6363 3. = 5.6.6363(0.4.45) = 5.6.6363(.05) = 5.6 +.67 = 6.7 = 7.6.6363(.45) = 7.6.6363(.45) = 7.6 +.9 = 7.89 = 0.4.6363(.8.45) = 0.4.6363(.35) = 0.4. = 0.8 Y4 0 =.6.6363(.6.45) =.6.6363(.5) =.6.73 = 0.87 3. Remembering that it is an ANCOVA, perform a comparison of Yoga vs. psy 40. (0 points) A A A MS F comp comp ( x ) ( ) n = = = 5.9 ( wjyj ) 5 (6.7) (0.87) wj + ( ) n = = =. ( wj X j ) 5 (0.4) (.6) wj + A. = MS + = + = S / A( x) 3. error ( A ) S / A comp = comp MS A comp error ( A comp ) comp ( x ).763.46 5.9 = = 36.3.46 Fcrit(,5)=4.4, since 36.3 > 4.4 reject ho.
4. What is multicollinearity? In the above data, the CV and DV are correlated at about.80. Does this show a problem with multicollinearity? Why, or why not? (5 points) Any acceptable definition of multicollinearity will do. The.80 is somewhat problematic and is at the bottom range of what would be indicative of multicollinear variables. 5. What is homogeneity of regression? Explain it in the context of the above data set (use the IV, CV and DV above). (5 points) Something like, the slope relating pretest to posttest should be roughly equal across the yoga, meditation, drugs and 40 groups.
Part : Output Interpretation Problem # A chef is interested in whether soaking long grain white rice before steaming it will improve the flavor. She creates 4 groups and feeds them white rice that has been soaked for different amounts of time. She randomly assigns 4 participants to eat rice that has been soaked either 5, 0, 5 or 0 minutes (Soaking Time) and has them rate the rice from -5 (Rating). In order to control for different levels of liking white rice she asked everyone how often they have eaten rice in the last month (Liking). Results are shown below. Soaking Time a = 5 min a = 0 min a 3 = 5 min a 4 = 0 min Liking Rating Liking Rating Liking Rating Liking Rating 4 6 0 6 8 0 6 8 8 0 4 0 4 8 0 8 4 8 8 8 0 8 8 6 0 0 4 4 4 8 4 6 6 0 8 4 6 8 Univariate Analysis of Variance Between-Subjects Factors SOAKING 3 4 Value Label N 5 minutes 6 0 minutes 6 5 minutes 6 0 minutes 6 Descriptive Statistics Dependent Variable: RATING SOAKING 5 minutes 0 minutes 3 5 minutes 4 0 minutes Mean Std. Deviation N 9.33 3.50 6.67 4.844 6 8.33 4.74 6 5.33 3.0 6 3.9 5.0 4 Levenes Test of Equality of Error Variances a Dependent Variable: RATING F df df Sig..9 3 0.448 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept+LIKING+SOAKING
Dependent Variable: RATING Source Corrected Model Intercept LIKING SOAKING Error Corrected Tests of Between-Subjects Effects Type III Sum Partial Eta of Squares df Mean Square F Sig. Squared 560.90 a 4 40.8 40.798.000.967 94.57 94.57 94.957.000.833 96.40 96.40 97.65.000.940 53.045 3 7.68 7.754.000.737 8.93 9.996 58.000 4 579.833 3 a. R Squared =.967 (Adjusted R Squared =.960) Estimated Marginal Means. Grand Mean Dependent Variable: RATING 95% Confidence Interval Mean Std. Error Lower Bound Upper Bound 3.97 a.04 3.490 4.343 a. Covariates appearing in the model are evaluated at the following values: LIKING = 9.9. Dependent Variable: RATING SOAKING 5 minutes 0 minutes 3 5 minutes 4 0 minutes. SOAKING 95% Confidence Interval Mean Std. Error Lower Bound Upper Bound.67 a.439.47 3.086 3.75 a.408.30 4.030 6.57 a.4 5.636 7.398 3.808 a.47.935 4.680 a. Covariates appearing in the model are evaluated at the following values: LIKING = 9.9.
Profile Plots 7 Estimated Marginal Means of RATING 6 5 Estimated Marginal Means 4 3 5 minutes 0 minutes 5 minutes 0 minutes SOAKING 6. Is the covariate significantly adjusting the scores? How do you know? (5 points) Yes, because the test for liking is significant 7. What are the adjusted means? (5 points) 5 minutes =.67, 0 minutes = 3.75, 5 minutes = 6.57, 0 minutes = 3.808 8. Any problems with homogeneity of variance? What is being tested in the Levene s test (what s different than previous analyses)? (5 points) No problem (it s not significant). It s different in ANCOVA because the test is on the adjusted scores 9. What follow-up tests would you perform? Be specific and include relevant info (means, etc.). (5 points) Anything that sounds relevant should be OK, they need to have the means and to mention whether they would do
Problem # A marketing firm is interested in whether consumers really prefer High Definition televisions over regular TVs and if the size of the TV makes a difference as well. They randomly select 0 people and have 5 of them watch regular TVs (9, 3 and 54 inches) and 5 watch high definition TVs (9, 3 and 54 inches). The firm decides to control for the amount of hours the person watches TV per week. Results are shown below. Regular High Definition CV Television Size Hours TV/Week 9 3 54 7 8 7 8 3 8 6 8 4 8 5 4 9 8 3 7 9 5 9 8 0 4 0 8 8 3 8 0 6 5 8 0 4 0 General Linear Model Within-Subjects Factors 3 Dependent Variable NINETEEN THIRTY FIFTY4 Between-Subjects Factors TV_TYPE Value Label N Regular 5 High Definition 5 Descriptive Statistics NINETEEN THIRTY FIFTY4 TV_TYPE Regular High Definition Regular High Definition Regular High Definition Mean Std. Deviation N 3.00.000 5.60.673 5 7.80 5.4 0 8.00.707 5 9.0.789 5 8.60.430 0 7.00.58 5 8.80.789 5.90 6.40 0
Mauchlys Test of Sphericity b Within Subjects Effect Epsilon a Approx. Greenhous Mauchlys W Chi-Square df Sig. e-geisser Huynh-Feldt Lower-bound.97.5.770.93.000.500 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+HOURS_WK+TV_TYPE Within Subjects Design: Tests of Within-Subjects Effects Source * HOURS_WK * TV_TYPE Error() Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Type III Sum Partial Eta of Squares df Mean Square F Sig. Squared 3.45.6.938.45.8 3.45.846.758.938.409.8 3.45.000.6.938.45.8 3.45.000 3.45.938.365.8 0.78 5.089.94.086.96 0.78.846 5.53.94.09.96 0.78.000 5.089.94.086.96 0.78.000 0.78.94.30.96 5.633.87 7.408.006.54 5.633.846 3.884 7.408.008.54 5.633.000.87 7.408.006.54 5.633.000 5.633 7.408.030.54 4. 4.730 4..94.874 4. 4.000.730 4. 7.000 3.460 Tests of Within-Subjects Contrasts Source * HOURS_WK * TV_TYPE Error() Linear Quadratic Linear Quadratic Linear Quadratic Linear Quadratic Type III Sum Partial Eta of Squares df Mean Square F Sig. Squared.39.39.69.694.04 3.005 3.005.473.64.74 4.458 4.458 3.39.0.30 5.70 5.70.804.38.86.06.06.074.793.0 5.57 5.57.54.00.64 9.94 7.40 4.80 7.040
NINETEEN THIRTY FIFTY4 Levenes Test of Equality of Error Variances a F df df Sig..05 8.335 3.747 8.089.63 8.94 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept+HOURS_WK+TV_TYPE Within Subjects Design: Transformed Variable: Average Source Intercept HOURS_WK TV_TYPE Error Tests of Between-Subjects Effects Type III Sum Partial Eta of Squares df Mean Square F Sig. Squared 34.88 34.88 5.364.006.687 Estimated Marginal Means.83.83.69.97.53 08.599 08.599 48.803.000.875 5.577 7.5. Grand Mean 95% Confidence Interval Mean Std. Error Lower Bound Upper Bound 9.767 a.7 9.3 0.4 a. Covariates appearing in the model are evaluated at the following values: HOURS_WK =.80. TV_TYPE Regular High Definition. TV_TYPE 95% Confidence Interval Mean Std. Error Lower Bound Upper Bound 6.440 a.549 5.43 7.737 3.093 a.549.796 4.39 a. Covariates appearing in the model are evaluated at the following values: HOURS_WK =.80.
3 3. 95% Confidence Interval Mean Std. Error Lower Bound Upper Bound 7.800 a.463 6.706 8.894 8.600 a.445 7.549 9.65.900 a.396.964 3.836 a. Covariates appearing in the model are evaluated at the following values: HOURS_WK =.80. TV_TYPE Regular High Definition 3 3 4. TV_TYPE * 95% Confidence Interval Mean Std. Error Lower Bound Upper Bound 3.06 a.93.00 5.40 7.554 a.895 5.437 9.67 8.560 a.797 6.674 0.446.394 a.93 0.90 4.599 9.646 a.895 7.58.763 7.40 a.797 5.354 9.6 a. Covariates appearing in the model are evaluated at the following values: HOURS_WK =.80.
Profile Plots 0 8 Estimated Marginal Means of MEASURE_ 6 4 Estimated Marginal Means 0 8 6 4 TV_TYPE Regular High Definition 3 0. Is the covariate significantly adjusting the scores? How do you know? (5 points) No, because hours_wk is not significant. What kind of design is this? (5 points) Mixed. Which effects are significant after controlling for the covariate? (6 points) TV_type and size*tv_type 3. Is there a difference between small and large TVs? How do you know? (8 points No, because the linear contrast is not significant. Or they could have said no because the effect for TV is not significant 4. Based on the output, is there a problem with any of the assumptions? Explain your answer. (6 points) The test for sphericity and for homogeneity of variance are all fine.