Tests of Between-Subjects Effects

1. Tests of Between-Subjects Effects Dependent Variable:Paper Type III Sum of Source Squares df Mean Square F Sig. 100467.089a 2 50233.544 60.029 .000 Intercept 194860.922 1 194860.922 232.860 .000 Paper_Avg 100467.089 2 50233.544 60.029 .000 Error 101254.901 121 836.817 Total 416319.750 124 Corrected Total 201721.990 123 Corrected Model a. R Squared = .498 (Adjusted R Squared = .490) Paper Tukey HSD Subset Paper_ Avg N 1 None 41 50 lbs 37 100 lbs 46 Sig. 2 3 11.33 30.78 77.28 1.000 1.000 1.000 Means for groups in homogeneous subsets are displayed. Based on observed means. The error term is Mean Square(Error) = 836.817. The data indicate that the form of the question influenced the reported average amount of paper consumed: F (2, 121) = 60.03, MSE = 836.82, p < .05. The results of the Tukey Test indicate that the subjects’ estimates of paper use differed in all three conditions. Increasing the average value in the question significantly increased their estimates of the amount of paper consumed. 2. Within-Subjects Factors Measure:MEASURE_1 Dependent Foodtype Variable 1 Fruits 2 Veggies Tests of Within-Subjects Effects Measure:MEASURE_1 Type III Sum of Source Squares Foodtype Error(Foodtype) df Mean Square F Sig. Sphericity Assumed .746 1 .746 .264 .608 Greenhouse-Geisser .746 1.000 .746 .264 .608 Huynh-Feldt .746 1.000 .746 .264 .608 Lower-bound .746 1.000 .746 .264 .608 Sphericity Assumed 347.334 123 2.824 Greenhouse-Geisser 347.334 123.000 2.824 Huynh-Feldt 347.334 123.000 2.824 Lower-bound 347.334 123.000 2.824 Foodtype Measure:MEASURE_1 95% Confidence Interval Foodtyp e Mean Std. Error Lower Bound Upper Bound 1 2.102 .196 1.714 2.491 2 2.212 .116 1.982 2.442 According to the repeated measures ANOVA above, there is not enough evidence to conclude that Amherst students eat different numbers of serving of vegetables and fruits: F (1, 123) = 0.264, MSE = 2.824, p > .05. There is no need to conduct a Tukey test here because we failed to reject the null. But, even if we had rejected the null, a Tukey test would have been unnecessary because there were only two levels of the independent variable. If there are only two levels of an IV, then we know that the significant difference (had there been one) would have been between fruits and vegetables. The conclusion we reached regarding the null is identical to the decision we made in response to question #4 on HW 4. Paired Samples Test Paired Differences 95% Confidence Interval Mean Pair 1 Std. Deviation Std. Error Mean Lower Upper t df Sig. (2-tailed) Fruits -.1097 2.3765 .2134 -.5321 .3128 -.514 123 Veggies The important thing to notice about the relationship between the Fobs for the ANOVA and tobs for the t-test is that F = t2 (0.264 = (0.514 * 0.514). This relationship occurs because the two tests are almost identical. The only difference is that the measure of variability for the t-test is based on the standard error, which is based on the standard deviation. The denominator of the F-ratio is the MSE, which is based on the SS, which is derived from the variance. The variance is equal to the standard deviation squared, so the F-ratio is equal to the t-value squared. If you understand this, great. If you don’t, just let it go. .608 3. Bristol-Meyers Squib, the company that makes Pepto-Bismol, wants to capitalize on the Thanksgiving Holiday. Last year, they ran a study to determine whether eating the big Thanksgiving meal at different times of day would influence the experience of indigestion. The data, which represent discomfort ratings at 11:00 pm, are presented in the table below. Higher ratings indicate more discomfort. Conduct a one-way ANOVA to determine if meal time influences indigestion. Be sure to report the results of your F-test in the proscribed manner and to conduct post-hoc tests if warranted. Based on the results of your test, would it be valuable for BMS to try to influence the American people? If so, how? 2:00 4:00 6:00 x x2 x x2 x x2 7 49 4 16 10 100 8 64 5 25 8 64 7 49 3 9 9 81 9 81 5 25 6 36 31 243 17 75 33 281 Ho: All dinner times equally indigestion inducing Ha: At least two dinner times differ Fcrit (alpha = .05, dfn = 2, dfd = 9) = 4.26 SStotal SSB SSE = = = = = = = = = = = = Anova Table Source df Time 2 Error 9 Total 11 (x2) – G2/N (243 + 75 + 281) - [(31+17+33)2 / 12] 599 - 546.75 52.25 [(T2/n)] - (G2/N) [312/4)] + [(172/4)] + [332/4)] - 546.75 240.25 + 72.25 + 272.25 - 546.75 38 [(x2) - (T2/n)] (243-240.25) + (75-72.25) + (281-272.25) 2.75 + 2.75 + 8.75 14.25 SS 38.00 14.25 52.25 MS 19.00 1.58 F 12.00 Because Fobs < Fcrit, I would reject the null. This means that at least one of the dinner times differs from the others. A Tukey test will be conducted to determine which dinner times are different from one another. HSD = q (MSE/n) = = = = q ( = .05; k=3, df = 9) = 3.82 3.95 (1.583/4) 3.95 (.40) 3.95 (.63) 2.49 Mean 2:00 = 7.75 Mean 4:00 = 4.25 Mean 6:00 = 8.25 Based on the analyses, I would tell Bristol-Meyers that dinner time definitely influences indigestion: F (2, 9) = 12, MSE = 1.58, p < .05. Tukey tests revealed that 4:00 produces less indigestion than either the earlier or later times, which do not differ from one another. Therefore, I would run a commercial campaign that would induce people to eat their big meal either early in the afternoon or in the evening.