Running a One-Way ANOVA

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Running a One-Way ANOVA

1 Week Five ANOVA Exemplar Template Research Question Does the mean change in number of days of cold symptoms differ among the three experimental populations: those who take placebo, those who take low doses of vitamin C, and those who take high doses of vitamin C? Hypotheses H0: The mean change in number of days of cold symptoms does not differ among the three experimental populations: those who take placebo, those who take low doses of vitamin C, and those who take high doses of vitamin C. H1: The mean change in number of days of cold symptoms does differ among the three experimental populations: those who take placebo, those who take low doses of vitamin C, and those who take high doses of vitamin C? Results A one-way ANOVA was conducted to evaluate the relationship between vitamin C and the change in the number of days with cold symptoms from the first year to the second year of the study. The independent variable, the vitamin C factor, included three levels: placebo, low doses of vitamin C, and high doses of vitamin C. The dependent variable was the change in the number of days of cold symptoms from the first to second year. The ANOVA was significant at the .05 level, F(2, 27) = 4.84, p = .02. The strength of the relationship between the vitamin C treatment and the change in the number of days with cold symptoms, as assessed by η2, was strong, with the vitamin C factor accounting for 26% of the variance of the dependent variable. 2 Follow-up tests were conducted to evaluate pairwise differences among means. Because the variances among the three groups ranged from 16.54 to 30.00, we chose not to assume that the variances were homogenous and conducted post hoc comparisons with the use of Dunnett’s C test, a test that does not assume equal variances among the three groups. There was a significant difference in the means betwee the group that received a low dose of vitamin C and the placebo group, but no significant difference differences between the two vitamin C groups and between the high dose and placebo groups. The group that received a low dose of vitamin C showed on average a greater decrease in number of days with cold symptoms in comparison to the placebo group. The 95% confidence interval for the pairwise differences, as well as the means and standard deviations for the thre groups are reported in Table 1. Figure 1 is a box-plot of experimental conditions. The appendix depicts the SPSS ANOVA output generated from the analysis. Table 1 95% Confidence Intervals of Parities Differences in Mean Change in Number of Days of Cold Symptoms Variable M SD 3.50 4.14 Low Dose (Vitamin C) -2.10 4.07 [.47, 10.73*] High Dose (Vitamin C) -2.00 5.48 [-.56, 11.56*] Placebo Placebo Low Dose [-6.12, 5.92] Note: An asterisk indicates that the 95% confidence interval does not contain zero, and therefore the difference in means is significant at the .05 significance using Dunnett’s C procedure. 3 Figure 1. Boxplot depicting time spent talking by stress condition. 4 Appendix Descriptive Statistics Dependent Variable: Difference in Days with Colds Vitamin C Treatment Placebo Low Vitamin C Dose High Vitamin C Dose Total Mean Std. Deviation 3.50 4.143 -2.10 4.067 -2.00 5.477 -.20 5.182 N 10 10 10 30 Levene’s Test of Equality of Error Variancesa Dependent Variable: Difference in Days with Colds F 1.343 df1 df2 2 27 Sig. .278 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + group Tests of Between-Subjects Effects Dependent Variable: Difference in Days with Colds Source Corrected Model Intercept group Error Total Corrected Total Type III Sum of Squares 205.400a 1.200 205.400 573.400 780.000 778.800 df Mean Square 2 1 2 27 30 29 a. R Squared = .264 (Adjusted R Squared = .209) 102.700 1.200 102.700 21.237 F 4.836 .057 4.836 Sig. .016 .814 .016 Partial Eta Squared .264 .002 .264 5 Multiple Comparisons Dependent Variable: Difference in Days with Colds (I) Vitamin C Treatment Placebo Tukey HSD Low Vitamin C Dose High Vitamin C Dose Placebo Dunnett C Low Vitamin C Dose High Vitamin C Dose (J) Vitamin C Treatment Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound .49 .39 -10.71 -5.21 -10.61 -5.01 .47 Upper Bound 10.71 10.61 -.49 5.01 -.39 5.21 10.73 Low Vitamin C Dose High Vitamin C Dose Placebo High Vitamin C Dose Placebo Low Vitamin C Dose Low Vitamin C Dose 5.60* 5.50* -5.60* -.10 -5.50* .10 5.60* 2.061 2.061 2.061 2.061 2.061 2.061 1.836 High Vitamin C Dose 5.50 2.172 -.56 11.56 -5.60* 1.836 -10.73 -.47 -.10 2.157 -6.12 5.92 -5.50 2.172 -11.56 .56 .10 2.157 -5.92 6.12 Placebo High Vitamin C Dose Placebo Low Vitamin C Dose Based on observed means. The error term is Mean Square(Error) = 21.237. *. The mean difference is significant at the .030 .033 .030 .999 .033 .999

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