Assignemnet #7

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Statistics

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Feb 20, 2024

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1. The independent variables are the learning environment. I have 3 different independent variables, “classroom”, “online” and “blended.” 2. The dependent variable is performance score. This is being measured by the three different types of learning environments that are being manipulated: “classroom”, “online” and “blended".” 3. Null : There is no difference in performance score for participants in group 1(“classroom”, group 2(“online” and group 3(“blended”). Alternative : There is a difference in performance scores for participants in group 1(“classroom”, group 2(“online” and group 3(“blended”). 4. > Data_Assignment7$group<- gl(3,10, labels = c("classroom", "online", "blended")) > Data_Assignment7$group [1] classroom classroom classroom classroom classroom classroom classroom classroom [9] classroom classroom online online online online online online [17] online online online online blended blended blended blended [25] blended blended blended blended blended blended Levels: classroom online blended > by(Data_Assignment7$outcome, Data_Assignment7$group, stat.desc) Data_Assignment7$group: classroom nbr.val nbr.null nbr.na min max range 10.00000000 0.00000000 0.00000000 5.47169811 6.69811321 1.22641509 sum median mean SE.mean CI.mean.0.95 var 61.69811321 6.22641509 6.16981132 0.12827722 0.29018323 0.16455045 std.dev coef.var 0.40564819 0.06574726 ---------------------------------------------------------------- Data_Assignment7$group: online nbr.val nbr.null nbr.na min max range 10.00000000 0.00000000 0.00000000 4.24528302 5.37735849 1.13207547 sum median mean SE.mean CI.mean.0.95 var 47.16981132 4.66981132 4.71698113 0.12340514 0.27916182 0.15228828 std.dev coef.var 0.39024131 0.08273116 ---------------------------------------------------------------- Data_Assignment7$group: blended nbr.val nbr.null nbr.na min max range 10.0000000 0.0000000 0.0000000 4.3396226 6.3207547 1.9811321 sum median mean SE.mean CI.mean.0.95 var 52.8301887 5.1415094 5.2830189 0.2118853 0.4793178 0.4489538

std.dev coef.var 0.6700401 0.1268290 group: classroom mean = 6.16981132, std.dev=0.40564819 group: online mean= 4.71698113, std.dev=0.39024131 group: blended mean= 5.2830189, std.dev=0.6700401 > leveneTest(Data_Assignment7$outcome, Data_Assignment7$group) Levene's Test for Homogeneity of Variance (center = median) Df F value Pr(>F) group 2 1.7343 0.1956 27 The data did meet the assumption of homogeneity of variance meaning that there is equal variance. The Levene test is ultimately testing the null. Here our P value is not smaller than .05 therefore showing that the variance is not significantly different from each other. > Learning.environmentANOVA<- aov(Data_Assignment7$outcome~Data_Assignment7$group, Data_Assignment7) > Learning.environmentANOVA Call: aov(formula = Data_Assignment7$outcome ~ Data_Assignment7$group, data = Data_Assignment7) Terms: Data_Assignment7$group Residuals Sum of Squares 10.725050 6.892132 Deg. of Freedom 2 27 Residual standard error: 0.5052367 Estimated effects may be unbalanced > summary(Learning.environmentANOVA) Df Sum Sq Mean Sq F value Pr(>F) Data_Assignment7$group 2 10.725 5.363 21.01 3.15e-06 *** Residuals 27 6.892 0.255 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 These are the values of the ANOVA

df=2, fvalue= 21.01, pvalue=3.15e-06 > eta_squared(Learning.environmentANOVA) For one-way between subjects designs, partial eta squared is equivalent to eta squared. Returning eta squared. # Effect Size for ANOVA Parameter | Eta2 | 95% CI -------------------------------------------- Data_Assignment7$group | 0.61 | [0.39, 1.00] - One-sided CIs: upper bound fixed at [1.00]. The results suggest a substantial effect of the independent variables on the dependent variable, with a high proportion of the variance explained. Eta squared = 0.61 which is relatively high. It suggests that approximately 61% of the variance in the dependent variable can be attributed to the group factor. Yes I will run a post hoc test because I have multiple groups. Running a post hoc test will help identify specific group differences and can limit the chances of a type 1 error as it is more likely for my results to have one becomes I have 3 variables. 5. The one-way ANOVA indicates a significant difference in the means among the groups (Data_Assignment7$group). The F-value of 21.01 with a very small p-value suggests that the observed differences are unlikely due to random chance. Therefore, you can reject the null hypothesis that the means of the groups are equal. In conclusion, there is strong evidence to suggest that there are significant differences in the outcome variable among the groups. 6. > pairwise.t.test(Data_Assignment7$outcome, Data_Assignment7$group, p.adjust.method = "holm") Pairwise comparisons using t tests with pooled SD data: Data_Assignment7$outcome and Data_Assignment7$group classroom online online 2.1e-06 - blended 0.0011 0.0186

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P value adjustment method: holm 7. "online" vs. "classroom" has a p-value of 2.1e-06 "blended" vs. "online" has a p-value of 0.0011. "blended" vs. "classroom" has a p-value of 0.0186. The p-value of 2.1e-06 for the "Online" vs. "Classroom" comparison is extremely small, showing a highly significant difference between these two groups in terms of the outcome variable. The p-value of 0.0011 for the "Blended" vs. "Online" comparison is also less than the significance level (0.05), suggesting a significant difference between these groups. The "Blended" vs. "Classroom" comparison has a p-value of 0.0186, which is significant after adjusting for multiple comparisons. This post hoc test showed me that the differences between groups and performance scores is significant. As well i learned that these differences are still significant even after adjusting for multiple comparisons.