Using the picture with the data below: Conduct an ANOVA statistical analysis. Wh

Question

Using the picture with the data below: Conduct an ANOVA statistical analysis. While doing this, add in the Bonferroni post box at the .05 level.

1) what is the output for the ANOVA. 2) what is F and what can we conduct from it in this case? 3) calculate the effect size and list it here along with whether it is a small, medium, or large effect size. 4) what is the post hoc output? 5) what are the sources of the differences based on the post hoc output? (Hint: which two groups have the signicant mean differences?) 6) what did you find in this research?
Dr. Good has three study groups in his class and he wants to know how significant the differences are in the groups'exam scores. The study groups are different in that they studyfor different amounts of hours, group 1-5 hours, group 2 = 7 hours, and group 3-10 hours per week. Data: Group Test Score 80 78 76 89 79 80 82 79 83 86 87 89 80 79 90 1 2 2 2 2 91 90 89 87 95 97

Explanation / Answer

(1)

> group <- c(1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3)
> testscore <- c(80,78,76,89,79,80,82,79,83,86,87,89,80,79,90,87,91,90,89,87,95,97,99,77)
> test <- aov(testscore ~ group)
> summary(test)
Df Sum Sq Mean Sq F value Pr(>F)   
group 1 420.2 420.2 16.71 0.000487 ***
Residuals 22 553.4 25.2
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(2)

F = 16.71

p-value = 0.000487

which is significant

We reject the null hypothesis of equality of means of test scores among the 3 groups.

Thus, we conclude that the mean test scores is not equal among the 3 groups.

(3)

Effect size

= SS group / (SS group + SS residual)

= 420.2 / (420.2 + 553.4)

= 0.4315941

This is a medium effect size.

(4)

Post-hoc output:

> pairwise.t.test(testscore, group, p.adjust.method = "bonferroni")

Pairwise comparisons using t tests with pooled SD

data: testscore and group

1 2   

2 0.234 -   

3 0.002 0.132

P value adjustment method: bonferroni

(5)

The p-value for the comaprison between group 1 and group 3 is 0.002 which is less than significance level 0.05

So, the groups 1 and group 3 have the significant mean difference.

(6)

Conclusion:

There is a significant difference between the student's scores of the groups of students who study 5 hrs a week and those who study 10 hrs a week.

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.