Question

You are interested in studying the neurological effects of dehydrogenated brominate oil, a food additive. You randomly select 25 Sprague-Dawley rats and add a dosage to their drinking water. Because the additive is odorless and colorless, the rats readily consume it. After six months you sacrifice the rats, microsection their brains and count the number of lesions in the hippocampus.

15mg	20mg	25mg	30mg	35mg
17	12	15	19	8
7	17	18	28	10
15	10	18	22	13
11	18	22	19	15
9	18	19	17	12

What is the null hypothesis?

What is the alternative hypothesis?

Perform the analysis manually or using Excel or r. What is the significance value?

Show the ANOVA summary table

Is there is significant difference? Explain.

Perform a post-hoc comparison, either manually or using r. Which post hoc differences are significant?

What do you conclude based on the primary and post-hoc analyses?

Answer 1

Null Hypothesis: Ho:4 = 4y = Uz = 44 = Ils That is, there is no mean difference between the dosages of Sprague-Dawley rats. Alternative Hypothesis: H:Atleast one u is different That is, there is a mean difference between the dosages of Sprague-Dawley rats. Excel add-in (Mega Stat) procedure:

Step 1: In EXCEL, Select Add-Ins > Mega Stat > Analysis of Variance Step 2: Choose One-Factor ANOVA. Step 3: In Input Range, enter the column of Al:E6. Step 4: In Post-Hoc Analysis. Choose When p <0.05. Step 5: Click OK Excel add-in (Mega Stat) output: One factor ANOVA n Mean 11.8 15.0 18.4 21.0 5 5 5 5 5 Std. Dev 4.15 15mg 3.74 20mg 2.51 25mg 4.30 30mg 2.70 35mg 4.97 Total 6 15. 2 ANOVA table Source SSdf Treatment 338.96 4 Error 253.20 20 Total 592.16 - 24 MSF 84.740 6.69 12.660 p-value .0014 The significance level is 0.05.

Conclusion: Use a significance level, a = 0.05. Here, p-value is 0.0014, which is less than the value of a -0.05. That is, p-value = 0.0014) sal=0.05). Therefore, by the rejection rule, reject the null hypothesis H. Interpretation: There is sufficient evidence at level of significance a = 0.05. That is, there is a mean difference between the dosages of Sprague-Dawley rats.

25mg 18.4 30mg 21.0 Post hoc analysis p-values for pairwise t-tests 35mg 15mg 20mg 11.6 11. 8 1 5.0 35mg 11.6 15mg 11.8L .9301 20mg 15.0 L .1465 .1704 25mg 18.4 006700821465 30mg 21.0 .0005 .0006 0148 A 2616 The means of dosage of 25mg and 35mg are significantly different. The means of dosage of 30mg and 35mg are significantly different. The means of dosage of 25mg and 15mg are significantly different. The means of dosage of 30mg and 15mg are significantly different. Comparison: There is a mean difference between the dosages of Sprague-Dawley rats.