Question

A study that assessed the effectiveness of a new drug designed to reduce repetitive behaviors in children affected with autism was conducted. A total of 8 children with autism enrolled in the study and the amount of time that each child is engaged in repetitive behavior during three hour observation periods were measured both before treatment and then again after taking the new medication for a period of 1 week. The data is provided in the Excel spreadsheet. Using Minitab or other statistical software: 1. Conduct a Wilcoxon Signed Rank test to determine whether or not the medicine was effective in decreasing the median amount of time the child engaged in repetitive behavior. Include relevant output from Minitab and use a significance level of α = 0.05. 2. This test was to determine whether or not the drug decreased the median time the child was engaged in repetitive behavior in order to assess the effectiveness of the medicine. Do you think that the use of the median was appropriate in this case for the sample data set or could you have used two-sample paired t-test for the difference in the means? Answer this question by preparing a box plot to determine if there are any outliers in the differences and assessing the normality of the data set with both a probability plot and histogram and explaining your conclusion. 3. Regardless of your answer in part 2, conduct a two-sample paired t-test for the mean and determine whether or not the medicine was effective in decreasing the median amount of time the child engaged in repetitive behavior. Include relevant output from Minitab and use a significance level of α = 0.05. Is your conclusion different than testing the median? Explain briefly any differences.

Child	Before Treatment	After 1 Week of Treatment
1	85	75
2	70	50
3	40	50
4	65	40
5	80	20
6	75	65
7	55	40
8	20	25

Answer 1

1.

MTB > let c4=c2-c3
MTB > WInterval 95.0 'Difference'.

Wilcoxon Signed Rank CI: Difference

Method

η: median of Difference

Descriptive Statistics

Sample	N	Median	CI for η	Achieved Confidence
Difference	8	13.75	(0, 35)	94.13%

Since, estimated lie within confidence interval, we fail to reject H0.

The medicine was not effective in decreasing the median amount of time the child engaged in repetitive behavior.

2. I think that the use of the median was not appropriate in this case for the sample data set, we can use two-sample paired t-test for the difference in the means

3.3.

Paired T-Test and CI: Before, After

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Before	8	61.25	22.00	7.78
After	8	45.63	18.60	6.58

Estimation for Paired Difference

Mean	StDev	SE Mean	95% CI for μ_difference
15.63	21.45	7.59	(-2.31, 33.56)

µ_difference: mean of (Before - After)

Test

Null hypothesis	H₀: μ_difference = 0
Alternative hypothesis	H₁: μ_difference ≠ 0

T-Value	P-Value
2.06	0.078

Since p-value > 0,05, we fail to reject H0.

The medicine was not effective in decreasing the median amount of time the child engaged in repetitive behavior.