Question

Comparing two drugs . Makers of generic drugs must show that they do not differ significantly from the “reference” drugs that they imitate. One aspect in which drugs might differ is their extent of absorption in the blood. We have some data taken from 20 healthy nonsmoking male subjects for one pair of drugs. This is a matched pairs design. Numbers 1 to 20 were assigned at random to the subjects. Subjects 1 to 10 received the generic drug first, followed by the reference drug. Subjects 11 to 20 received the reference drug first, followed by the generic drug. In all cases, a washout period separated the two drugs so that the first had disappeared from the blood before the subject took the second. By randomizing the order, we eliminate the order in which the drugs were administered from being confounded with the difference in the absorption in the blood. We want to know: Do the drugs differ significantly in the amount absorbed in the blood? To answer this, complete the steps below.

Subj	Ref	Generic
15	4108	1755
3	2526	1138
9	2779	1613
13	3852	2254
12	1833	1310
8	2463	2120
18	2059	1851
20	1709	1878
17	1829	1682
2	2594	2613
4	2344	2738
16	1864	2302
6	1022	1284
10	2256	3052
5	938	1287
7	1339	1930
14	1262	1964
11	1438	2549
1	1735	3340
19	1020	3050

Explain how you know that this is a matched pairs t test. Be specific. ( Please use Excel)  

Your data is the difference between the amount of drug absorbed in the blood by the two drugs. Find the difference in absorption using Reference –Generic . You will then create a histogram of the differences.   Use bin limits starting at -2000 to 2500 in increments of 500. Show the table you used to create the histogram and the histogram with appropriate labels.

It is appropriate to use a matched pairs t-test here? Answer this question by reviewing the underlying assumptions for using t procedures.

Assuming that a matched pairs t-test is appropriate, complete the test by finding:

Ho:

Ha:

Find the test statistic using Excel

Find the pvalue of the test using Excel.

State your conclusion in practical terms using a significance level of 5%. Do the drugs differ significantly in the amount absorbed in the blood?

Answer 1

Following table shows the differences:

Subj	Ref	Generic	d=ref-generic
15	4108	1755	2353
3	2526	1138	1388
9	2779	1613	1166
13	3852	2254	1598
12	1833	1310	523
8	2463	2120	343
18	2059	1851	208
20	1709	1878	-169
17	1829	1682	147
2	2594	2613	-19
4	2344	2738	-394
16	1864	2302	-438
6	1022	1284	-262
10	2256	3052	-796
5	938	1287	-349
7	1339	1930	-591
14	1262	1964	-702
11	1438	2549	-1111
1	1735	3340	-1605
19	1020	3050	-2030

To make histigram go to excel Megastate -> Frequency dstributions ->quantitaive and add data as follows;

Following is the output:

Histigram shows that distributon is reasonable symmetric and have no outliers. So normality can be assumed.

Following is the output of paired t test:

Hypothesis Test: Paired Observations
	0.000	hypothesized value
	2,048.500	mean Ref
	2,085.500	mean Generic
	-37.000	mean difference (Ref - Generic)
	1,070.622	std. dev.
	239.398	std. error
	20	n
	19	df
	-0.15	t
	.8788	p-value (two-tailed)

Hypotheses are:

The test statistics is:

t = -0.15

The p-value is: 0.8788

Since p-value is greater than 0.05 so we fail to reject the null hypothesis. We cannot conclude that the drugs differ significantly in the amount absorbed in the blood.