Question

The data below are comparing two different methods of measuring blood alcohol concentration. Test the hypothesis that these two methods differ, with the assumption that these data are not normally distributed, with an α = 0.01. Which test would be most appropriate? Provide critical value and calculated test statistic, and then state your conclusion.

Subject	Method 1	Method 2
1	0.55	0.49
2	0.4	0.38
3	2.4	2.48
4	0.87	0.82
5	1.68	1.67
6	1.81	1.81
7	1.44	1.42
8	0.75	0.71
9	1.91	1.94
10	0.79	0.8
11	2.11	2.09
12	1.09	1.09
13	1.15	1.1
14	1.53	1.52

Answer 1

Since we do not know the distribution of the data values and taking the assumption that data values are not normal, the non-parametric method is used to test the hypothesis.

Mann Whitney U Test

The Mann-Whitney test is performed in the following steps in excel.

Step 1: Sort the combined value of both sample from smallest to largest,

Step 2: The rank for each data point is obtained using the excel function =RANK.AVG(). The screenshot is shown below,

Step 3: Now, place the rank for each data point in the table.

Method 1 (sorted)	Rank	Method 2(sorted)	Rank
0.4	2	0.38	1
0.55	4	0.49	3
0.75	6	0.71	5
0.79	7	0.8	8
0.87	10	0.82	9
1.09	11.5	1.09	11.5
1.15	14	1.1	13
1.44	16	1.42	15
1.53	18	1.52	17
1.68	20	1.67	19
1.81	21.5	1.81	21.5
1.91	23	1.94	24
2.11	26	2.09	25
2.4	27	2.48	28
Sum	206		200

Step 4: The sum of ranks for both old and new drug is,

Step 5: The U value for each method is obtained using the formulas,

Method 1

Method 2

Step 5: The critical value for U is obtained from the critical value table for n1 = 14 and n2 = 14 and significance level = 0.01,

Conclusion: Since the U value is greater than the critical value, at a 5% significance level, the null hypothesis is not rejected. Hence we can conclude that both the sample are from the same population.