** MANN-WHITNEY TEST OR U TEST**

**INTRODUCTION**

The test is used to examine whether two samples have been drawn from the same population or not. This test is an alternative to‘t’ test for testing the equality of means of two independent samples; provided the samples are small (sample size is maximum 30). It is a widely used statistical analysis as it does not require the assumption that the samples are drawn from the normal population.

**CASE ANALYSIS- 1**

**PROBLEM**

The zonal manager of Amul India Company wants to compare the average sales of Amul Spray in two districts A and B.

The hypotheses for the analysis are:

Null hypothesis-H_{0}: The average sales in two districts are equal

Alternative Hypothesis- H_{1}: The average sales in two districts are not equal **(two tailed test)**

**Input Data**

The data collected randomly from 25 retail shops of two districts A and B are given in the following table. The test variable is the average sales in kg. and it should be numeric data. The district is a group variable or coded variable. (Code = 1 for district A and code = 2 for district B)

**Table-1:** Input Data

**Performing the Analysis with SPSS**

For SPSS Version 11, click on **Analyze ⇒ ****Non parametric tests ⇒ 2- Independent Samples. **This will bring up the SPSS screen dialogue box as shown below.

After clicking **2- Independent Samples, **this will bring up the following SPSS screen dialogue box.

Select the variable and move it to the **Test variable list** box. Select the coded variable and move it to Grouping variable box.

Define the groups of values of the grouping variable by clicking on **Define** **Groups** just below the grouping variable box. This will bring up the **dialogue box** as shown above. Code 1 is used for district A and code 2 is used for district B. Now click button **Continue. **This will bring **Two-independent sample- tests **dialogue box as shown below.

Now, click on **Mann-Whitney U **and then OK**.**

**SPSS Output**

The SPSS outputs of the analysis are depicted in table-2 and table-3.

**Mann-Whitney Test**

**Table-2:** Ranks

**Table-3:** Test Statistics

* a Not corrected for ties.*

* b Grouping Variable: district*

**From the output, Mann-Whitney U = 66.500**

**DECISION**

Reject the null hypothesis if p-value is (Asymp. Sig. (2-tailed)) ≤ 0.05

** ****INTERPRETATION**

The p-value is in this case is 0.531, which is higher than 0.05 (5% level of significance). So, there is not much evidence to reject the null hypothesis at 5% level of significance. In other words the average sales in two districts are equal.

**CASE ANALYSIS- 2**

**PROBLEM**

A pharmaceutical company wants to test the effectiveness of its drug A in reducing the weights. The purpose is to test the claim that drug A can reduce the weight more effectively as compared to another drug B existing in the market.

The hypotheses for the analysis are:

Null hypothesis-H_{0}: The average decrease in weights using drugs A and B are equal.

Alternative Hypothesis- H_{1}: The average decrease in weight using drug A is less than the average decrease in weight using drug B. **(single tailed test)**

**Input Data**

For the purpose of testing, 30 people were randomly selected and 17 of them were subjected to drug A and 13 with drug B. The decrease in weight in kg. is given below.

**Table-1:** Input Data

**SPSS Output**

**Mann-Whitney Test**

**Table-2:** Ranks

* a Not corrected for ties.*

* b Grouping Variable: Drug*

**From the output, Mann-Whitney U = **80.500

**DECISION**

Reject the null hypothesis if p-value is (Asymp. Sig. (2-tailed)) ≤ 0.05

The p-value for one-tailed test would be .

**INTERPRETATION**

The p-value is 0.206/2= 0.013 is less than 0.05 (5% level of significance). So, we reject the null hypothesis and accept the alternative hypothesis at 5% level of significance. It can be concluded that the drug A can reduce the weight more effectively.

**SPSS command **

- Click on ANALYZE at the SPSS menu bar (in older versions of SPSS, click on STATISTICS instead of ANALYZE).
- Click on NONPARAMETRIC TEST followed by 2 INDEPENDENT SAMPLES.
- Select the test variable and move it TEST VARIABLE LIST box. Similarly select the coded variable and move it to GROUPING VARIABLE BOX followed by DEFINE GROUPS. Fill in the box with appropriate codes and click CONTINUE.
- Click MANN-WHITNEY U TEST.
- Select OK of the main dialogue box.