In statistics, the association tests commonly conducted by researchers consist of tests of influence, relationship, and difference. Researchers often use the t-test to examine the mean difference between two sample groups. Typically, the measurement scale used in the t-test is the interval and ratio scales, which are normally distributed.
The next question is, what if the variables used by the researcher are non-parametric variables that are not normally distributed? If the measurement scale used by the researcher is ordinal or a higher scale where the normality test results indicate non-normal distribution, then the researcher can choose a difference test for non-parametric variables.
When conducting a difference test for two independent sample groups on a non-parametric variable measured on an ordinal scale, researchers may consider using the Mann-Whitney test. In this tutorial, Kanda Data will provide a step-by-step guide on how to perform a difference test for two independent sample groups on non-parametric variables using the Mann-Whitney test.
Assumptions of the Mann-Whitney test
As with statistical tests in general, when researchers choose to use a statistical test, they must consider its prerequisite assumptions. Although using non-parametric variables, researchers need to be aware that there are assumptions that need to be fulfilled in order to obtain unbiased estimates.
However, the assumptions for non-parametric variables are generally less complex compared to the assumptions for parametric variables. The main assumption that must be met in the Mann-Whitney U test is that the measurement scale of the variable is at least ordinal.
Therefore, if the measurement scale of the variable is ordinal, or if the researcher uses an interval/ratio scale but it is not normally distributed, the researcher can consider using the Mann-Whitney test.
Next, the second assumption is that the data comes from two sample groups. If the data comes from three or more sample groups, researchers should not consider using the Mann-Whitney test. Researchers can consider other non-parametric tests such as the Kruskal-Wallis test.
The third assumption is that the variables are independent or not paired. Thus, since the samples belong to different groups, it is not required for the compared sample sizes to be equal. Another assumption is that the variances of the two groups are equal or homogenous.
Case Study: Mann-Whitney Test
To provide a better understanding of how to conduct the Mann-Whitney test, in this case study, Kanda Data presents a research study aimed at determining the performance differences of fried chicken sales between Jakarta and Semarang.
There were 27 fried chicken outlets observed in this study, consisting of 15 outlets in Jakarta and 12 outlets in Semarang. Next, the researcher assigned scores to the outlet locations and sales performance categories as follows:
Outlet Locations:
1 = Jakarta
2 = Semarang
Sales Performance Category:
1 = Very poor
2 = Poor
3 = Acceptable
4 = Good
5 = Very good
Based on the research findings, the data was inputted into an Excel application. Subsequently, the researcher assigned scores based on the aforementioned criteria for outlet locations and sales performance. The inputted data and scoring performed by the researcher can be seen in the table below:
Creating the Research Statistical Hypotheses
Before providing a tutorial on the steps for conducting the Mann-Whitney test, researchers need to establish the statistical hypotheses. In line with the research objective of determining the performance differences in fried chicken outlet sales between Jakarta and Semarang, the null and alternative hypotheses are formulated.
The formulation of the statistical hypotheses is as follows:
Ho: The performance of fried chicken outlet sales in Jakarta is equal to the performance of fried chicken outlet sales in Semarang.
H1: The performance of fried chicken outlet sales in Jakarta significantly differs from the performance of fried chicken outlet sales in Semarang.
After formulating the null and alternative hypotheses, the next step is to establish the confidence interval for the research. In the above study, a confidence interval of 95% or a significance level (alpha) of 5% is applied. Therefore, the statistical hypotheses can be established as follows:
p-value > 0.05 = Ho is accepted.
p-value < 0.05 = Ho is rejected (accepting the alternative hypothesis).
Performing the Mann-Whitney Test in SPSS
In this tutorial, the Mann-Whitney U test will be analyzed using SPSS. The first step that researchers need to take is to set up the variable view in SPSS.
Please enter the variable names in the “Name” column. Then set the decimals to 0 and fill in the labels with complete information about the variable names.
Next, researchers need to set the values for the outlet locations and sales performance categories, assigning scores as mentioned earlier. A detailed description of setting up the variable view in SPSS can be seen in the image below:
Now, please click on “Data View” to input the data in SPSS. Since the analysis results and scoring have been previously inputted in Excel, you can directly copy and paste the data from Excel to SPSS.
Copy and paste the variables into the corresponding columns that have been set up in the variable view of SPSS. The next step is to perform the Mann-Whitney test using SPSS.
Click on “Analyze,” then select “Nonparametric Tests,” followed by “Legacy Dialogs,” and then choose “2 Independent Samples.” A window for the two independent samples test will appear.
Move the sales performance variable to the “Test Variable List” box and move the location variable to the “Grouping Variable” box. Define the groups by entering “1” for Group 1 and “2” for Group 2, then click “Continue.”
In step 4, for the “Test Type,” select “Mann-Whitney U.” To display descriptive statistics, click “Options” and enable “Descriptive,” and finally, click “Continue.” A detailed explanation of these analysis steps can be seen in the image below:
Mann-Whitney Analysis Output and Interpretation of Results
After completing all the analysis steps following the tutorial above, the output of the analysis will appear in SPSS. The analysis results include descriptive statistics and the Mann-Whitney test results. A detailed output of the Mann-Whitney test results can be seen in the image below:
Based on the image above, it is known that there are a total of 27 outlets in the outlet locations, with 15 fried chicken outlets in Jakarta and 12 fried chicken outlets in Semarang. The Mann-Whitney test result is 38.5 with a significance level of 0.007.
Let’s recall the hypothesis testing criteria as follows:
p-value > 0.05 = Ho is accepted
p-value < 0.05 = Ho is rejected (accepting the alternative hypothesis)
Based on the hypothesis testing criteria, it is known that the p-value of 0.007 is less than 0.05. Therefore, because the p-value is less than 0.05, the null hypothesis (Ho) is rejected.
Since the null hypothesis is rejected, we accept the alternative hypothesis. Thus, it can be concluded that the performance of fried chicken outlet sales in Jakarta significantly differs from the performance of fried chicken outlet sales in Semarang.
This is the tutorial article that Kanda Data can provide on this occasion. Hopefully, it is useful and provides insight to those who need it. See you in the next educational article!
