** KOLMOGOROV AND SMIRNOV TEST**

**Introduction**

Statistical tests are used to analyze some aspects of a sample selected from a population. The results of the sample tests are then used to generalize the population; in other words, the sample results are required to represent the parameters of the population. Parametric statistical tests are used in the problem when the sample meets this requirement*. *The use of parametric statistics requires that the sample data should be normally distributed. So, checking the normality of the distribution of a variable is very important because parametric statistics require the normality condition of the population as a prerequisite. Kolmogorov and Smirnov Test is used to test the normality condition of the data.

**PROBLEM**

The distribution of marks of 12 college students selected at random is as follows.

**Table-1: **Sample Data

We want to test the normality condition of the distribution. The hypotheses for the problem are:

The hypotheses for the analysis are:

Null hypothesis-H_{0}: The distribution of marks is normal.

Alternative Hypothesis- H_{1}: The distribution of marks is not normal.

**Performing the Analysis with SPSS**

For SPSS Version 11, click on **Analyze ⇒** **Non parametric test ⇒1-Sample K-S. **This will bring up the SPSS screen dialogue box as shown below.

After clicking **1-Sample K-S, **this will bring up the following SPSS screen dialogue box

Select the variable **Marks** and click it to move to **Test Variable List** and click **Normal.**

Finally click OK to get the output.

**SPSS Output**

The SPSS output is as follows.

**DECISION**

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

**INTERPRETATION**

The p-value is 0.963 and it is more than 0.05 (**5% level of significance**), so we accept the null hypothesis and reject the alternative hypothesis at 5% level of significance. It is concluded that the mark is normally distributed.