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.


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-H0: The distribution of marks is normal.

Alternative Hypothesis- H1: 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.


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


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.

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