Normality Test of Kolmogorov-Smirnov Using SPSS

Normality testing is a common practice before the statistical method. Normality test is one part of the test data analysis requirements or can be called a classic assumption. The purpose of the normality test is to find out whether the distribution of a data follows or approaches a normal distribution, namely the distribution of data that has a pattern such as a normal distribution.

Probability Test of Normal Distribution

The basis for decision making can be based on normal data that can be measured by looking at the probability number (Asymptotic Significance), namely:

1. If the probability value > 0.05 then the distribution of the population is normal.

2. If the probability value <0.05, the population is not normally distributed.

Visual testing can also be done using the Normal Image Probability Plots method in the SPSS program. Basic decision making:

1. If the data spreads around the diagonal line and follows the direction of the diagonal line, it can be concluded that the regression model meets the assumptions of normality.

2. If the data spreads far from the diagonal line and does not follow the direction of the diagonal line, it can be concluded that the regression model does not meet the assumption of normality.

In addition, the normality test is used to find out that the data taken comes from a population with normal distribution. The test used to test normality is the Kolmogorov-Smirnov test. Based on this sample the null hypothesis will be tested that the sample originates from a normally distributed population against the rival hypothesis that the population is abnormally distributed.

As an example of this test, e-guides have a company's income statement data where the variables are Net Profit (Y) and Income (X). Where the data is as follows:

Years	Income (X)	Net Income (Y)
2014	Rp         8.810.164.143	Rp  4.505.095.216
2015	Rp         3.931.105.865	Rp      622.325.559
2016	Rp       12.275.751.456	Rp  8.844.480.929
2017	Rp       12.703.254.096	Rp  8.693.647.027
2018	Rp         5.703.315.375	Rp  1.650.685.099

How to Test Kolmogorov-Smirnov with SPSS

1.  The first step is to prepare the data to be tested in the form of an excel, docx, txt or other file to facilitate filling in the data on the SPSS worksheet. After that, open the SPSS program on your computer, then click Variable View and fill in the image below:

2. After that, click "Data View" and enter the data into each variable.

3. The next step, we will bring up the residual unstandardized value (RES_1) which we will then test for normality. The trick is to click Analyze  menu >> Regressions >> Linear. 

4. A dialog box will appear with the name "Linear Regressions", then input the Net Income variable to Dependent and the Income variable to Independent then save.

5. Then the dialog box appears again with the name "Linear Regression: Save", in the "Residual" section, check Unstandardized and ignore the other columns and choices. Next, click Continue and Ok.

6. Ignore the display of output that appears from the SPSS program. pay attention to the "Data View" view, a new variable appears with the name RES_1.

7. Now the final step is to test the Normality of the group using the Residual (RES_1) data that has been obtained previously. Select menu Analyze >> Nonparametric Test >> Legacy Dialogs >> 1-Sample K-S.

8. A dialog box appears called "One-Sample Kolmogorov-Smirnov Test". Next, enter the Unstandardized Residual (RES_1) variable into the Test Variable List box and in Test Distribution, check or select Normal. Then OK.

9. Now, pay attention to the results in the Output sheet it will look like this.

Interpretation of the Kolmogorov-Smirnov Normality Test with SPSS

Based on the SPSS output table, it is known that Asiymp.Sig (2-tailed) significance value is 0.200 greater than 0.05. So according to the basis of decision making in the Kolmogorov-Smirnov normality test above, it can be concluded that the data is normally distributed. Thus, the assumptions or normality requirements in the regression model have been fulfilled.

Note: In addition to comparing the Asiymp.Sig (2-tailed) value with 0.05, there are other ways to find out whether the regression model is normally distributed or not by comparing the z-calculated value of the SPSS result with the Z-table value.

This is the guideline on how to do the Kolmogorov-Smirnov normality test with the SPSS program.

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