In order to test for normality with Kolmogorov-Smirnov test or Shapiro-Wilk test you select analyze, Descriptive Statistics and Explore. After select the dependent variable you go to graph and select normality plot with test (continue and OK). Among Q-Q plots and boxplot you have a table with Kolmogorov-Smirnov test or Shapiro-Wilk test results.

Here is a link where it is nicely explained about K-S test!

Normality can also be observed -

- by Shapiro- Wilk test- Comes with K-S test in SPSS

- By observing normal Q-Q Plot of Time

- By observing Histogram of the data

- By observing the box plot of the data

- by observing the scatter plot of the data

https://statistics.laerd.com/spss-tutorials/testing-for-normality-using-spss-statistics.php

In order to test for normality with Kolmogorov-Smirnov test or Shapiro-Wilk test you select analyze, Descriptive Statistics and Explore. After select the dependent variable you go to graph and select normality plot with test (continue and OK). Among Q-Q plots and boxplot you have a table with Kolmogorov-Smirnov test or Shapiro-Wilk test results.

For statistical tests, I would suggest you to try R-statistical software. It can give you the output with readily available functions and packages.

Alternate ways of testing normality:

1. Draw a histogram of the responses. You get a fair idea about the normality.

2. Q-Q plots. http://www.itl.nist.gov/div898/handbook/eda/section3/qqplot.htm

3. Check kurtosis and skewness. General rule of thumb for normality- kurtosis ~3; Skewness : -1 to 1.

On a side note, K-S is a very conservative test. Even if there are small deviations, it may affect your result. Chi square test is another option, which may not be much affected by small deviations. Selection of test depends on the extend to which the assumption of normality must be true. In many cases, especially in linear regression, I have read that assumption of normality (of errors) is not strictly followed, Hope this helps.

http://www.itl.nist.gov/div898/handbook/eda/section3/qqplot.htm

Hello, 

To check normality, I am inclined on not only using KS or Shapiro tests. It is also important to check graphically what is happening. Maybe check in a histogram you kurtosis and skewness to see how your data is behaving. 

My advice would be to combine techniques, look at your data (with histograms), use significant testing such as KS model of fit and finally decide. 

Always take into account that not many things are really normally distributed, the world is a bit more complex. 

As stated above, if you are going to do a linear regression normality is important but in won't change dramatically if your distribution is a bit skewed. Regression are robust enough to handle that, the important thing is that the association is linear. 

Hope this helps,

Regards

One problem I have with normality tests in SPSS is that the Q-Q plots don't have confidence intervals so are very hard to interpret. Also agree with the comment re the K-S test . I've taken to doing normality testing using minitab which gives CI's and uses the anderson-darling test.

Please see link regarding normality tests. 

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3693611/

Thank you everyone for your helpful answers !

According to Ghasemi & Zahediasl (2012), if the p values of the variables are less than 0.05, the data are not normally distributed. Since the p values of the three variables in my study (I am just using 3 variables as an example) are less than 0.05, the data of these three variables are not normally distributed. 

Is that right? When the data are not normally distributed, can independent T-tests still be conducted to compare the differences between two groups of participants?  If not, what are the alternatives to T-tests?

 Please see the attached file for the output of test of normality of 3 variables.

(N=167 in my study)

Thanks in advance !

Ghasemi, A. & Zahediasl, S. (2012). Normality Tests for Statistical Analysis: A Guide for Non-Statisticians. Int J Endocrinol Metab. 10(2):486-9. Retrieved on March 20,2015 from

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3693611/

I tried running the tests of normality on the first 5 items of my survey (which has 50 items in total). Attached is the output.

How come all of the p values of these five items are 0.000 ? Does it mean that

 the data of these five items are not normally distributed ?

Thank you for your attention to my questions!

Looking at yout doc the data is not normally distributed but your ssmple size is >40 and even if normality assumption is violated it should not cause a problem. So you can di independent sample T-test or the non parametric Mann Whitney test.

Jeganathan,

Thanks for your answer !

Is there a citation reference of what you just said above?

I need to cite a reference for that.

Thanks.