Testing for Normality

Many specific tests exist for testing for normality, for example:

1. Goodness-of-Fit Tests (e.g., Kolmogorov-Smirnov Test)
2. Graphical Assessment of Normality (probability plots)
3. Shapiro-Wilk's Test (W-statistic)
4. D'Agostino Test (D-statistic)

Approaches Discussed Today:

        1. NormQuant (download)
        2. XLSTAT-PRO (SC118)

1. NormQuant
Professor Scott Guth at Mt. San Antonio College is going to help us out with #1 and #2 above.  [If you're dying to try out #3 and #4, visit SC118 and run with XLSTAT-Pro.]  Dr. Guth has brought a test to your desktop without charging you an arm and a leg, in fact, it's free!  Can't beat that!!!
All you need to do is download his Excel file called NormQuant.xls and then add your data to the spreadsheet.  The program will tell you if your data conform to a normal distribution ( :-)), or not ( :-( ).

Download NormQuant.xls

Let's not forget the hypotheses:
Ho: The sampled population is normally distributed.
HA: The sampled population is not normally distributed.

This is what the file will look like, without the yellow scribbles.

All you need to do is:
1. In a separate Excel file (e.g., your data file) sort your data in ascending order.  Note: When testing for normality, be sure to run each group (population) separately.  Recall, for example in ANOVA, you are comparing a number of normal curves along an axis.  Each normal curve must obviously be a "normal curve."
[To do this select from the top menu Data and then Sort.  Be sure the correct column is selected before sorting].

2. Copy and paste the sorted column of data into the first column above.  Just click on the first existing entry and then paste.  The new numbers will appear correctly.

3. Check out what the outcome is in the alpha = 0.05 column.

4. Also check out the Normal Quantile Plot; if your data set is normally distributed the plot will approximate a straight line.  [A leptokurtic distribution (on the skinny side of normality) will exhibit a sigmoid (s-shaped) plot, whereas a platykurtic distribution (on the broad side of normality) will appear as a reverse sigmoid curve.

5. If you want to test another set of data, Edit/Unpaste the data you first added and then add your new set. Otherwise you may get an error stating that it's a read-only file and that you can't modify it without a password.

This is the response you get if your data set is not randomly distributed:

Looking at the plot you'll notice that your data set is pretty heavy on the high end which would suggest that your data set is skewed to the left.

Although it requires hiking over to SC118, this program is a quick way to test for normality.  You have already used XLSTAT-PRO to run ANOVA and pairwise comparisons.  Testing for normality is just a different option within the program.  The following illustrations should easily lead you down the right path.


All in all...
being normal is a good thing, at least in statistics!