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encouraging academics to share statistics support resources
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© Ellen Marshall and Tanya Waqanika
Sheffield Hallam University and University of Sheffield
stcp-marshall-normalityX
Checking normality in Excel
One of the assumptions for most parametric tests to be reliable is that the data is approximately
normally distributed. The normal distribution peaks in the middle and is symmetrical about the
mean. Data does not need to be perfectly normally distributed for the tests to be reliable. There
are several methods for checking normality which include graphical methods, tests for normality
and assessing skewness figures. It is not necessary to use all the methods; just select one or two.
Excel’s options are limited for methods for checking normality. A histogram can be constructed
using the standard ‘Data analysis toolpak’ add in package. You could use the ‘Real-statistics’ add
in package, http://www.real-statistics.com/tests-normality-and-symmetry/
or an online calculator
tool such as the webpage https://www.ai-therapy.com/psychology-statistics/distributions/normal
which contain more options. This sheet discusses the methods for checking normality and how to
obtain the output using the three methods.
Data for this sheet: Open the Excel file ‘NormX’
which contains two columns of data. The two
columns of data are not related and they will be
checked for normality separately. Comparing the
means (=AVERAGE(A:A)) and medians (=MEDIAN(A:A)) can help assess normality as for
skewed data they are very different. Here they are similar for the ‘normal’ data and quite different
for the ‘skewed’ data.
Graphical methods for assessing if data is normally distributed
will give an indication of the shape of the distribution and is the most commonly used. A normal
approximation curve can also be added by editing the graph. Below are examples of histograms
Histogram of approximately normally distributed data Histogram of skewed data
The following resources are associated:
Excel data file ‘NormX’ and ‘Additional toolpaks in Excel’
Checking normality in Excel
stats
tutor community project www.statstutor.ac.uk
It is very unlikely that a histogram of sample data will produce a perfectly smooth normal curve like
the one displayed over the histogram, especially if the sample size is small. As long as the data is
approximately normally distributed, with a peak in the middle and fairly symmetrical, the
assumption of normality has been met.
The normal Q-Q plot is an alternative graphical method of assessing normality to the histogram
and is easier to use when there are small sample sizes. The scatter should lie as close to the line
as possible with no obvious pattern coming away from the line for the data to be considered
normally distributed. Below are the same examples of normally distributed and skewed data.
Q-Q plot of approximately normally distributed data
Q-Q plot of skewed data
Tests for assessing if data is normally distributed
The Kolmogorov-Smirnov test and the Shapiro-Wilk’s W test are two specific methods for testing
normality of data but these should be used in conjunction with either a histogram or a Q-Q plot as
both tests are sensitive to outliers and are influenced by sample size:
• For smaller samples, non-normality is less likely to be detected but the Shapiro-Wilk test
should be preferred as it is generally more sensitive
• For larger samples (i.e. more than one hundred), the normality tests are overly conservative
and the assumption of normality might be rejected too easily.
Null hypothesis for test of normality: The data is normally distributed.
If the p-value is under 0.05, the null is rejected and there is significant evidence of non-normal data.
normal
skewed
For both of these examples, the sample size is 35 so the Shapiro-Wilk test should be used. For
the skewed data, p = 0.002 suggesting strong evidence of non-normality. For the approximately
normally distributed data, p = 0.585, so normality can be assumed and provided any other test
assumptions are satisfied, an appropriate parametric test can be used.
What if the data is not normally distributed?
If the checks suggest that the data is not normally distributed, there are two options:
• Transform the dependent variable (repeating the normality checks on the transformed data):
Common transformations include taking the log or square root of the dependent variable.
• Use a non-parametric test: Non-parametric tests are often called distribution free tests and
can be used instead of their parametric equivalent.
Checking normality in Excel
stats
tutor community project www.statstutor.ac.uk
Key non-parametric tests
Parametric test
What to check for normality
Non-parametric test
Independent t-test
Dependent variable by group
Mann-Whitney test
Paired t-test
Paired differences
Wilcoxon signed rank test
One-way ANOVA
Residuals/ dependent variable by group
Kruskal-Wallis test
Repeated measures ANOVA
Residuals at each time point
Friedman test
Pearson’s correlation coefficient
Both variables
Spearman’s correlation
Simple linear regression
Residuals
N/A
Note: The residuals are the differences between the observed and expected values.
Excel will not perform non-parametric tests even with the data analysis toolpak add in. Both AI-
therapy and the ‘Real-Statistics’ add in will though.
Using the data analysis toolpak
Although this is a standard Excel add in package, you will need to
add it via File > Options > Add-Ins (see ‘Additional toolpaks in Excel’
sheet for details). The ‘Data Analysis’ button then appears on the
Data menu.
Before creating the histogram decide on the cut-offs where the bars of the histogram meet (called
bins). It is better to specify these yourself as Excel chooses badly! Calculate the minimum and
maximum and create 5 -10 equally
spaced categories between the
minimum and a value above the
maximum.
Go to Data > Data Analysis and
select the ‘Histogram’ option from
the first menu which opens the
Histogram dialog box.
Input range: Select the data you
wish to plot in a histogram.
Bin Range: Select the upper cut
off’s you defined. Labels: Tick this if
the range includes the data name.
Output range: Where you want the
output to go.
Select the ‘Chart Output’ option and
click OK.
The frequencies for each of your specified ‘bins’
appear along with this chart. Excel does not appear
to know what a histogram is as the bars should meet
and the ‘bin’ labels should separate the bars!
However for the purposes of assessing normality, the
data can be seen to be approximately normal. If it’s
hard to tell, changing the number of bins can help so
choose different bin cut-offs and follow the procedure
again.
You must select ‘Chart
Output’ to get a histogram
Checking normality in Excel
stats
tutor community project www.statstutor.ac.uk
Using the real-statistics add in package
downloaded, you can access the menu from the ‘Add-Ins’ tab.
Select ‘Descriptive Statistics and Normality’ and click OK to open the following dialog box.
There’s a lot of output but
concentrate on the QQ-plot and the
Shapiro-Wilk to assess normality.
The Shapiro-Wilk p-value of 0.5847
is much bigger than 0.05 so
normality can be assumed. In the
QQ-plot the data points are close to
the line of the perfect normal
distribution also suggesting that the
data are approximately normally
distributed.
Using AI-therapy to check normality
Copy the data from the ‘normal’ column in the Excel file and add it to the ‘Data’
section of the webpage
https://www.ai-therapy.com/psychology-
statistics/distributions/normal.
If your data is skewed and a non-parametric test is needed, comparisons of two sets of data can
be accessed at https://www.ai-therapy.com/psychology-statistics/hypothesis-testing/two-samples
and for comparisons of more than two sets at:
https://www.ai-therapy.com/psychology-statistics/hypothesis-testing/anova
Cell where
output will begin
Ask for a QQ-plot as
well as default options
Copy the ‘normal’ column of data from Excel
and paste it in the ‘Data’ box
You can give the data set a name
and a description in these boxes
When finished, click
‘Submit Query’
