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How to Perform a Normality Test on Minitab

Last Updated: January 31, 2020

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Before you start performing any statistical analysis on the given data, it is important to identify if the data follows normal distribution. If the given data follows normal distribution, you can make use of parametric tests (test of means) for further levels of statistical analysis. If the given data does not follow normal distribution, you would then need to make use of non-parametric tests (test of medians). As we all know, parametric tests are more powerful than non-parametric tests. Hence, checking the normality of the given data becomes all the more important.

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1-Sample Hypothesis Test

To add output from a 1-sample hypothesis test, go to Add and complete a form .

In This Topic

1 proportion, 1-sample wilcoxon, 1 variance test, 1-sample sign.

For example, you can test whether a new setting significantly changes the proportion defective. To see an example, go to Minitab Help: Example of 1 Proportion .

Data considerations

Your data must contain only two categories, such as pass/fail. For details, go to Minitab Help: Data considerations for 1 Proportion .

For example, you can test whether the mean output from the controlled improved process is different from the pre-project mean. To see an example, go to Minitab Help: Example of 1-Sample t .

The data must be continuous and reasonably normal. A 1-sample t-test is robust to violations of the normality assumption, especially if the sample size is large (n > 25). For more details, go to Minitab Help: Data considerations for 1-Sample t .

For example, you can test whether the mean output from the controlled improved process is different from the pre-project mean. To see an example, go to Minitab Help: Example of 1-Sample Wilcoxon .

Your data must be a continuous value for Y (output). The data should come from a symmetric distribution, such as the uniform or Cauchy distributions. If your data do not come from a symmetric distribution, use a 1-sample sign test. For more details, go to Minitab Help: Data considerations for 1-Sample Wilcoxon .

For example, a quality analyst uses a 1 variance test to determine whether the variance of the moisture content in a shipment of unprocessed lumber is too high. To see an example, go to Minitab Help: Example of 1 Variance .

Your data must be continuous Y (output) values. For more details, go to Minitab Help: Data considerations for 1 Variance .

For example, you can test whether the mean output from the controlled improved process is different from the pre-project mean. To see an example, go to Minitab Help: Example of 1-Sample Sign .

• Use the 1-sample t-test when the data are reasonably normal (or the sample size is large).
• Use the 1-sample Wilcoxon test as an alternative to the 1-sample t-test as long as the data are reasonably symmetric.
• Use the 1-sample sign test as a last resort.
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What Should I Do If My Data Is Not Normal?

Topics: Lean Six Sigma , Six Sigma , Data Analysis , Statistics

One common question  Minitab trainers  receive is, "What should I do when my data isn’t normal?" A large number of statistical tests are based on the assumption of normality, so not having data that is normally distributed typically instills a lot of fear.

Many practitioners suggest that if your data are not normal, you should do a nonparametric version of the test, which does not assume normality. From my experience, I would say that if you have non-normal data, you may look at the nonparametric version of the test you are interested in running. But  more important , if the test you are running is not sensitive to normality, you may still run it even if the data are not normal.

What tests are robust to the assumption of normality? 

Several tests are "robust" to the assumption of normality, including t-tests (1-sample, 2-sample, and paired t-tests), Analysis of Variance (ANOVA), Regression, and Design of Experiments (DOE). The trick I use to remember which tests are robust to normality is to recognize that tests which make inferences about means, or about the expected average response at certain factor levels, are generally robust to normality. That is why even though normality is an underlying assumption  for the tests above , they should work for nonnormal data almost as well as if the data (or residuals) were normal. 

The following  example that illustrates this point.  (You can download the data set here and follow along if you would like.  If you don't have Minitab, download the free 30-day trial version, too.)  

Generating random data from a Gamma distribution with a scale of 1 and a shape of 2 will produce data that is bounded at 0, and highly skewed. The theoretical mean of this data is 2. It should be clear that the data is not normal—not even approximately normal!

What if I want to test the hypothesis that the population mean is 2? Would I be able to do it effectively with a 1-sample t-test? If normality is not strictly required, I should be able to run the test and have the correct conclusion about 95% of the time — or, in more technical terms, with roughly 95% confidence, right?

To test this, I am providing a little bit of code that will generate 40 samples from a Gamma (1, 2) and will store the p-value for a 1-sample t-test in column C9 of an empty worksheet. To reproduce similar results on your own, copy the following commands and paste them into Notepad. (Alternatively, you can download this file .) Save the file with the name “p-values.mtb”, and make sure to use the double quotes as part of the file name to ensure that the extension becomes MTB and not the default TXT.

Once the file is saved, choose Tools > Run an Exec . In Number of times to execute the file, enter a relatively large number, such as 1000 , and hit Select File , browse to the location on your computer where the p-values.MTB file is saved, and select the executable you just created. Click Open . Grab a cup of coffee, and once you get back to your desk, the simulation should be about done. Once the simulation is complete, create a histogram of column C9 (p-values) by choosing Graph > Histogram . This shows that the p-values are uniformly distributed between 0 and 1, just like they should when the null hypothesis is true.

What percentage of the time in the simulation above did we fail to reject the null?  In the simulation I ran, this happened in 95.3% of the instances.  Amazing, huh?  What does this really mean, though?  In layman’s terms, the test is working with approximately 95% confidence, despite the fact that the data is clearly not normal!  

For more on simulated p-values for a 1-sample t-test, be sure check out this recent post on “ p-value roulette .”

Note that if you’re following along and running your own simulation, the histogram and output above will most likely not match yours precisely. This is the beauty of simulated data—it’s going to be a little different each time. However, even with slightly different numbers, the conclusion you reach from the analysis should be about the same.

At this point, I hope you feel a little more comfortable about using these tests that are robust to normality, even if your data don't meet the normality assumption. The Assistant menu can also help you, as some of these “rules of thumb” are built into the Report Card, which informs you that this particular test would be accurate even with nonnormal data. 

It is also worth mentioning that the unusual data check in the Assistant even offers a warning about some unusual observations. These unusual observations could have been outliers if the data were normally distributed. In this case though, since we know this data was generated at random, we can be confident that they are not outliers, but proper observations the reflect an underlying nonnormal distribution.  

Whenever a normality test fails, an important skill to develop is to determine the reason for why the data is not normal. A few common reasons include:

• The underlying distribution is nonnormal.
• Outliers or mixed distributions are present.
• A low discrimination gauge is used.
• Skewness is present in the data.
• you have a large sample size.  

What tests are not robust to the normality assumption?

If tests around means are—in general—robust to the normality assumption, then when is normality a critical assumption? In general, tests that try to make inferences about the tails of the distribution will require the distribution assumption to be met. 

Some examples include:

1.     Capability Analysis and determining Cpk and Ppk 2.     Tolerance Intervals 3.     Acceptance Sampling for variable data 4.     Reliability Analysis to estimate low or high percentiles

The tests for equal variances also are known to be extremely sensitive to the normality assumption.

If you would like to learn how to assess normality by understanding the sensitivity of normality tests under different scenarios, or to analyze nonnormal data when the assumption is extremely critical, or not so critical, you should check out our new course on Analysis of Nonnormal Data for Quality .

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Normality Test in Minitab: Minitab with Statistics

Normality is one of the major concepts in statistics used for various statistical calculations. Normality Test helps one to determine whether a data is following a normal distribution or not. A normal distribution is a bell-shaped curve that is symmetric about its mean. The normal distribution is the most common statistical distribution because approximate normality arises naturally in many physical, biological, and social measurement situations. Many statistical analyses require that the data come from normally distributed populations. One can conduct a Normality test using Minitab . Minitab has statistical tools that allow one to perform statistical calculations with ease. Let’s have a look at the steps to perform a normality test using Minitab. Step 1: Go to File menu, click Open Project and then load the data to be analyzed. Step 2: Go to Start menu and then move to Basic Statistics. Step 3: Click on Normality Test and then enter the variables on the respective columns. Step 4: Click Ok. After clicking OK, Minitab generates the probability plot in a separate window. Example of conducting a Normality Test Taking the example of Cholesterol levels at fasting, before breakfast and after breakfast levels, let’s conduct a normality test.

Read more: Process Capability Analysis: Minitab with Statistics To know more about Normality Test, you can explore Simplilearn’s Minitab with Statistics Training. Simplilearn offers Minitab training course  online with Statistics.

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Minitab Quick Reference

Each screen in Minitab has a help button you can click for additional help. This document is intended to get you to the right place in Minitab, not be a comprehensive guide of how to use it.

Unit 1: The Basics

Stat » basic statistics » display descriptive statistics.

Used to summarize numerical data, find the mean, standard deviation, variance, etc. The by variables is an optional variable used to group the data. Use the statistics button to change what values are displayed. In particular, we will often turn on the variance.

Almost all of the graphs except for the graphical summary are found here.

Numerical Data

• Histogram is the most common. There is a with fit option to see if the 68-95-99.7 rule applies.
• Dot plots, stem-and-leaf plots, and box plots are other options

Categorical Data

• Pie charts are the most common graph for categorical data. The category variable represents the labels on the slices of the pie.
• A bar chart is another option for categorical data when the values don't make 100% of the choices or you can select more than one option.

Stat » Basic Statistics » Graphical Summary

This is a graph with multiple plots that show a lot of the information about a numerical variable. It includes a numerical summary, histogram, confidence interval, and test for normality.

Calc » Calculator

Used to transform the data or generate new variables.

Unit 2: Probability

Calc » make patterned data » simple set of numbers.

Create a list of numbers without having to type them all in.

Calc » Make Patterned Data » Text

Create a sequence using text. Separate your words with spaces. If there are spaces within your phrases, enclose them in quotes (Alien "American Pie" Jaws).

Calc » Random Data » Sample from columns

Useful for simulation purposes and sampling.

Calc » Probability Distributions » Binomial

Find binomial probabilities. The cumulative probability is the area to the left of the value and the probability is the chance of getting that value.

Graph » Probability Distribution Plot

Used to graph a distribution.

Calc » Probability Distributions » Normal

Find normal probabilities. This is easier done with the online probability calculator, but Minitab does allow you to specify a different mean and standard deviation.

Unit 3: Inferential Statistics

Stat » basic statistics.

Almost everything we do in this unit is a choice under basic statistics.

• 1 Sample t for confidence intervals for μ and hypothesis tests of form μ = 20.
• 2 Sample t for hypothesis tests of form μ 1 = μ 2
• Paired t for hypothesis tests of form μ d = 0
• 1 proportion for confidence intervals for p and hypothesis tests of form p = 0.23. Be sure to check "use normal approximation" under options.
• 2 proportions for hypothesis tests of form p 1 = p 2 . Be sure to check "use pooled proportion" under options.

Used to graph a distribution. Choose view probability when creating hypothesis testing graphs.

Graph » Probability Plot

Don't confuse this with the probability distribution plot. This is used to see whether a group of data has a particular distribution. We are usually checking for normality. The data has the distribution you're testing for if the points basically fall along the line with no systematic patterns or outliers.

Unit 4: Advanced Topics

Stat » tables » chi-square goodness-of-fit test (one variable).

Use this to perform the chi-square goodness of fit test.

Stat » Tables » Cross Tabulation and Chi-Square

Use this to perform a test for independence. Click the chi-square button and select the chi-square analysis.

Stat » ANOVA » One Way

Use this to perform a one-way ANOVA test. There should be two columns, one for the factor (grouping) variable and one for the response (numerical) variable. If you created a variable for each group, then use the unstacked test.

Stat » ANOVA » Two Way

Use this to perform a two-way ANOVA test. There should be three columns, two grouping variables for the row and column factors and one for the response (numerical) variable.

Graph » Scatterplot

Used to graph two paired numerical variables.

Stat » Basic Statistics » Correlation

Used to perform correlation between two or more variables.

Stat » Regression » Regression

Used to perform both simple and multiple linear regression.

Go to Math 113 homepage.

Last updated January 5, 2011 6:57 PM

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8.1.2.2 - minitab: hypothesis tests for one proportion.

A hypothesis test for one proportion can be conducted in Minitab. This can be done using raw data or summarized data.

• If you have a data file with every individual's observation, then you have  raw data .
• If you do not have each individual observation, but rather have the sample size and number of successes in the sample, then you have summarized data.

The next two pages will show you how to use Minitab to conduct this analysis using either raw data or summarized data .

Note that the default method for constructing the sampling distribution in Minitab is to use the exact method.  If \(np_0 \geq 10\) and \(n(1-p_0) \geq 10\) then you will need to change this to the normal approximation method.  This must be done manually.  Minitab will use the method that you select, it will not check assumptions for you!