how to do null hypothesis on minitab

How to Run a 2-Sample T Test in Minitab

When working with data sets in six sigma projects, often there will be a need to compare two groups to each other. A 2-sample T test in Minitab is a hypothesis test to study whether there is a statistically significant difference between the means of two populations. The 2-sample T test runs a comparison of two categories within the same categorical variable, which becomes valuable when trying to answer questions that involve understanding the effects of the addition of a program or change to a sample of subjects.

How to Run a 2-Sample t Test in Minitab

In this example, we will be using a 2-Sample t data file for Minitab. Clicking the previous link will download the file for your use. Once you have the file open in Minitab we will be comparing the price of gasoline between State A and State B. We will use a data set assuming that each data set is normally distributed with equal variances. The hypothesis will be: Null Hypothesis (H0): μ1 = μ2 Alternative Hypothesis (Ha): μ1 ≠ μ2

Where μ1 is the mean of one population and μ2 is the mean of the other population of our interest.

A new window named “Two-Sample t for the Mean” pops up.

Step 2:  Click in the blank box next to “Samples” and the “Gas Price” appears in the list box on the left.

Select “Gas Price” as the “Samples.”

Step 3:  Click in the blank box next to “Sample IDs” and the “State” appears in the list box on the left.

Select “State” as the “Sample IDs.”

Step 4:  Click options.

Check the box that says “Assume Equal Variances”

Click “OK” to save, and click “OK” again to run the test.

Results of our 2-Sample t Test in Minitab:

The study resutls of how to run a 2-sample t test in Minitab (when σ 1  = σ 2 ) appear automatically in the session window after clicking “OK.” Minitab's output is below. Take notice of a couple of important bits of information provided by the output. The mean of state A and state B, the number of data points for each state represented by 'N' as well as each standard deviation.

The key statistical output provided by Minitab when running a 2-sample t test is the P-Value. Since the p-value of the t-test (assuming equal variance) is 0.665, it's greater than the alpha level of 0.05. Therefore we fail to reject the null hypothesis which was (H0): μ1 = μ2. Our conclusion in this case is that the means of the two data sets are equal.

Join Our Community

Instant access to hundreds of "How to" articles, Tools , Templates , Roadmaps , Data-Files .. Everything Lean Six Sigma! Come on in! Welcome to our community of Lean Six Sigma certified professionals.

About Lean Sigma Corporation

Lean Sigma Corporation is a trusted leader in Lean Six Sigma training and certification, boasting a rich history of providing high-quality educational resources. With a mission to honor and maintain the traditional Lean Six Sigma curriculum and certification standards, Lean Sigma Corporation has empowered thousands of professionals and organizations worldwide with over 5,300 certifications, solidifying its position and reputation as a go-to source for excellence through Lean Six Sigma methodologies.

Best account I have seen of the 2 sample T test

very helpful

Get Our Career Advancement 9-Skills Checklist

9-skills checklist.

Remember Me

• EXPLORE Random Article

How to Perform a Normality Test on Minitab

Last Updated: January 31, 2020

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, volunteer authors worked to edit and improve it over time. This article has been viewed 37,603 times.

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.

Expert Q&A

You might also like.

• http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/introductory-concepts/normality/test-for-normality/
• https://en.wikipedia.org/wiki/Minitab

About this article

Did this article help you.

• About wikiHow
• Terms of Use
• Privacy Policy
• Do Not Sell or Share My Info
• Not Selling Info

What is a test statistic?

A test statistic is a random variable that is calculated from sample data and used in a hypothesis test. You can use test statistics to determine whether to reject the null hypothesis. The test statistic compares your data with what is expected under the null hypothesis. The test statistic is used to calculate the p-value.

A test statistic measures the degree of agreement between a sample of data and the null hypothesis. Its observed value changes randomly from one random sample to a different sample. A test statistic contains information about the data that is relevant for deciding whether to reject the null hypothesis. The sampling distribution of the test statistic under the null hypothesis is called the null distribution. When the data show strong evidence against the assumptions in the null hypothesis, the magnitude of the test statistic becomes too large or too small depending on the alternative hypothesis. This causes the test's p-value to become small enough to reject the null hypothesis.

For example, the test statistic for a Z-test is the Z-statistic, which has the standard normal distribution under the null hypothesis. Suppose you perform a two-tailed Z-test with an α of 0.05, and obtain a Z-statistic (also called a Z-value) based on your data of 2.5. This Z-value corresponds to a p-value of 0.0124. Because this p-value is less than α, you declare statistical significance and reject the null hypothesis.

• Minitab.com
• License Portal
• Cookie Settings

You are now leaving support.minitab.com.

Click Continue to proceed to:

• Quality Improvement
• Talk To Minitab

Data Not Normal? Try Letting It Be, with a Nonparametric Hypothesis Test

Topics: Hypothesis Testing , Data Analysis , Statistics

So the data you nurtured, that you worked so hard to format and make useful, failed the normality test.

Time to face the truth: despite your best efforts, that data set is never going to measure up to the assumption you may have been trained to fervently look for.

Your data's lack of normality seems to make it poorly suited for analysis. Now what?

Take it easy. Don't get uptight. Just let your data be what they are, go to the Stat menu in Minitab Statistical Software, and choose "Nonparametrics."

If you're stymied by your data's lack of normality, nonparametric statistics might help you find answers. And if the word "nonparametric" looks like five syllables' worth of trouble, don't be intimidated—it's just a big word that usually refers to "tests that don't assume your data follow a normal distribution."

In fact, nonparametric statistics don't assume your data follow any distribution at all . The following table lists common parametric tests, their equivalent nonparametric tests, and the main characteristics of each.

Nonparametric analyses free your data from the straitjacket of the  normality  assumption. So choosing a nonparametric analysis is sort of like removing your data from a stifling, conformist environment , and putting it into a judgment-free, groovy idyll , where your data set can just be what it is, with no hassles about its unique and beautiful shape. How cool is that , man? Can you dig it?

Of course, it's not quite that carefree. Just like the 1960s encompassed both Woodstock and Altamont , so nonparametric tests offer both compelling advantages and serious limitations.

Advantages of Nonparametric Tests

Both parametric and nonparametric tests draw inferences about populations based on samples, but parametric tests focus on sample parameters like the mean and the standard deviation, and make various assumptions about your data—for example, that it follows a normal distribution, and that samples include a minimum number of data points.

In contrast, nonparametric tests are unaffected by the distribution of your data. Nonparametric tests also accommodate many conditions that parametric tests do not handle, including small sample sizes, ordered outcomes, and outliers.

Consequently, they can be used in a wider range of situations and with more types of data than traditional parametric tests. Many people also feel that nonparametric analyses are more intuitive.

Drawbacks of Nonparametric Tests

But nonparametric tests are not  completely  free from assumptions—they do require data to be an independent random sample, for example.

And nonparametric tests aren't a cure-all. For starters, they typically have less statistical power than parametric equivalents. Power is the probability that you will correctly reject the null hypothesis when it is false. That means you have an increased chance making a Type II error with these tests.

In practical terms, that means nonparametric tests are less likely to detect an effect or association when one really exists.

So if you want to draw conclusions with the same confidence level you'd get using an equivalent parametric test, you will need larger sample sizes. 

Nonparametric tests are not a one-size-fits-all solution for non-normal data, but they can yield good answers in situations that parametric statistics just won't work.

Is Parametric or Nonparametric the Right Choice for You?

I've briefly outlined differences between parametric and nonparametric hypothesis tests, looked at which tests are equivalent, and considered some of their advantages and disadvantages. If you're waiting for me to tell you which direction you should choose...well, all I can say is, "It depends..." But I can give you some established rules of thumb to consider when you're looking at the specifics of your situation.

Keep in mind that nonnormal data does not immediately disqualify your data for a parametric test . What's your sample size?  As long as a certain minimum sample size is met, most parametric tests will be  robust to the normality assumption .  For example, the Assistant in Minitab (which uses Welch's t-test) points out that while the 2-sample t-test is based on the assumption that the data are normally distributed, this assumption is not critical when the sample sizes are at least 15. And Bonnett's 2-sample standard deviation test performs well for nonnormal data even when sample sizes are as small as 20. 

In addition, while they may not require normal data, many nonparametric tests have other assumptions that you can’t disregard.  For example, t he Kruskal-Wallis test assumes your samples come from populations that have similar shapes and equal variances.  And the 1-sample Wilcoxon test does not assume a particular population distribution, but it does assume the distribution is symmetrical. 

In most cases, your choice between parametric and nonparametric tests ultimately comes down to sample size, and whether the center of your data's distribution is better reflected by the mean or the median.

• If the mean accurately represents the center of your distribution and your sample size is large enough, a parametric test offers you better accuracy and more power. 
• If your sample size is small, you'll likely need to go with a nonparametric test. But if the median better represents the center of your distribution, a nonparametric test may be a better option even for a large sample.

You Might Also Like

• Trust Center

© 2023 Minitab, LLC. All Rights Reserved.

• Terms of Use
• Privacy Policy
• Cookies Settings