27.2 Statistical Tests

Most of the relevant hypothesis tests in Minitab are found either under Stat > Basic Statistics or Stat > Nonparametics. The most relevant tests found under Stat > Basic Statistics are:

• 1 Sample Z
• 1 Sample t
• 2 Sample t
• Paired t
• 1 Proportion
• 2 Proportion
• 1 Variance
• 2 Variance
• Normality Test

You might notice that the tests found under Basic Statistics tend to be the tests used for discrete or normally distributed continuous data. The test for nonnormally distributed continuous data can be found under Stat > Nonparametrics.

Running Hypothesis Tests

Example 1: 1 Proportion Test Let’s look at a few examples of hypothesis tests in Minitab. We’ll look again at some of the problems discussed in the hypothesis testing chapter. Problem: A school administrator believes that the students in a certain classroom are being impacted by some environmental issue with that room. The administrator wants to see if the students in that room perform statistically lower on tests than the students throughout the school; she has already noted that different classes in that room are taught by other teachers. The administrator gathers data. The rate of failure for classes taught in any other classroom is 20 percent. Out of 142 students who have a class in the classroom in question, 38 are failing that particular class. Running Hypothesis TestsExample 1: 1 Proportion Test Let’s look at a few examples of hypothesis tests in Minitab. We’ll look again at some of the problems discussed in the hypothesis testing chapter. Problem: A school administrator believes that the students in a certain classroom are being impacted by some environmental issue with that room. The administrator wants to see if the students in that room perform statistically lower on tests than the students throughout the school; she has already noted that different classes in that room are taught by other teachers. The administrator gathers data. The rate of failure for classes taught in any other classroom is 20 percent. Out of 142 students who have a class in the classroom in question, 38 are failing that particular class.

The number of events is the number of outcomes that you are measuring. Here, the administrator was measuring failure rates, and there were 38 failures. The number of trials is the total number of data points. In this case, the school administrator looked at scores for 142 students. Check the box to perform a hypothesis test and enter the hypothesized proportion. In this case, you are comparing the actual failure rate of the classroom group to the overall failure rate of 20 percent. The hypothesized portion is written as a decimal between 0 and 1. Click Options.

Minitab usually defaults the confidence level to 95, which would set alpha at 0.05. Unless you have a specific need for greater confidence, you can leave this as is. Select the appropriate alternative hypothesis from the drop down menu. In this case, we are testing whether the proportion of our data is greater than the hypothesized proportion. Click OK. Click OK again. Minitab displays the results, including a p-value you can use to decide to reject or not reject the null hypothesis.

Example 2: 1 Sample T Test Problem: An agriculture company growing corn produced an average of 168 bushels of corn per acre each year for five years. The company made a change to its seeding process in an attempt to increase the yield of its fields. The harvest following the seed change resulted in an average of 175 bushels of corn per acre each year over 500 acres of fields. The standard deviation is 2.2 bushels. Did the seeding change result in a statistically different outcome in yield per acre? Select Stat > Basic Statistics > 1 Sample T. Choose summarized data.

Enter the sample size, sample mean, and sample standard deviation from the problem. Check the box to perform a hypothesis test and enter the hypothesized mean. In this case, you want to know whether the new mean is greater than the old mean, so the old mean is the hypothesized mean. Click Options. Choose the appropriate hypothesis test from the drop down menu.

Click OK. Click OK again.

Minitab displays the results, including a p-value you can use to decide to reject or not reject the null hypothesis. Example 3 – 2 – Sample T Test Copy the data from the table below into Minitab. If you recall from chapter 21, a law firm believed there was a statistical difference between the time employees on two different teams were spending on tasks.

Minutes Spent on Quarter-Hour Tasks
Attorney A’s Team	Attorney B’s Team
10	8
8	7
15	10
16	12
17	18
5	6
8	9
16	12
12	11
11	11
8	9
9	8
15	14
17	15
22	16
25	12
30	19
2	8
9	12
4	6
5	8
7	11
8	12
12	13
13	15
15	17
16	13
18	15
19	15
20	12
22	21
25	32
15	18
14	11

Select Stat > Basic Statistics > 2 – Sample T Test. From the drop down, select that each sample is in its own column. You can also choose to analyze samples when the data is all in one column or you can enter summarized data about each sample. Select the appropriate columns into the Samples 1 and 2 boxes. In this case, you are selecting the columns that hold the data for each of the teams. Click Options.

In this case, we only want to know if there is a difference between the two teams, so we’ll leave the alternative hypothesis as simply not equal to the hypothesized difference. In this case, we are assuming there is no difference, so we’ll leave the hypothesized difference as 0.

Click OK. Click OK again.

Minitab displays the results, including a p-value you can use to decide to reject or not reject the null hypothesis.

Hypothesis Test Steps Are Similar for all Types of Tests

All of the hypothesis tests in Minitab are run using basically the same steps as in the examples above. For most test types, you can choose to test the raw data or you can enter summarized data. Remember, each type of hypothesis test requires different summarized data. Proportion testing requires rates, means testing usually requires standard deviations and means of samples, and variance testing requires sample variance. Some of the tests you might use on data that isn’t normally distributed require the median instead of the mean. If you have the right descriptive statistics or have your data in columns in Minitab, it is a matter of a few clicks to set up and run a hypothesis test. The challenge isn’t in running, or interpreting, the tests. It is usually in determining which test is the right option for your data. It’s worth reviewing the information in chapter 21 again to understand what types of hypothesis tests are used with different data types and scenarios. It’s also important to test your data for normality before running hypothesis tests. Remember that you can easily test for normality by running the Graphical Summary under Basic Statistics. Some other things to keep in mind when dealing with hypothesis tests in Minitab are that you should always click the Options button to verify that your confidence interval is set appropriately and that the appropriate hypothesis test is selected. Minitab defaults to a confidence interval of 95% and an alternative hypothesis of not equal. However, if you are working during the same session – meaning you haven’t closed Minitab since the last time you ran that specific hypothesis test, the program will remember what settings you entered and apply them automatically to the new test you are running. This can be a problem if you want to run a test on different data or run a test on the same data with a different confidence interval or alternative hypothesis and you forgot to make the change. It’s also worth noting that a few of the means tests are also located under Stat > Equivalence Test.

If you are working in Minitab and have questions about these tests, you can access the Help menu for information about choosing, running, and interpreting each test. Select Help > StatGuide. The topics are organized just like the Minitab menus. Simply select the test you want help with and Minitab offers a dozen or so pages of help content for each.