Chi-square test

Use chi-square tests to determine whether the distribution of observations for one variable differs depending on the category of the second variable.

In This Topic

Chi-square goodness-of-fit
Chi-square test of independence

Chi-square goodness-of-fit

Use a chi-square goodness of fit analysis to test whether an experimental profile is the same as or different than a baseline profile. For example, is the current accounts payable aging profile the same as or different than the accounts payable historical profile? The input data from the process must describe two separate profiles.

Answers the question:

Does the profile of my sample data match the baseline profile?

Guidelines

The results tell you whether the profiles are different. You must look at the raw data to determine the location of any differences and whether any observed differences are "good" or "bad."

How-to

In Minitab, enter the data as follows:

In the first column, enter the name of the categories:
- Example 1: <30 days, 30 to 60 days, 60 to 90 days, or over 90 days
- Example 2: Conservative, Liberal, Independent, or Unknown
In the second column, set up the baseline profile by entering either counts or percents for each category.
In the third column, set up the experimental profile by entering counts for each category.

For more information, go to Insert an analysis capture tool.

Chi-square test of independence

Use a chi-square test of independence to assess the observed differences in the rates of occurrence for a categorical output at different levels (settings) of an input. To use this test, the data for both variables (input and output) must be discrete or categorical. For example, X could be five different named hospitals and Y could be the likelihood of recovery (high, moderate, low, or unlikely).

Answers the question:

If the level of a discrete input changes, do the rates of occurrence of the possible outcomes also change?

When to Use	Purpose
Mid-project	Fixing an input at two or more different settings (levels) helps to determine which inputs have significant influence on the output profile (% by category).
Mid-project	Verify changes to inputs result in significant differences from the pre-project output profile.

Data

Your data must be a table containing the counts of each combination of the categorical X and Y values.

Guidelines

If an association exists between X and Y (low p-value), you must look at the chi-square contributions in the output table to locate any differences and look at the observed versus the expected values in the output table to determine if any observed differences are good or bad.

How-to

You can enter data in two ways:

Enter a table in Minitab with the levels of one variable as columns and the levels of the second variable as rows. Note: It does not matter which variable, X or Y, is the column and which is the row. Enter the counts of the XY combinations into the table as shown in this example:

Hospital

Chance of Recovery A B C

Good 78 45 98

Moderate 45 57 55

Poor 44 68 25
Enter raw categorical data in columns, one column for the y-variable, and a second column for the x-variable. In this case, both columns must be the same length. For example, enter the value of the y-variable, Status (on time, late), in one column and the value of the x-variable, Publication Type (fiction, nonfiction, reference), into a second column.

For more information, go to Insert an analysis capture tool.

	Hospital
Chance of Recovery	A	B	C
Good	78	45	98
Moderate	45	57	55
Poor	44	68	25