To make objective decisions about the processes that are critical to your organization, you often need to examine categorical data. You may know to use a t-test or an ANOVA when you compare measurement data (like weight, length, revenue, and so on), but do you know how to compare attribute or counts data?
One person may look at this bar chart and decide that each line produced the same proportion of defects. But another person may focus on the small difference between the bars and decide that one of the lines has outperformed the others. Without an appropriate statistical analysis, you cannot know which person is right.
Here, you can see that some brands of soap seem to be favored by men, while others are preferred by women. But how much does soap preference truly rely on gender? Are these groups related at all?
When time, money, and quality depend on your answers, you can’t rely on subjective visual assessments alone. To answer questions like these with statistical objectivity, use a Chi-Square analysis. In this article, we’ll discuss the different types of Chi-Square analyses and show how easy it is to use them in Minitab.
Which Analysis Is Right for Me?
Minitab offers three Chi-Square analyses. The appropriate analysis depends on the number of variables that you want to examine and the way that your data are organized.
Chi-Square Goodness-of-Fit Test (One Variable)
Choose this analysis when you want to analyze just one variable that is organized either as raw data or as a frequency table.
Raw Data
Frequency Table
The Chi-Square Goodness-of-Fit Test can tell you whether the proportions of all the groups are equal or whether the proportions of each category are equal to specific values. For example:
- A company that rents moving trucks owns 65 small trucks, 150 medium trucks, 100 large trucks, and 50 extra large trucks. The rental company uses the Chi-Square Goodness-of-Fit Test to determine whether the proportion of trucks that they own in each size matches customers’ requests.
- A bottle cap manufacturer operates four production lines and records which line produced each defective cap. The manufacturer uses the Chi-Square Goodness-of-Fit Test to determine whether each line produced the same proportion of the total defects. Any difference in the proportions could mean that one of the lines is malfunctioning.
Chi-Square Test (Two-Way Table in Worksheet)
Choose this analysis when you have two variables that are summarized in a two-way table.
In a two-way table, the categories of the first variable are listed left to right. In this example, the first variable is gender (Boys, Girls). Each row corresponds to a different value in the second categorical variable. In this example, the second variable is program (A, B, or C).
A Chi-Square Test allows you to test for an association between two variables. Here are two examples:
- A company that specializes in clothing for girls wants to advertise its products during a children’s TV program. The company’s advertising firm uses a Chi-Square Test to determine whether the girls’ preferences for any TV programs differ significantly from the boys’ preferences.
- A credit card billing center records the type of billing error that is made, as well as the type of form that is used. The billing center uses a Chi-Square Test to determine whether certain types of errors are related to certain forms.
Cross Tabulation and Chi-Square
Choose this analysis when you have two or more variables that are organized either as raw data or as frequency data.
Raw Data
Frequency Table
If you simply want to test for associations between two variables, you can choose between a Cross Tabulation and Chi-Square analysis and a Chi-Square Test based on the layout of your data. However, Cross Tabulation and Chi-Square also lets you control for the effect of additional variables. Here’s an example:
- A dairy processing plant records information about each defective milk carton that it produces. The plant uses a Cross Tabulation and Chi-Square analysis to look for dependencies between the types of defect and the machine that produces the carton, while controlling for any effect of Shift. Perhaps a particular filling machine is prone to a certain type of defect, but only during the first shift.
This analysis also offers advanced options for particular cases. For example, if your categories are ordinal (good, better, best; small, medium, large) you can include a special test for concordance.
Conducting a Chi-Square Analysis in Minitab
Each analysis is easy to run as long as you’re aware of how your data are organized.
Chi-Square Goodness-of-Fit Test
- Choose Stat > Tables > Chi-Square Goodness-of-Fit Test (One Variable).
- If you have frequency data, choose Observed counts. If you have raw data, choose Categorical data.
- Enter your data.
- Under Test, choose whether to test for equal proportions among all categories, for specific proportions, or for proportions determined by counts.
- From the drop down, choose to specify the hypothesized proportions or the counts with an Input column or with individual Input constants.
- Enter the hypothesized values and click OK.
Chi-Square Test (Two-Way Table in Worksheet)
- Choose Stat > Tables > Chi-Square Test (Two-Way Table).
- In Columns containing the table, enter the columns that contain the summary data and click OK.
Cross Tabulation and Chi-Square
- Choose Stat > Tables > Cross Tabulation and Chi-Square.
- Enter one column in For rows and one column in For columns. If you have additional columns of categorical variables that you want to control for, enter them in For layers.
- Click Chi-Square and check Chi-Square analysis.
- Choose any other display items or tests that you want to add, and then click OK in each dialog box.
Putting It to Use
It may be tempting to make subjective assessments about the groups within your data, their makeup, and possible interdependencies. But why risk an error in judgment when a Chi-Square analysis is so simple? Whether you’re interested in one variable, two variables, or more, Minitab has a Chi-Square analysis that can help you make a clear, statistically sound assessment.
