11.3.2 - Minitab: Test of Independence

Raw vs Summarized Data Section

If you have a data file with the responses for individual cases then you have "raw data" and can follow the directions below. If you have a table filled with data, then you have "summarized data." There is an example of conducting a chi-square test of independence using summarized data on a later page. After data entry the procedure is the same for both data entry methods.

Minitab 18

Minitab®  – Chi-square Test Using Raw Data

Research question: Is there a relationship between where a student sits in class and whether they have ever cheated?

  • Null hypothesis: Seat location and cheating are not related in the population. 
  • Alternative hypothesis: Seat location and cheating are related in the population.

To perform a chi-square test of independence in Minitab using raw data:

  1. Open Minitab file: class_survey.mpx
  2. Select Stat > Tables > Chi-Square Test for Association
  3. Select Raw data (categorical variables) from the dropdown.
  4. Choose the variable Seating to insert it into the Rows box
  5. Choose the variable Ever_Cheat to insert it into the Columns box
  6. Click the Statistics button and check the boxes Chi-square test for association and Expected cell counts
  7. Click OK and OK

This should result in the following output:

Rows: Seating Columns: Ever_Cheat
  No Yes All
Back 24 8 32
  24.21 7.79  
Front 38 8 46
  34.81 11.19  
Middle 109 39 148
  111.98 36.02  
All 1714 55 226
Chi-Square Test
  Chi-Square DF P-Value
Pearson 1.539 2 0.463
Likelihood Ratio 1.626 2 0.443


All expected values are at least 5 so we can use the Pearson chi-square test statistic. Our results are \(\chi^2 (2) = 1.539\). \(p = 0.463\). Because our \(p\) value is greater than the standard alpha level of 0.05, we fail to reject the null hypothesis. There is not enough evidence of a relationship in the population between seat location and whether a student has cheated.