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