How to Solve Crosstab and Homogeneity Assignments Using Minitab

• Row variable (GG): Represents the treatment group (Gamma globulin or Aspirin).
• Column variable (CA): Represents the outcome (presence or absence of coronary abnormalities).

Assigning GG as the row and CA as the column ensures a logical representation of the data.

Enabling Required Display Options

To ensure a complete statistical output:

1. Navigate to Stat > Tables > Cross Tabulation and Chi-Square.
2. In the Cross Tabulation window, assign the row and column variables.
3. Under the Display tab, make sure both “Row percents” and “Column percents” are selected. These percentages are critical for interpreting data in context.

This setup provides a compact and informative view of the relationships within the dataset.

Running Chi-Square and Fisher’s Exact Test in Minitab

Once the table is set, statistical testing helps validate whether any observed association is statistically significant.

Enabling Chi-Square Test Options

Minitab allows users to perform a Chi-square test of homogeneity directly:

1. Open the Chi-Square settings window.
2. Check Chi-Square analysis and Expected cell counts.

These options are essential for computing the test statistic and evaluating whether the differences between observed and expected values are due to chance.

Including Fisher’s Exact Test for 2x2 Tables

When working with a 2×2 contingency table and small sample sizes (expected frequencies < 5 in any cell), Fisher’s Exact Test provides more reliable results.

1. In the Other Statistics section, enable Fisher’s exact test for 2x2 tables.
2. Click “OK” to execute the analysis.

The results will include both the Chi-square output and Fisher’s test, allowing students to choose the appropriate method based on their data characteristics.

Interpreting the Chi-Square Test of Homogeneity

The Chi-square test evaluates whether the proportions of a certain characteristic are the same across different groups.

Formulating Hypotheses for the Test

A key component of any assignment is setting up the correct hypotheses:

• Null hypothesis (H0): The proportions are the same across treatment groups (p₀ = p₁ or RR = 1).
• Alternative hypothesis (Ha): The proportions differ (p₀ ≠ p₁ or RR ≠ 1).

In our example, the goal is to determine if coronary abnormalities occur at the same rate for Gamma globulin and Aspirin treatments.

Analyzing the Test Statistic and p-value

After running the Chi-square test, the following output may be observed:

• Chi-square value (χ²): 11.436
• Critical value at α = 0.05: 3.84
• p-value: 0.001

Since the test statistic exceeds the critical value and the p-value is less than 0.05, we reject the null hypothesis. This indicates a statistically significant difference in coronary abnormality rates between the two treatment groups.

Evaluating Fisher’s Exact Test and Risk Estimation

Fisher’s Exact Test is especially valuable when working with small samples. It confirms the presence or absence of association without the assumptions required for Chi-square tests.

Applying Fisher’s Exact Test to Small Samples

In the example data:

• Gamma globulin group: 6% developed abnormalities
• Aspirin group: 25% developed abnormalities

The difference suggests a potential treatment effect. With expected cell frequencies below 5, Fisher’s Exact Test becomes the preferred option.

• Null hypothesis (H0): RR = 1
• Alternative hypothesis (Ha): RR ≠ 1
• p-value: 0.001

Given that the p-value is lower than the standard threshold (0.05), the test supports the rejection of the null hypothesis. The treatment with Gamma globulin appears significantly more effective in reducing abnormalities.

Calculating the Estimated Risk and Relative Risk

Risk and relative risk are central concepts in such assignments:

• Overall abnormality risk: 26 out of 167 = 0.1157
• Expected abnormalities in Gamma group: 0.1157 × 83 = 9.6031
• Estimated RR: 0.06 / 0.25 = 0.24

These calculations not only confirm statistical significance but also allow for a meaningful interpretation in real-world terms. A relative risk of 0.24 means that patients treated with Gamma globulin have only 24% of the risk compared to those treated with Aspirin.

Writing Clear Conclusions for Assignments

The final component of a well-executed Minitab assignment is drawing conclusions that synthesize the statistical findings with the research question.

Stating Validity Conditions and Limitations

Chi-square tests assume that the expected frequency in each cell is at least 5. If this condition is not met, Fisher’s Exact Test must be used instead. Ignoring this condition can lead to misleading conclusions.

In the given example:

• Validity condition met: Yes, for Chi-square (most expected counts > 5).
• Exception noted: Use Fisher’s test for accurate inference with smaller counts.

Understanding when to apply which test is essential to submitting accurate and complete assignments.

Conclusion

Crosstab and homogeneity assignments using Minitab involve several key steps: setting up the contingency table, performing the appropriate statistical test (Chi-square or Fisher’s Exact), interpreting the results, and drawing meaningful conclusions. Each step requires attention to detail, but with Minitab’s interface and built-in statistical tools, students can complete these assignments efficiently and accurately.

When working on these assignments, always:

• Ensure variables are assigned logically (row vs. column).
• Enable the right display and analysis options.
• Understand and validate the test assumptions.
• Accurately interpret test results and relative risk.
• Craft well-structured conclusions with relevant statistical evidence.

With these steps in place, students can confidently tackle Crosstab and Homogeneity assignments using Minitab, ensuring both analytical rigor and clear academic communication. Whether you're analyzing treatment outcomes or categorical patterns, this approach equips you with the clarity needed to do your statistics assignment effectively.