Summary of "35- Chi Square test and Fisher's Exact test"

Summary of “35- Chi Square test and Fisher’s Exact test”

This video provides an in-depth explanation of the Chi-Square test and Fisher’s Exact test, focusing on their use in analyzing relationships between categorical variables. The main ideas, concepts, and practical lessons are outlined below.

Main Ideas and Concepts

Purpose of Chi-Square Test The Chi-Square test is used to examine the relationship or difference between two categorical variables (e.g., gender and smoking status, preference for tea or coffee by males and females). A difference between groups implies a relationship, and vice versa. The test compares observed data (actual counts) with expected data (what would be expected if there were no association).
Formulating Research Questions Research questions can be phrased as “Is there a difference between groups?” or “Is there a relationship between variables?” Both are conceptually the same in this context. Examples:
- Is there a difference between males and females in smoking habits?
- Is there a relationship between smoking and lung cancer occurrence?
Observed vs Expected Counts
- Observed counts (O): The actual data collected.
- Expected counts (E): Calculated assuming no association: [ E = \frac{(\text{Row total}) \times (\text{Column total})}{\text{Grand total}} ] The Chi-Square test evaluates whether observed counts significantly deviate from expected counts.
Assumptions and Conditions for Chi-Square Test
- Data must be independent (each subject belongs to only one group).
- Expected counts in each cell should generally be 5 or more.
- If more than 20% of cells have expected counts less than 5, the Chi-Square test may not be valid.
Handling Small Expected Counts When expected counts are too low (less than 5 in more than 20% of cells), alternatives are needed:
- Fisher’s Exact Test: Used for 2x2 tables (two groups by two categories).
- Likelihood Ratio Test (G-test) or other exact tests for larger tables (e.g., 2x3 or more).
- Combining categories may be considered to increase expected counts if logically justifiable.
Using SPSS for Chi-Square and Fisher’s Exact Tests
- SPSS outputs observed and expected counts, and flags cells with expected counts less than 5.
- It reports the percentage of such cells to assess the validity of the Chi-Square test.
- If the Chi-Square test is invalid due to low expected counts, SPSS can perform Fisher’s Exact Test or other alternatives.
- Users can request additional outputs like row percentages or column percentages to better interpret results.
Interpreting Results
- The Chi-Square statistic and associated p-value indicate whether there is a significant association or difference.
- Percentages (row or column) help understand the nature of the difference.
- Example: If 42% of males prefer coffee vs 48% of females, the test determines if this difference is statistically significant.
Additional Notes
- The Chi-Square test is widely used in medical research to compare groups (e.g., treatment vs control, disease vs no disease).
- Presentation of data should match the research question and audience needs (counts, percentages, or graphs).
- Bar charts with percentages are preferred for clear visualization.
- McNemar’s test is introduced as a related test for paired nominal data (e.g., smoking status before and after an intervention in the same individuals), not for independent groups.

Methodology / Instructions for Conducting Chi-Square Test and Alternatives

Formulate the Research Question Define the two categorical variables and the hypothesis about their association.
Collect Data and Construct Contingency Table Organize observed frequencies in a table (e.g., gender vs drink preference).
Calculate Expected Counts Use the formula: [ E = \frac{(\text{Row total}) \times (\text{Column total})}{\text{Grand total}} ]
Check Assumptions Verify that expected counts are ≥5 in at least 80% of cells. If more than 20% of cells have expected counts <5, consider alternatives.
Perform Chi-Square Test (e.g., using SPSS)
- Use crosstabs with Chi-Square option enabled.
- Review output for Chi-Square statistic, p-value, and expected counts.
- Request row/column percentages for better interpretation.
If Chi-Square Test is Invalid Due to Small Expected Counts
- For 2x2 tables: Use Fisher’s Exact Test.
- For larger tables (e.g., 2x3): Use Likelihood Ratio Test or exact tests if available.
- Consider combining categories logically to increase expected counts.
Interpret Results
- If p < 0.05, conclude a statistically significant association/difference.
- Use percentages and bar charts to explain the direction and magnitude of differences.
For Paired Data (Same Subjects Before/After) Use McNemar’s test instead of Chi-Square.

Key Terms Explained

Observed Count (O): Actual number of cases in each cell of the contingency table.
Expected Count (E): Number expected in each cell if no association exists.
Chi-Square Statistic (χ²): Measures discrepancy between observed and expected counts.
p-value: Probability that observed differences are due to chance.
Fisher’s Exact Test: An exact test used when sample sizes are small or expected counts are low, applicable to 2x2 tables.
McNemar’s Test: Used for paired nominal data to test changes in proportions.

Speakers / Sources Featured

Primary Speaker: Unnamed instructor or lecturer presenting the statistical concepts, examples, and SPSS demonstration throughout the video.

This summary captures the core lessons and practical guidance on using Chi-Square and Fisher’s Exact tests, including when and how to apply them, interpret results, and handle common challenges such as small expected counts.