Chi-Square
Definition:
Chi-Square is a statistical measure used to determine the significance of the association between categorical variables in a data set. It is a non-parametric test that helps us understand whether the observed frequencies of different categories in the data significantly differ from the expected frequencies.
Usage and Interpretation:
The Chi-Square test is often used in research studies to assess whether there is a relationship between two or more categorical variables. It compares the observed frequencies of the variables with the frequencies that would be expected if there were no association or dependency between them.
Based on the calculated Chi-Square statistic, we can determine the p-value, which indicates the probability of obtaining the observed data if the variables are independent. If the p-value is below a chosen significance level (e.g., 0.05), we reject the null hypothesis of independence and conclude that there is a significant association between the variables.
Assumptions:
The Chi-Square test makes several assumptions:
- The data must be obtained from a random sample.
- Each observation must fall into one and only one category.
- The expected frequency for each category should be at least 5.
Limitations:
While Chi-Square is a widely used test, it also has some limitations:
- It can only be used with categorical data, not continuous variables.
- Chi-Square does not provide information about the strength or direction of the relationship.
- A significant Chi-Square test result does not indicate the cause and effect relationship; it only tells us that there is an association between the variables.
Example:
Suppose we want to investigate whether there is an association between smoking habits (categories: “smoker” and “non-smoker”) and the occurrence of lung cancer (categories: “lung cancer” and “no lung cancer”). We collect data from a sample of 1000 individuals and observe the following frequencies:
| Lung Cancer | No Lung Cancer | |
|---|---|---|
| Smoker | 215 | 285 |
| Non-Smoker | 135 | 365 |
By applying the Chi-Square test to these data, we calculate a Chi-Square statistic of 14.79 and find a p-value of 0.001. Since the p-value is less than 0.05, we reject the null hypothesis of independence and conclude that there is a significant association between smoking habits and the occurrence of lung cancer in the population of interest.