📚 Topic Summary
The Chi-Square test is a statistical method used to determine if there is a significant association between two categorical variables. It assesses whether the observed data differs significantly from what would be expected if there were no association between the variables. In simpler terms, it helps us figure out if the differences we see in our data are just due to chance, or if there's a real relationship happening. There are two main types: the Chi-Square test for independence (association) and the Chi-Square goodness-of-fit test (compares observed with expected distribution).
🧠 Part A: Vocabulary
Match the term to its definition:
- Observed Frequency
- Expected Frequency
- Degrees of Freedom
- Null Hypothesis
- Chi-Square Statistic
Definitions:
- The frequencies you would expect to see if the null hypothesis were true.
- A measure of the difference between observed and expected frequencies.
- The hypothesis that there is no significant relationship between the variables.
- The number of independent pieces of information used to calculate the statistic.
- The actual frequencies obtained from the sample data.
| Term |
Definition |
| Observed Frequency |
|
| Expected Frequency |
|
| Degrees of Freedom |
|
| Null Hypothesis |
|
| Chi-Square Statistic |
|
📊 Part B: Fill in the Blanks
The Chi-Square test is used for _______ data. It compares the _______ frequencies with the _______ frequencies. A high Chi-Square value suggests that the _______ hypothesis should be rejected. The _______ of _______ is calculated as the number of categories minus one, often represented as (rows - 1) * (columns - 1) in a contingency table.
🤔 Part C: Critical Thinking
Explain a real-world scenario where a Chi-Square test for independence would be useful, and why it would be the appropriate statistical test to use.