What are Expected Frequencies in a Test of Independence?

📚 Quick Study Guide

• 📊 Test of Independence: Determines if there's a significant association between two categorical variables.
• 🤔 Null Hypothesis: Assumes no association between the variables.
• ➕ Observed Frequencies: The actual counts from your sample data.
• 🔢 Expected Frequencies: The counts we'd expect if the variables were independent. Calculated using the formula: $E = \frac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}}$
• ✅ Chi-Square Test: Compares observed and expected frequencies to determine significance.

Practice Quiz

1. Question 1: What does a test of independence primarily assess?
   1. A) The mean difference between two groups.
   2. B) The association between two categorical variables.
   3. C) The correlation between two continuous variables.
   4. D) The probability of an event occurring.
2. Question 2: If two variables are independent, what should be true of the observed and expected frequencies?
   1. A) Observed frequencies should be much larger than expected frequencies.
   2. B) Observed frequencies should be much smaller than expected frequencies.
   3. C) Observed and expected frequencies should be similar.
   4. D) Observed frequencies should always be zero.
3. Question 3: How is the expected frequency for a cell in a contingency table calculated?
   1. A) (Row Total + Column Total) / Grand Total
   2. B) (Row Total) * (Column Total) * Grand Total
   3. C) (Row Total) * (Column Total) / Grand Total
   4. D) Grand Total / (Row Total * Column Total)
4. Question 4: What does the null hypothesis in a test of independence typically state?
   1. A) There is a strong association between the variables.
   2. B) There is no association between the variables.
   3. C) The variables are causally related.
   4. D) The variables are perfectly correlated.
5. Question 5: In a 2x2 contingency table, if all expected frequencies are less than 5, what should you do?
   1. A) Proceed with the Chi-Square test as usual.
   2. B) Use a different statistical test, like Fisher's exact test.
   3. C) Increase the sample size and recalculate.
   4. D) Conclude that the variables are independent.
6. Question 6: Why are expected frequencies important in a Chi-Square test for independence?
   1. A) They represent the actual observed data.
   2. B) They are used to calculate the p-value directly.
   3. C) They provide a baseline for comparison against the observed frequencies.
   4. D) They are only used for calculating degrees of freedom.
7. Question 7: What happens to the expected frequencies if the sample size increases, assuming the proportions within each category remain the same?
   1. A) They decrease.
   2. B) They remain the same.
   3. C) They increase.
   4. D) They become more variable.