What are degrees of freedom in tests of independence?

📚 Quick Study Guide

• 🔢 The degrees of freedom (df) in a test of independence tells you how many values in your calculation are free to vary.
• 📊 For a contingency table (used in tests of independence), the formula to calculate df is: $df = (r - 1)(c - 1)$, where $r$ is the number of rows and $c$ is the number of columns.
• 📝 The null hypothesis in a test of independence is that the two categorical variables are independent of each other.
• 📈 A larger chi-square statistic and a smaller p-value provide evidence against the null hypothesis, suggesting the variables are dependent.
• 🧮 If $df = 1$, it means you have a 2x2 contingency table.

Practice Quiz

1. Which formula is used to calculate degrees of freedom in a test of independence?
   1. A) $df = n - 1$
   2. B) $df = (r - 1)(c - 1)$
   3. C) $df = r \times c$
   4. D) $df = n - k - 1$
2. What does 'r' represent in the degrees of freedom formula for a test of independence?
   1. A) Number of columns
   2. B) Number of rows
   3. C) Total sample size
   4. D) Number of categories
3. In a contingency table with 3 rows and 4 columns, what are the degrees of freedom?
   1. A) 12
   2. B) 9
   3. C) 6
   4. D) 3
4. What does a higher degrees of freedom generally indicate in a test of independence?
   1. A) Smaller sample size
   2. B) Larger sample size or more categories
   3. C) Stronger dependence between variables
   4. D) Weaker dependence between variables
5. If the degrees of freedom is 1 in a test of independence, what does this imply about the contingency table?
   1. A) It's a 3x3 table
   2. B) It's a 2x2 table
   3. C) It's a 1x2 table
   4. D) It's a table with only one variable
6. What is the null hypothesis in a test of independence?
   1. A) The variables are dependent
   2. B) The variables are independent
   3. C) There is a causal relationship
   4. D) There is no relationship at all
7. A researcher is testing the independence of two categorical variables and calculates a chi-square statistic with df=2. What does this mean?
   1. A) The contingency table is 2x2.
   2. B) The contingency table could be 2x3 or 3x2.
   3. C) The variables are highly dependent.
   4. D) The sample size is small.