Chi Squared Independence Homogeneity Flashcards
(15 cards)
What is the purpose of the Chi-Squared Test for Independence?
To determine if two categorical variables are independent.
What is the purpose of the Chi-Squared Test for Homogeneity?
To determine if the distribution of a categorical variable is the same across multiple populations.
When should you use a Test for Independence?
When you have one large random sample and record two categorical variables for each unit.
When should you use a Test for Homogeneity?
When you have separate random samples from different populations and want to compare distributions.
What is the formula for the expected count in a contingency table?
E_ij = (Row Total_i × Column Total_j) / Grand Total.
What is the Chi-Squared test statistic formula?
W = Σ (O_ij - E_ij)² / E_ij over all cells.
How do you calculate the degrees of freedom for the test?
df = (number of rows - 1) × (number of columns - 1).
What is the rejection rule for the Chi-Squared Test?
Reject H₀ if W > Chi-Squared critical value at significance level α with df degrees of freedom.
What does a large test statistic W indicate?
Strong evidence against the null hypothesis (variables are dependent or distributions differ).
Are the steps for computing Independence and Homogeneity tests different?
No, the steps and formulas are the same; the difference lies in how the data was sampled.
What is a contingency table?
A table showing observed frequencies for two categorical variables.
What happens if observed counts are very different from expected counts?
We are more likely to reject the null hypothesis.
Under the null hypothesis, what distribution does W follow?
A Chi-Squared distribution with df = (rows-1)(columns-1).
What is the null hypothesis in a Test for Independence?
The two categorical variables are independent.
What is the null hypothesis in a Test for Homogeneity?
The distributions across the populations are the same.
