All Flashcards
What are the differences between Chi-Squared Test for Independence and Homogeneity?
Independence: One sample, two variables. | Homogeneity: Two or more samples, one variable.
What are the differences between Chi-Squared Test for Goodness of Fit and Independence?
Goodness of Fit: One sample, one variable compared to a theoretical distribution. | Independence: One sample, two variables looking for association.
What are the differences between the null hypothesis for a test of independence and a test of homogeneity?
Independence: No association between two categorical variables within a single population. | Homogeneity: The distribution of a categorical variable is the same across different populations.
What are the differences between observed and expected counts?
Observed: The actual frequencies in the sample data. | Expected: The frequencies predicted under the null hypothesis.
What are the differences between rejecting and failing to reject the null hypothesis?
Rejecting: Evidence supports the alternative hypothesis. | Failing to reject: Insufficient evidence to support the alternative hypothesis.
Define Chi-Squared Goodness of Fit Test.
A test to determine if sample data fits a known distribution.
Define Chi-Squared Test for Independence.
A test to determine if two categorical variables are related in a single sample.
Define Chi-Squared Test for Homogeneity.
A test to determine if the distribution of a categorical variable is the same across two or more populations.
Define Null Hypothesis in the context of Chi-Squared tests.
A statement of no association or no difference between groups.
Define Alternative Hypothesis in the context of Chi-Squared tests.
A statement of association or difference between groups.
What is the formula for the Chi-Squared test statistic?
<math-inline>\chi^2 = \sum \frac{(O - E)^2}{E}, where O is observed frequency and E is expected frequency.
How do you calculate expected counts in a Chi-Squared test?
Expected Count = (Row Total * Column Total) / Grand Total
How do you calculate degrees of freedom for a Chi-Squared test for independence?
df = (number of rows - 1) * (number of columns - 1)
How do you calculate degrees of freedom for a Chi-Squared Goodness of Fit test?
df = (number of categories - 1)
What is the general formula for calculating expected values in a chi-squared test?
E = (Row Total * Column Total) / Grand Total