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.
Explain the concept of degrees of freedom in a Chi-Squared test.
Degrees of freedom represent the number of independent pieces of information used to calculate the test statistic. It affects the shape of the chi-squared distribution.
Explain the concept of expected counts in a Chi-Squared test.
Expected counts are the frequencies we would expect to see in each cell of a contingency table if the null hypothesis were true (i.e., no association between variables).
Explain the role of p-value in Chi-Squared tests.
The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true. A small p-value suggests evidence against the null hypothesis.
Explain why categorical data is required for Chi-Squared tests.
Chi-squared tests analyze frequencies of categories. Continuous data needs to be grouped into categories to be used.
Explain the importance of checking conditions for Chi-Squared tests.
Conditions like randomness, independence, and large counts ensure the validity of the test results. Violating these conditions can lead to inaccurate conclusions.
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.
