All Flashcards
Explain the concept of the Chi-Square Test for Goodness of Fit.
It examines if a sample distribution matches a hypothesized distribution. It tests if your data "fits" a particular model.
Explain the concept of the Chi-Square Test for Independence.
It determines if two categorical variables are independent of each other. It assesses whether they are related or if the observed relationship is due to chance.
Explain the concept of the Chi-Square Test for Homogeneity.
It compares distributions of a categorical variable across different populations or treatments to determine if the groups are similar or different.
Explain the 'Large Counts' condition in Chi-Square tests.
All expected counts must be at least 5. This ensures the sampling distribution of the test statistic is approximately chi-square.
Explain the meaning of a low p-value in a Chi-Square test.
A low p-value means we have evidence to reject the null hypothesis, suggesting a significant association or difference.
What are the differences between the Chi-Square Test for Independence and Homogeneity?
Independence: Tests relationship between two variables in a single population. | Homogeneity: Compares distributions of a variable across multiple populations.
What are the differences between observed and expected frequencies?
Observed: Actual counts in your sample data. | Expected: Counts predicted under the null hypothesis (no association).
What are the differences between Goodness of Fit and Independence tests?
Goodness of Fit: Tests if one sample matches a hypothesized distribution. | Independence: Tests if two categorical variables are related.
What are the differences between a Chi-Square test and a z-test for proportions?
Chi-Square: Used for categorical variables with two or more categories. | Z-test: Used for comparing proportions of a single categorical variable with two categories.
What are the differences between rejecting and failing to reject the null hypothesis?
Rejecting: There is enough evidence to support the alternative hypothesis. | Failing to reject: There is not enough evidence to support the alternative hypothesis.
What is a Chi-Square Test?
A statistical test used to determine if observed data significantly differs from expected data, especially with categorical variables.
What is observed frequency?
The actual frequencies you see in your data.
What is expected frequency?
The frequencies you'd expect if there was no relationship between variables.
What is a two-way table?
A table that organizes categorical data, making it easier to calculate expected counts and perform the chi-square test.
What is a frequency table distribution?
A table showing the distribution of categorical data, used to calculate expected counts and perform the chi-square test.