Selecting Appropriate Inference Procedures: Categorical Data - AP Statistics
Card 1 of 30
Which method can be used when chi-square assumptions are violated?
Which method can be used when chi-square assumptions are violated?
Tap to reveal answer
Fisher's exact test. Provides exact probabilities without large-sample assumptions.
Fisher's exact test. Provides exact probabilities without large-sample assumptions.
← Didn't Know|Knew It →
What is the null hypothesis for a chi-square test of independence?
What is the null hypothesis for a chi-square test of independence?
Tap to reveal answer
The variables are independent. This states no relationship exists between the variables.
The variables are independent. This states no relationship exists between the variables.
← Didn't Know|Knew It →
What is the alternative hypothesis for a chi-square test of independence?
What is the alternative hypothesis for a chi-square test of independence?
Tap to reveal answer
The variables are not independent. This states a relationship exists between the variables.
The variables are not independent. This states a relationship exists between the variables.
← Didn't Know|Knew It →
Identify the test: Comparing observed vs. expected frequencies in categories.
Identify the test: Comparing observed vs. expected frequencies in categories.
Tap to reveal answer
Chi-square goodness-of-fit test. Tests if observed data matches a theoretical distribution.
Chi-square goodness-of-fit test. Tests if observed data matches a theoretical distribution.
← Didn't Know|Knew It →
Which test checks if proportions differ across groups?
Which test checks if proportions differ across groups?
Tap to reveal answer
Chi-square test of homogeneity. Compares proportions of a categorical variable across multiple groups.
Chi-square test of homogeneity. Compares proportions of a categorical variable across multiple groups.
← Didn't Know|Knew It →
What statistic measures how well observed frequencies fit expected frequencies?
What statistic measures how well observed frequencies fit expected frequencies?
Tap to reveal answer
Chi-square statistic. Measures the discrepancy between observed and expected values.
Chi-square statistic. Measures the discrepancy between observed and expected values.
← Didn't Know|Knew It →
What is a contingency table used for in statistics?
What is a contingency table used for in statistics?
Tap to reveal answer
To display the frequency distribution of variables. Shows the relationship between two categorical variables.
To display the frequency distribution of variables. Shows the relationship between two categorical variables.
← Didn't Know|Knew It →
Identify the degrees of freedom for a chi-square test of independence.
Identify the degrees of freedom for a chi-square test of independence.
Tap to reveal answer
$(r-1)(c-1)$ where $r$ is rows, $c$ is columns. Calculated using rows minus 1 times columns minus 1.
$(r-1)(c-1)$ where $r$ is rows, $c$ is columns. Calculated using rows minus 1 times columns minus 1.
← Didn't Know|Knew It →
Which test is appropriate for comparing two proportions?
Which test is appropriate for comparing two proportions?
Tap to reveal answer
Two-sample z-test for proportions. Used when comparing proportions from two independent groups.
Two-sample z-test for proportions. Used when comparing proportions from two independent groups.
← Didn't Know|Knew It →
Identify the test used for paired categorical data.
Identify the test used for paired categorical data.
Tap to reveal answer
McNemar's test. Analyzes matched pairs with binary outcomes.
McNemar's test. Analyzes matched pairs with binary outcomes.
← Didn't Know|Knew It →
What is the purpose of Fisher's exact test?
What is the purpose of Fisher's exact test?
Tap to reveal answer
To assess the significance of the association in a $2\times^2$ table. Used when sample sizes are too small for chi-square test.
To assess the significance of the association in a $2\times^2$ table. Used when sample sizes are too small for chi-square test.
← Didn't Know|Knew It →
What assumption is crucial for chi-square tests?
What assumption is crucial for chi-square tests?
Tap to reveal answer
Expected frequencies should be at least 5. Ensures valid chi-square distribution approximation.
Expected frequencies should be at least 5. Ensures valid chi-square distribution approximation.
← Didn't Know|Knew It →
Which test examines whether distribution matches a specified distribution?
Which test examines whether distribution matches a specified distribution?
Tap to reveal answer
Chi-square goodness-of-fit test. Compares one sample distribution to a theoretical model.
Chi-square goodness-of-fit test. Compares one sample distribution to a theoretical model.
← Didn't Know|Knew It →
Identify the test: Comparing categorical data from more than two groups.
Identify the test: Comparing categorical data from more than two groups.
Tap to reveal answer
Chi-square test of homogeneity. Tests if distributions are the same across different populations.
Chi-square test of homogeneity. Tests if distributions are the same across different populations.
← Didn't Know|Knew It →
Which test would you use for the relationship between two nominal variables?
Which test would you use for the relationship between two nominal variables?
Tap to reveal answer
Chi-square test of independence. Tests association between two categorical variables.
Chi-square test of independence. Tests association between two categorical variables.
← Didn't Know|Knew It →
Find the degrees of freedom: $3\times^4$ contingency table.
Find the degrees of freedom: $3\times^4$ contingency table.
Tap to reveal answer
Degrees of freedom = $(3-1)(4-1) = 6$. Multiply rows minus 1 by columns minus 1.
Degrees of freedom = $(3-1)(4-1) = 6$. Multiply rows minus 1 by columns minus 1.
← Didn't Know|Knew It →
When is a chi-square test of homogeneity used?
When is a chi-square test of homogeneity used?
Tap to reveal answer
To compare distributions of a categorical variable across groups. Examines whether groups have the same categorical distribution.
To compare distributions of a categorical variable across groups. Examines whether groups have the same categorical distribution.
← Didn't Know|Knew It →
What is the null hypothesis for a chi-square test of homogeneity?
What is the null hypothesis for a chi-square test of homogeneity?
Tap to reveal answer
Proportions are the same across groups. Assumes no difference in distributions between groups.
Proportions are the same across groups. Assumes no difference in distributions between groups.
← Didn't Know|Knew It →
What are expected frequencies in a chi-square test?
What are expected frequencies in a chi-square test?
Tap to reveal answer
Theoretical frequencies if null hypothesis is true. Calculated assuming the null hypothesis is true.
Theoretical frequencies if null hypothesis is true. Calculated assuming the null hypothesis is true.
← Didn't Know|Knew It →
Which test is used for exact tests of independence in small samples?
Which test is used for exact tests of independence in small samples?
Tap to reveal answer
Fisher's exact test. Computes exact probabilities for small sample contingency tables.
Fisher's exact test. Computes exact probabilities for small sample contingency tables.
← Didn't Know|Knew It →
Identify the test: Testing a single categorical distribution.
Identify the test: Testing a single categorical distribution.
Tap to reveal answer
Chi-square goodness-of-fit test. Examines if data follows a specific categorical distribution.
Chi-square goodness-of-fit test. Examines if data follows a specific categorical distribution.
← Didn't Know|Knew It →
What outcome does a large chi-square statistic suggest?
What outcome does a large chi-square statistic suggest?
Tap to reveal answer
Greater deviation from the expected frequencies. Indicates poor fit between observed and expected data.
Greater deviation from the expected frequencies. Indicates poor fit between observed and expected data.
← Didn't Know|Knew It →
Which test is used for two related samples in categorical data?
Which test is used for two related samples in categorical data?
Tap to reveal answer
McNemar's test. Compares before and after measurements on same subjects.
McNemar's test. Compares before and after measurements on same subjects.
← Didn't Know|Knew It →
For what type of data is a chi-square test inappropriate?
For what type of data is a chi-square test inappropriate?
Tap to reveal answer
Continuous data. Chi-square tests require categorical, not continuous variables.
Continuous data. Chi-square tests require categorical, not continuous variables.
← Didn't Know|Knew It →
What is the key assumption of the chi-square test of independence?
What is the key assumption of the chi-square test of independence?
Tap to reveal answer
Observations are independent. Each observation must not influence others.
Observations are independent. Each observation must not influence others.
← Didn't Know|Knew It →
What is the primary use of a chi-square test?
What is the primary use of a chi-square test?
Tap to reveal answer
To test categorical data for independence or fit. Analyzes relationships and distributions in categorical data.
To test categorical data for independence or fit. Analyzes relationships and distributions in categorical data.
← Didn't Know|Knew It →
When should Fisher's exact test be used instead of chi-square?
When should Fisher's exact test be used instead of chi-square?
Tap to reveal answer
When sample sizes are too small for chi-square assumptions. When expected cell counts fall below 5.
When sample sizes are too small for chi-square assumptions. When expected cell counts fall below 5.
← Didn't Know|Knew It →
Identify the type of data suitable for McNemar's test.
Identify the type of data suitable for McNemar's test.
Tap to reveal answer
Paired categorical data. Uses matched pairs from the same subjects.
Paired categorical data. Uses matched pairs from the same subjects.
← Didn't Know|Knew It →
What does a p-value in a chi-square test indicate?
What does a p-value in a chi-square test indicate?
Tap to reveal answer
Probability of observing data as extreme as current, under null hypothesis. Probability of obtaining results this extreme by chance.
Probability of observing data as extreme as current, under null hypothesis. Probability of obtaining results this extreme by chance.
← Didn't Know|Knew It →
What is required for a valid chi-square test of homogeneity?
What is required for a valid chi-square test of homogeneity?
Tap to reveal answer
Random samples from each group. Ensures valid comparison across independent groups.
Random samples from each group. Ensures valid comparison across independent groups.
← Didn't Know|Knew It →