AP Statistics Flashcards: Selecting Appropriate Inference Procedures Categorical Data

What this deck covers

This deck focuses on Selecting Appropriate Inference Procedures Categorical Data, giving you a quick way to review the definitions, rules, and examples that matter most for AP Statistics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is required for a valid chi-square test of homogeneity?

Answer: Random samples from each group. Ensures valid comparison across independent groups.

Flashcard 2: What are expected frequencies in a chi-square test?

Answer: Theoretical frequencies if null hypothesis is true. Calculated assuming the null hypothesis is true.

Flashcard 3: What statistic measures how well observed frequencies fit expected frequencies?

Answer: Chi-square statistic. Measures the discrepancy between observed and expected values.

Flashcard 4: Which test would you use for a $2\times^2$ contingency table with small counts?

Answer: Fisher's exact test. Appropriate when chi-square assumptions aren't met.

Flashcard 5: What does a p-value in a chi-square test indicate?

Answer: Probability of observing data as extreme as current, under null hypothesis. Probability of obtaining results this extreme by chance.

Flashcard 6: Identify the degrees of freedom for a chi-square test of independence.

Answer: $(r-1)(c-1)$ where $r$ is rows, $c$ is columns. Calculated using rows minus 1 times columns minus 1.

Flashcard 7: What is the null hypothesis for a chi-square test of homogeneity?

Answer: Proportions are the same across groups. Assumes no difference in distributions between groups.

Flashcard 8: Which test examines whether distribution matches a specified distribution?

Answer: Chi-square goodness-of-fit test. Compares one sample distribution to a theoretical model.

Flashcard 9: Which inference procedure is appropriate for categorical data in one group?

Answer: Chi-square goodness-of-fit test. Tests distribution shape for a single categorical variable.

Flashcard 10: What is the null hypothesis for a chi-square goodness-of-fit test?

Answer: Sample distribution fits the expected distribution. Assumes observed data matches the theoretical model.

Flashcard 11: Which test checks if proportions differ across groups?

Answer: Chi-square test of homogeneity. Compares proportions of a categorical variable across multiple groups.

Flashcard 12: Find the degrees of freedom: $3\times^4$ contingency table.

Answer: Degrees of freedom = $(3-1)(4-1) = 6$. Multiply rows minus 1 by columns minus 1.

Flashcard 13: What statistic measures how well observed frequencies fit expected frequencies?

Answer: Chi-square statistic. Measures the discrepancy between observed and expected values.

Flashcard 14: Identify the test: Comparing categorical data from more than two groups.

Answer: Chi-square test of homogeneity. Tests if distributions are the same across different populations.

Flashcard 15: Identify the test: Comparing observed vs. expected frequencies in categories.

Answer: Chi-square goodness-of-fit test. Tests if observed data matches a theoretical distribution.

Flashcard 16: Identify the test used for paired categorical data.

Answer: McNemar's test. Analyzes matched pairs with binary outcomes.

Flashcard 17: What assumption is crucial for chi-square tests?

Answer: Expected frequencies should be at least 5. Ensures valid chi-square distribution approximation.

Flashcard 18: What is a contingency table used for in statistics?

Answer: To display the frequency distribution of variables. Shows the relationship between two categorical variables.

Flashcard 19: Which test is used for exact tests of independence in small samples?

Answer: Fisher's exact test. Computes exact probabilities for small sample contingency tables.

Flashcard 20: Identify the degrees of freedom for a chi-square test of independence.

Answer: $(r-1)(c-1)$ where $r$ is rows, $c$ is columns. Calculated using rows minus 1 times columns minus 1.

Flashcard 21: What conclusion is drawn if $\chi^2$ is significant in a test of independence?

Answer: Variables are not independent. Evidence of association between the categorical variables.

Flashcard 22: Identify the type of data suitable for McNemar's test.

Answer: Paired categorical data. Uses matched pairs from the same subjects.

Flashcard 23: What outcome does a large chi-square statistic suggest?

Answer: Greater deviation from the expected frequencies. Indicates poor fit between observed and expected data.

Flashcard 24: What does a significant chi-square statistic indicate?

Answer: Observed frequencies differ from expected frequencies. Evidence against the null hypothesis of independence or fit.

Flashcard 25: Which method can be used when chi-square assumptions are violated?

Answer: Fisher's exact test. Provides exact probabilities without large-sample assumptions.

Flashcard 26: What is a contingency table used for in statistics?

Answer: To display the frequency distribution of variables. Shows the relationship between two categorical variables.

Flashcard 27: What is required for a valid chi-square test of homogeneity?

Answer: Random samples from each group. Ensures valid comparison across independent groups.

Flashcard 28: When is a chi-square test of homogeneity used?

Answer: To compare distributions of a categorical variable across groups. Examines whether groups have the same categorical distribution.

Flashcard 29: What assumption is crucial for chi-square tests?

Answer: Expected frequencies should be at least 5. Ensures valid chi-square distribution approximation.

Flashcard 30: Which test is appropriate for comparing two proportions?

Answer: Two-sample z-test for proportions. Used when comparing proportions from two independent groups.

Flashcard 31: What is the null hypothesis for a chi-square test of independence?

Answer: The variables are independent. This states no relationship exists between the variables.

Flashcard 32: Which method can be used when chi-square assumptions are violated?

Answer: Fisher's exact test. Provides exact probabilities without large-sample assumptions.

Flashcard 33: Identify the test: Comparing categorical data from more than two groups.

Answer: Chi-square test of homogeneity. Tests if distributions are the same across different populations.

Flashcard 34: What is the key assumption of the chi-square test of independence?

Answer: Observations are independent. Each observation must not influence others.

Flashcard 35: Which test is used for two related samples in categorical data?

Answer: McNemar's test. Compares before and after measurements on same subjects.

Flashcard 36: Identify the test: Testing a single categorical distribution.

Answer: Chi-square goodness-of-fit test. Examines if data follows a specific categorical distribution.

Flashcard 37: Which test checks if proportions differ across groups?

Answer: Chi-square test of homogeneity. Compares proportions of a categorical variable across multiple groups.

Flashcard 38: Which test is appropriate for comparing two proportions?

Answer: Two-sample z-test for proportions. Used when comparing proportions from two independent groups.

Flashcard 39: Identify the test used for paired categorical data.

Answer: McNemar's test. Analyzes matched pairs with binary outcomes.

Flashcard 40: What is the purpose of Fisher's exact test?

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.

Flashcard 41: Which test is used for exact tests of independence in small samples?

Answer: Fisher's exact test. Computes exact probabilities for small sample contingency tables.

Flashcard 42: Which test examines whether distribution matches a specified distribution?

Answer: Chi-square goodness-of-fit test. Compares one sample distribution to a theoretical model.

Flashcard 43: Identify the test: Comparing observed vs. expected frequencies in categories.

Answer: Chi-square goodness-of-fit test. Tests if observed data matches a theoretical distribution.

Flashcard 44: Identify the type of data suitable for McNemar's test.

Answer: Paired categorical data. Uses matched pairs from the same subjects.

Flashcard 45: What is the null hypothesis for a chi-square test of homogeneity?

Answer: Proportions are the same across groups. Assumes no difference in distributions between groups.

Flashcard 46: How is the chi-square distribution described?

Answer: A family of distributions that vary with degrees of freedom. Shape depends on degrees of freedom parameter.

Flashcard 47: What is the alternative hypothesis for a chi-square test of independence?

Answer: The variables are not independent. This states a relationship exists between the variables.

Flashcard 48: Which inference procedure is appropriate for categorical data in one group?

Answer: Chi-square goodness-of-fit test. Tests distribution shape for a single categorical variable.

Flashcard 49: What is the alternative hypothesis for a chi-square test of independence?

Answer: The variables are not independent. This states a relationship exists between the variables.

Flashcard 50: For what type of data is a chi-square test inappropriate?

Answer: Continuous data. Chi-square tests require categorical, not continuous variables.

Flashcard 51: How is the chi-square distribution described?

Answer: A family of distributions that vary with degrees of freedom. Shape depends on degrees of freedom parameter.

Flashcard 52: What outcome does a large chi-square statistic suggest?

Answer: Greater deviation from the expected frequencies. Indicates poor fit between observed and expected data.

Flashcard 53: Find the degrees of freedom: $3\times^4$ contingency table.

Answer: Degrees of freedom = $(3-1)(4-1) = 6$. Multiply rows minus 1 by columns minus 1.

Flashcard 54: State the formula for the chi-square statistic.

Answer: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$. Sums squared differences between observed and expected, divided by expected.

Flashcard 55: Which test would you use for a $2\times^2$ contingency table with small counts?

Answer: Fisher's exact test. Appropriate when chi-square assumptions aren't met.

Flashcard 56: What does a p-value in a chi-square test indicate?

Answer: Probability of observing data as extreme as current, under null hypothesis. Probability of obtaining results this extreme by chance.

Flashcard 57: What conclusion is drawn if $\chi^2$ is significant in a test of independence?

Answer: Variables are not independent. Evidence of association between the categorical variables.

Flashcard 58: What is the purpose of Fisher's exact test?

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.

Flashcard 59: Which test is used for two related samples in categorical data?

Answer: McNemar's test. Compares before and after measurements on same subjects.

Flashcard 60: When should Fisher's exact test be used instead of chi-square?

Answer: When sample sizes are too small for chi-square assumptions. When expected cell counts fall below 5.

Flashcard 61: For what type of data is a chi-square test inappropriate?

Answer: Continuous data. Chi-square tests require categorical, not continuous variables.

Flashcard 62: When should Fisher's exact test be used instead of chi-square?

Answer: When sample sizes are too small for chi-square assumptions. When expected cell counts fall below 5.

Flashcard 63: What is the null hypothesis for a chi-square test of independence?

Answer: The variables are independent. This states no relationship exists between the variables.

Flashcard 64: What is the null hypothesis for a chi-square goodness-of-fit test?

Answer: Sample distribution fits the expected distribution. Assumes observed data matches the theoretical model.

Flashcard 65: What is the primary use of a chi-square test?

Answer: To test categorical data for independence or fit. Analyzes relationships and distributions in categorical data.

Flashcard 66: Identify the test: Testing a single categorical distribution.

Answer: Chi-square goodness-of-fit test. Examines if data follows a specific categorical distribution.

Flashcard 67: Which test would you use for the relationship between two nominal variables?

Answer: Chi-square test of independence. Tests association between two categorical variables.

Flashcard 68: What are expected frequencies in a chi-square test?

Answer: Theoretical frequencies if null hypothesis is true. Calculated assuming the null hypothesis is true.

Flashcard 69: Which test would you use for the relationship between two nominal variables?

Answer: Chi-square test of independence. Tests association between two categorical variables.

Flashcard 70: What is the primary use of a chi-square test?

Answer: To test categorical data for independence or fit. Analyzes relationships and distributions in categorical data.

Flashcard 71: When is a chi-square test of homogeneity used?

Answer: To compare distributions of a categorical variable across groups. Examines whether groups have the same categorical distribution.

Flashcard 72: What is the key assumption of the chi-square test of independence?

Answer: Observations are independent. Each observation must not influence others.