AP Statistics Flashcards: Chi Square Homogeneity Or Independence Setup

What this deck covers

This deck focuses on Chi Square Homogeneity Or Independence Setup, 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: Determine the test: Evaluating if gender is related to voting preference.

Answer: Chi-Square Test of Independence. Tests if gender and voting preference are associated variables.

Flashcard 2: What is the alternative hypothesis for a Chi-Square Test of Homogeneity?

Answer: The distributions are different. Homogeneity tests check if categorical distributions vary across groups.

Flashcard 3: What assumption does a Chi-Square test make about samples?

Answer: Samples are randomly selected. Random sampling ensures independence and representative results.

Flashcard 4: Calculate degrees of freedom for a 4x3 contingency table.

Answer: $(4-1)(3-1) = 6$. Use the formula $(r-1)(c-1)$ where $r=4$ rows and $c=3$ columns.

Flashcard 5: Which test uses the contingency table to organize data?

Answer: Both Chi-Square Tests. Both tests use contingency tables to organize observed frequencies.

Flashcard 6: Which test checks if proportions differ across multiple populations?

Answer: Chi-Square Test of Homogeneity. Homogeneity tests compare categorical proportions across multiple populations.

Flashcard 7: What does a significant Chi-Square statistic indicate?

Answer: Reject the null hypothesis. Significant results lead to rejecting the null hypothesis.

Flashcard 8: What is the formula for the Chi-Square statistic?

Answer: $\text{Chi-Square} = \frac{(O-E)^2}{E}$ summed over all cells. Sum the squared standardized deviations across all contingency table cells.

Flashcard 9: What is the null hypothesis for a Chi-Square Test of Independence?

Answer: The variables are independent. For independence tests, we assume no relationship exists between variables.

Flashcard 10: What is the degree of freedom formula for a Chi-Square Test of Independence?

Answer: $(r-1)(c-1)$, where $r$ is rows, $c$ is columns. Degrees of freedom account for constraints in the contingency table.

Flashcard 11: State the formula for the expected frequency in a contingency table cell.

Answer: $E = \frac{(row\text{ }total \times column\text{ }total)}{grand\text{ }total}$. Expected frequency equals the product of marginal totals divided by sample size.

Flashcard 12: What is the null hypothesis for a Chi-Square Test of Homogeneity?

Answer: The distributions are the same. Assumes categorical distributions are identical across all groups.

Flashcard 13: What type of test is the Chi-Square Test of Homogeneity?

Answer: Non-parametric test. Non-parametric tests don't assume specific population distributions.

Flashcard 14: Which test assesses if sample proportions are equal across groups?

Answer: Chi-Square Test of Homogeneity. Homogeneity tests compare proportions of categorical outcomes across groups.

Flashcard 15: What describes a contingency table with 3 rows and 2 columns?

Answer: 3x2 table. Describes the dimensions of a two-way frequency table.

Flashcard 16: Calculate $\text{Chi-Square}$: $O=10, E=8$ in one cell.

Answer: $\frac{(10-8)^2}{8} = 0.5$. Apply the Chi-Square formula: $(O-E)^2/E$ for this cell.

Flashcard 17: What is the critical value for a Chi-Square test with 2 df at 0.05 significance?

Answer: 5.991. Standard critical value for 2 degrees of freedom at 5% significance level.

Flashcard 18: Find the expected frequency: $60$ total, $15$ in row, $4$ in column.

Answer: $E = \frac{(15 \times 4)}{60} = 1$. Apply the expected frequency formula: row total × column total ÷ grand total.

Flashcard 19: Determine the test: Evaluating if study fields affect job types.

Answer: Chi-Square Test of Independence. Tests association between study field and job type variables.

Flashcard 20: Identify the test: Comparing categorical distributions across multiple groups.

Answer: Chi-Square Test of Homogeneity. This test compares how categorical variables are distributed across groups.

Flashcard 21: State the alternative hypothesis for a Chi-Square Test of Independence.

Answer: The variables are dependent. Independence alternative hypothesis states variables are related or associated.

Flashcard 22: Identify the test: Comparing response frequency across different age groups.

Answer: Chi-Square Test of Homogeneity. Compares response distributions across different age group populations.

Flashcard 23: Find the expected frequency: $60$ total, $15$ in row, $4$ in column.

Answer: $E = \frac{(15 \times 4)}{60} = 1$. Apply the expected frequency formula: row total × column total ÷ grand total.

Flashcard 24: How are the observed frequencies denoted in Chi-Square tests?

Answer: $O$. O represents the actual counts observed in each cell.

Flashcard 25: What is a common use of the Chi-Square Test of Independence?

Answer: To assess relationships between categorical variables. Independence tests determine if categorical variables are associated.

Flashcard 26: Which test applies when examining if two variables interact?

Answer: Chi-Square Test of Independence. Independence tests examine relationships between two categorical variables.

Flashcard 27: Which test applies when examining if two variables interact?

Answer: Chi-Square Test of Independence. Independence tests examine relationships between two categorical variables.

Flashcard 28: State the formula for the expected frequency in a contingency table cell.

Answer: $E = \frac{(row\text{ }total \times column\text{ }total)}{grand\text{ }total}$. Expected frequency equals the product of marginal totals divided by sample size.

Flashcard 29: Identify the type of variable suitable for Chi-Square tests.

Answer: Categorical variables. Chi-Square tests require qualitative data with distinct categories.

Flashcard 30: What is the formula for the Chi-Square statistic?

Answer: $\text{Chi-Square} = \frac{(O-E)^2}{E}$ summed over all cells. Sum the squared standardized deviations across all contingency table cells.

Flashcard 31: Find expected frequency: $100$ total, $25$ in row, $10$ in column.

Answer: $E = \frac{(25 \times 10)}{100} = 2.5$. Calculate using the standard expected frequency formula.

Flashcard 32: What assumption must be met regarding expected frequencies for Chi-Square tests?

Answer: Expected frequencies should be at least 5. This ensures the Chi-Square distribution approximation is valid.

Flashcard 33: When is a Chi-Square test considered invalid?

Answer: When expected frequencies are less than 5. Low expected frequencies violate the Chi-Square distribution assumption.

Flashcard 34: What is the minimum sample size recommended for Chi-Square tests?

Answer: No specific size, but expected counts > 5. Focus is on expected counts rather than total sample size.

Flashcard 35: What describes a contingency table with 3 rows and 2 columns?

Answer: 3x2 table. Describes the dimensions of a two-way frequency table.

Flashcard 36: Calculate degrees of freedom for a 4x3 contingency table.

Answer: $(4-1)(3-1) = 6$. Use the formula $(r-1)(c-1)$ where $r=4$ rows and $c=3$ columns.

Flashcard 37: What is the general purpose of a Chi-Square test?

Answer: To test the association between categorical variables. Chi-Square tests evaluate relationships and patterns in categorical data.

Flashcard 38: What type of distribution is used in Chi-Square tests?

Answer: Chi-Square distribution. Chi-Square distribution is the theoretical basis for these hypothesis tests.

Flashcard 39: Identify the symbol commonly used for the Chi-Square statistic.

Answer: $\text{Chi-Square}$ or $\text{X}^2$. Both symbols represent the calculated test statistic in Chi-Square tests.

Flashcard 40: Identify the test: Assessing relationship between two categorical variables.

Answer: Chi-Square Test of Independence. This test determines if two categorical variables are associated.

Flashcard 41: What is required for valid Chi-Square results concerning data collection?

Answer: Random sampling. Random sampling ensures valid statistical inferences from Chi-Square tests.

Flashcard 42: What condition must be met for Chi-Square tests regarding sample size?

Answer: Expected frequencies must be at least 5. All expected frequencies must meet the minimum threshold of 5.

Flashcard 43: What is the range of values for a Chi-Square statistic?

Answer: 0 to $\text{infinity}$. Chi-Square statistics are always non-negative with no upper bound.

Flashcard 44: What do you compare the Chi-Square statistic to for hypothesis testing?

Answer: Chi-Square critical value. Compare calculated test statistic to tabled critical value for decision.