Chi-Square Homogeneity or Independence (Setup) - AP Statistics
Card 1 of 30
State the formula for the expected frequency in a contingency table cell.
State the formula for the expected frequency in a contingency table cell.
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$E = \frac{(row\text{ }total \times column\text{ }total)}{grand\text{ }total}$. Expected frequency equals the product of marginal totals divided by sample size.
$E = \frac{(row\text{ }total \times column\text{ }total)}{grand\text{ }total}$. Expected frequency equals the product of marginal totals divided by sample size.
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What is the formula for the Chi-Square statistic?
What is the formula for the Chi-Square statistic?
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$\text{Chi-Square} = \frac{(O-E)^2}{E}$ summed over all cells. Sum the squared standardized deviations across all contingency table cells.
$\text{Chi-Square} = \frac{(O-E)^2}{E}$ summed over all cells. Sum the squared standardized deviations across all contingency table cells.
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Find the expected frequency: $60$ total, $15$ in row, $4$ in column.
Find the expected frequency: $60$ total, $15$ in row, $4$ in column.
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$E = \frac{(15 \times 4)}{60} = 1$. Apply the expected frequency formula: row total × column total ÷ grand total.
$E = \frac{(15 \times 4)}{60} = 1$. Apply the expected frequency formula: row total × column total ÷ grand total.
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What describes a contingency table with 3 rows and 2 columns?
What describes a contingency table with 3 rows and 2 columns?
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3x2 table. Describes the dimensions of a two-way frequency table.
3x2 table. Describes the dimensions of a two-way frequency table.
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Which test applies when examining if two variables interact?
Which test applies when examining if two variables interact?
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Chi-Square Test of Independence. Independence tests examine relationships between two categorical variables.
Chi-Square Test of Independence. Independence tests examine relationships between two categorical variables.
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Calculate degrees of freedom for a 4x3 contingency table.
Calculate degrees of freedom for a 4x3 contingency table.
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$(4-1)(3-1) = 6$. Use the formula $(r-1)(c-1)$ where $r=4$ rows and $c=3$ columns.
$(4-1)(3-1) = 6$. Use the formula $(r-1)(c-1)$ where $r=4$ rows and $c=3$ columns.
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Which test applies when examining if two variables interact?
Which test applies when examining if two variables interact?
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Chi-Square Test of Independence. Independence tests examine relationships between two categorical variables.
Chi-Square Test of Independence. Independence tests examine relationships between two categorical variables.
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Calculate degrees of freedom for a 4x3 contingency table.
Calculate degrees of freedom for a 4x3 contingency table.
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$(4-1)(3-1) = 6$. Use the formula $(r-1)(c-1)$ where $r=4$ rows and $c=3$ columns.
$(4-1)(3-1) = 6$. Use the formula $(r-1)(c-1)$ where $r=4$ rows and $c=3$ columns.
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Identify the symbol commonly used for the Chi-Square statistic.
Identify the symbol commonly used for the Chi-Square statistic.
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$\text{Chi-Square}$ or $\text{X}^2$. Both symbols represent the calculated test statistic in Chi-Square tests.
$\text{Chi-Square}$ or $\text{X}^2$. Both symbols represent the calculated test statistic in Chi-Square tests.
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What is the range of values for a Chi-Square statistic?
What is the range of values for a Chi-Square statistic?
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0 to $\text{infinity}$. Chi-Square statistics are always non-negative with no upper bound.
0 to $\text{infinity}$. Chi-Square statistics are always non-negative with no upper bound.
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Which test checks if proportions differ across multiple populations?
Which test checks if proportions differ across multiple populations?
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Chi-Square Test of Homogeneity. Homogeneity tests compare categorical proportions across multiple populations.
Chi-Square Test of Homogeneity. Homogeneity tests compare categorical proportions across multiple populations.
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What is required for valid Chi-Square results concerning data collection?
What is required for valid Chi-Square results concerning data collection?
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Random sampling. Random sampling ensures valid statistical inferences from Chi-Square tests.
Random sampling. Random sampling ensures valid statistical inferences from Chi-Square tests.
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Identify the test: Assessing relationship between two categorical variables.
Identify the test: Assessing relationship between two categorical variables.
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Chi-Square Test of Independence. This test determines if two categorical variables are associated.
Chi-Square Test of Independence. This test determines if two categorical variables are associated.
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Calculate $\text{Chi-Square}$: $O=10, E=8$ in one cell.
Calculate $\text{Chi-Square}$: $O=10, E=8$ in one cell.
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$\frac{(10-8)^2}{8} = 0.5$. Apply the Chi-Square formula: $(O-E)^2/E$ for this cell.
$\frac{(10-8)^2}{8} = 0.5$. Apply the Chi-Square formula: $(O-E)^2/E$ for this cell.
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What is the general purpose of a Chi-Square test?
What is the general purpose of a Chi-Square test?
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To test the association between categorical variables. Chi-Square tests evaluate relationships and patterns in categorical data.
To test the association between categorical variables. Chi-Square tests evaluate relationships and patterns in categorical data.
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What is the critical value for a Chi-Square test with 2 df at 0.05 significance?
What is the critical value for a Chi-Square test with 2 df at 0.05 significance?
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5.991. Standard critical value for 2 degrees of freedom at 5% significance level.
5.991. Standard critical value for 2 degrees of freedom at 5% significance level.
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What is a common use of the Chi-Square Test of Independence?
What is a common use of the Chi-Square Test of Independence?
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To assess relationships between categorical variables. Independence tests determine if categorical variables are associated.
To assess relationships between categorical variables. Independence tests determine if categorical variables are associated.
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Identify the test: Comparing categorical distributions across multiple groups.
Identify the test: Comparing categorical distributions across multiple groups.
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Chi-Square Test of Homogeneity. This test compares how categorical variables are distributed across groups.
Chi-Square Test of Homogeneity. This test compares how categorical variables are distributed across groups.
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What assumption does a Chi-Square test make about samples?
What assumption does a Chi-Square test make about samples?
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Samples are randomly selected. Random sampling ensures independence and representative results.
Samples are randomly selected. Random sampling ensures independence and representative results.
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Find expected frequency: $100$ total, $25$ in row, $10$ in column.
Find expected frequency: $100$ total, $25$ in row, $10$ in column.
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$E = \frac{(25 \times 10)}{100} = 2.5$. Calculate using the standard expected frequency formula.
$E = \frac{(25 \times 10)}{100} = 2.5$. Calculate using the standard expected frequency formula.
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What type of distribution is used in Chi-Square tests?
What type of distribution is used in Chi-Square tests?
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Chi-Square distribution. Chi-Square distribution is the theoretical basis for these hypothesis tests.
Chi-Square distribution. Chi-Square distribution is the theoretical basis for these hypothesis tests.
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What is the degree of freedom formula for a Chi-Square Test of Independence?
What is the degree of freedom formula for a Chi-Square Test of Independence?
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$(r-1)(c-1)$, where $r$ is rows, $c$ is columns. Degrees of freedom account for constraints in the contingency table.
$(r-1)(c-1)$, where $r$ is rows, $c$ is columns. Degrees of freedom account for constraints in the contingency table.
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State the formula for the expected frequency in a contingency table cell.
State the formula for the expected frequency in a contingency table cell.
Tap to reveal 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.
$E = \frac{(row\text{ }total \times column\text{ }total)}{grand\text{ }total}$. Expected frequency equals the product of marginal totals divided by sample size.
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What is the formula for the Chi-Square statistic?
What is the formula for the Chi-Square statistic?
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$\text{Chi-Square} = \frac{(O-E)^2}{E}$ summed over all cells. Sum the squared standardized deviations across all contingency table cells.
$\text{Chi-Square} = \frac{(O-E)^2}{E}$ summed over all cells. Sum the squared standardized deviations across all contingency table cells.
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What do you compare the Chi-Square statistic to for hypothesis testing?
What do you compare the Chi-Square statistic to for hypothesis testing?
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Chi-Square critical value. Compare calculated test statistic to tabled critical value for decision.
Chi-Square critical value. Compare calculated test statistic to tabled critical value for decision.
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Which test assesses if sample proportions are equal across groups?
Which test assesses if sample proportions are equal across groups?
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Chi-Square Test of Homogeneity. Homogeneity tests compare proportions of categorical outcomes across groups.
Chi-Square Test of Homogeneity. Homogeneity tests compare proportions of categorical outcomes across groups.
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What is the alternative hypothesis for a Chi-Square Test of Homogeneity?
What is the alternative hypothesis for a Chi-Square Test of Homogeneity?
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The distributions are different. Homogeneity tests check if categorical distributions vary across groups.
The distributions are different. Homogeneity tests check if categorical distributions vary across groups.
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What is the null hypothesis for a Chi-Square Test of Independence?
What is the null hypothesis for a Chi-Square Test of Independence?
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The variables are independent. For independence tests, we assume no relationship exists between variables.
The variables are independent. For independence tests, we assume no relationship exists between variables.
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Determine the test: Evaluating if gender is related to voting preference.
Determine the test: Evaluating if gender is related to voting preference.
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Chi-Square Test of Independence. Tests if gender and voting preference are associated variables.
Chi-Square Test of Independence. Tests if gender and voting preference are associated variables.
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Identify the type of variable suitable for Chi-Square tests.
Identify the type of variable suitable for Chi-Square tests.
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Categorical variables. Chi-Square tests require qualitative data with distinct categories.
Categorical variables. Chi-Square tests require qualitative data with distinct categories.
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