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  1. AP Statistics
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Explain the concept of homogeneity in the context of chi-squared tests.

Tests if different populations are similar in their distribution of a categorical variable.

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Explain the concept of homogeneity in the context of chi-squared tests.

Tests if different populations are similar in their distribution of a categorical variable.

Explain the concept of independence in the context of chi-squared tests.

Tests if two variables are not associated with each other.

Explain the purpose of calculating expected counts.

To determine what the cell values would be if there is no association between the variables.

What is the formula for calculating expected counts in a two-way table?

Expected Count = (Row Total * Column Total) / Table Total

What is the formula for the Chi-Squared Test Statistic?

χ2=∑(Observed−Expected)2Expected\chi^2 = \sum \frac{(Observed - Expected)^2}{Expected}χ2=∑Expected(Observed−Expected)2​

What is the formula for calculating degrees of freedom in a Chi-Squared Test?

df=(number of rows−1)∗(number of columns−1)df = (number\ of\ rows - 1) * (number\ of\ columns - 1)df=(number of rows−1)∗(number of columns−1)

What is a two-way table?

A grid showing the relationship between two categorical variables.

Define Chi-Squared Test for Homogeneity.

Compares the distribution of a categorical variable across two or more independent groups/populations.

Define Chi-Squared Test for Independence.

Examines the relationship between two categorical variables within a single population.

What are expected counts?

The counts we expect to see if there's no association (independence) or no difference (homogeneity).

Define Null Hypothesis.

States that there is no association between the two categorical variables.