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  1. AP Statistics
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Glossary

A

Alternative Hypothesis (Hₐ)

Criticality: 3

A statement that contradicts the null hypothesis, proposing that there is an effect, a difference, or a relationship between variables.

Example:

The alternative hypothesis for a homogeneity test might state that the distribution of preferred study methods is not the same for high school and college students.

C

Categorical Variables

Criticality: 2

Variables that place individuals into categories, rather than measuring numerical quantities.

Example:

Hair color (blonde, brown, black) or type of pet (dog, cat, fish) are examples of categorical variables.

Chi-Squared Test for Homogeneity

Criticality: 3

A chi-squared test used to compare the distribution of a single categorical variable across two or more independent populations or groups.

Example:

A researcher might use a chi-squared test for homogeneity to determine if the proportion of students who plan to attend college is the same across different high schools in a district.

Chi-Squared Test for Independence

Criticality: 3

A chi-squared test used to determine if there is a statistically significant association between two categorical variables within a single population.

Example:

To see if there's a relationship between a person's favorite genre of music and their preferred social media platform, you would use a chi-squared test for independence.

Chi-squared (χ²) tests

Criticality: 3

Statistical tests used to analyze categorical data, often to determine if there's a significant association between variables or if observed frequencies differ from expected frequencies.

Example:

An AP Stats student might use a chi-squared test to see if there's a relationship between a student's favorite subject and their preferred learning style.

D

Degrees of Freedom (df)

Criticality: 3

A value that indicates the number of independent pieces of information used to calculate a statistic, crucial for determining the shape of the chi-squared distribution.

Example:

For a 3x4 two-way table, the degrees of freedom would be (3-1)*(4-1) = 6.

E

Expected Counts

Criticality: 3

The frequencies that would be anticipated in each cell of a two-way table if the null hypothesis (of no association or homogeneity) were true.

Example:

If 50% of students prefer chocolate ice cream, and you have 100 students, the expected count for chocolate lovers would be 50.

N

Null Hypothesis (H₀)

Criticality: 3

A statement of no effect, no difference, or no relationship between variables, which is assumed to be true until evidence suggests otherwise.

Example:

For a chi-squared test of independence, the null hypothesis would state that there is no association between a person's favorite color and their birth month.

O

Observed Counts

Criticality: 2

The actual frequencies or counts recorded in each cell of a two-way table from the collected data.

Example:

In a survey of 100 students, if 60 actually said they prefer chocolate ice cream, then 60 is the observed count for that category.

P

P-value

Criticality: 3

The probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.

Example:

If a p-value is 0.02, it means there's a 2% chance of seeing your results if the null hypothesis were actually true, leading you to consider rejecting it.

T

Two-Way Table

Criticality: 3

A table that displays the counts of observations for two categorical variables, organizing data into rows and columns to show their relationship.

Example:

A two-way table could show the number of students who prefer online vs. in-person classes, broken down by grade level (freshman, sophomore, etc.).