AP Statistics: Unit 2 Overview — Exploring Two-Variable Data

Bivariate data

Analyzing two variables simultaneously to describe relationships between them.

Explanatory Variable

The variable that attempts to explain or predict changes in another variable, plotted on the x-axis.

Response Variable

The variable that measures the outcome, plotted on the y-axis.

Scatterplot

A graph showing the relationship between two quantitative variables measured on the same individuals.

DUFS

An acronym used to describe relationships: Direction, Unusual features, Form, Strength.

Direction (in scatterplots)

The way the data points trend; can be positive, negative, or no association.

Outlier

A point that falls outside the overall pattern of the data.

Clusters

Groups of points in a scatterplot that are separated by gaps.

Linear relationship

A relationship where the data points generally follow a straight line.

Curved relationship

A relationship where the data points do not follow a straight line, but a curve.

Correlation Coefficient (r)

A numerical measure of the direction and strength of a linear relationship between two quantitative variables.

Formula for correlation coefficient

r = (1/(n-1)) * Σ ((xi - x̄)/sx) * ((yi - ȳ)/sy) for two variables.

Magnitude of r

The strength of the relationship; 1 or -1 indicates perfect linearity, 0 indicates no linear relationship.

Positive association

When an increase in one variable tends to correspond with an increase in the other variable.

Negative association

When an increase in one variable tends to correspond with a decrease in the other variable.

Perfect linear relationship

When r = 1 or r = -1.

Weak correlation

When 0.0 ≤ |r| < 0.5, indicating little to no linear relationship.

Symmetry (in correlation)

Correlations do not depend on which variable is independent or dependent.

Unit independence (of r)

The correlation coefficient r has no units and remains unchanged with unit conversions.

Non-resistant correlation

Correlation can be greatly affected by outliers; one outlier can distort the correlation value.

Lurking variables

Variables that are not included in the study but could influence the relationship between the studied variables.

Correlation vs. Causation

A strong correlation does not imply that changes in one variable cause changes in another.

Mistake: Assuming linearity based on r

Misinterpreting r as the only indicator of a relationship without considering the form of the data.

Mistake: Confusing correlation and association

Using 'correlation' for non-linear or categorical data; should be restricted to linear, quantitative relationships.

Mistake: Ignoring context

Failing to provide full descriptors in a conclusion about relationships between variables.

Mistake: Claiming causation

Asserting a cause-and-effect relationship without proper experimental evidence.

Mistake: Forgetting axes labels

Omitting unit and variable labels on graphs, negatively impacting scores on exams.