Interpreting data displays: correlation coefficients, effect size and statistical significance

What the exam asks

• Section I (Multiple Choice): Set-based questions present a bar graph, line graph, table, or scatterplot and ask you to identify variables, describe trends, compare correlation coefficients ($r$), or interpret $p$-values and effect sizes.
• Section II (AAQ & EBQ): In AAQ Part C, you must explain what a reported statistic (including correlation, effect size, or statistical significance) indicates in the context of the study. In AAQ Part F and the EBQ, you must use data displays and statistical findings to argue whether a hypothesis or claim is supported.

Core ideas

Reading data displays

Before analyzing numbers, check the labels on any table, graph, chart, or diagram:

• In experiments: The independent variable (IV) or grouping variable is conventionally placed on the horizontal x-axis (or forms the rows/columns of a table), while the dependent variable (DV)—the measured outcome—is placed on the vertical y-axis.
• In correlational scatterplots: Either measured variable can be on the x-axis or y-axis because neither variable is manipulated. Each dot represents one participant’s pair of scores.
• Describing trends: State how one variable changes in relation to the other (e.g., “As daily screen time increases, reported sleep quality decreases” or “The imagery group recalled a higher mean number of words than the rehearsal group”).

Scatterplots and correlation coefficients ($r$)

A correlation coefficient ($r$) is a statistic ranging from $-1.00$ to $+1.00$ that quantifies two things about the linear relationship between two variables:

1. Direction (the sign, $+$ or $-$):
   • Positive correlation ($r > 0$): Both variables move in the same direction (as one increases, the other increases; as one decreases, the other decreases). On a scatterplot, the cluster of dots slopes upward from left to right.
   • Negative (inverse) correlation ($r < 0$): Variables move in (as one increases, the other decreases). On a scatterplot, the cluster of dots slopes .