Ch. 11: Quantifying and Interpreting Relationships Among Variables

Correlation Coefficient A single number indicating the strength of association between 2 variables. To what extent does the association resemble a straight line? Pearson r as coefficient of choice Value ranges from 0 (no relationship) to 1 (perfect linear relationship) Sign indicates direction of relationship

Correlation and Causation Causation implies correlation, but correlation does not imply causation. Temporal precedence problem Third variable problem

Types of Variables Continuous variables Discrete variables Dichotomous variables

Example of a Scatter Plot This person scores a 10 on Exam 1 and a 40 on Exam 2

Scatter Plots of Different Values of the Correlation Coefficient

Pearson r Assesses the linear relationship between two continuous variables Product Moment Correlation Conceptual Formula:

Alternative Formula for Pearson r

Spearman Rho Assesses the linear relationship between two variables that are in the form of ranked data Formula: “D” is the difference between the pairs of ranked scores “6” is a constant “N” is the number of score pairs

Point-Biserial Correlation One variable is continuous and the other is dichotomous Dummy coding is used to quantify the one dichotomous variable Formula is same as Pearson r

Phi Coefficient Both variables are dichotomous Could convert scores to z-scores and use Pearson r formula

Alternative Formula for Phi “2 X 2 Table of Frequencies (or Counts)” A D C B