Chapter 11: Correlation

correlation

Association between scores on two variables.

Scatter diagram

A graph showing the relationship between two variables: the values of one variable are along the horizontal axis and the values of the other variable are along the vertical axis; each score is shown as a dot in this two-dimensional space.

linear correlation

A relation between two variables that shows up on a scatter diagram as the dots roughly following a straight line.

curvilinear correlation

A relation between two variables that shows up on a scatter diagram as dots following a systematic pattern that is not a straight line.

no correlation

No systematic relationship between two variables

Positive correlation

A relation between two variables in which high scores on one go with high scores on the other, mediums with mediums, and lows with lows; on a scatter diagram, the dots roughly follow a straight line sloping up and to the right.

Negative correlation

A relation between two variables in which high scores on one go with low scores on the other, mediums with mediums, and lows with highs; on a scatter diagram, the dots roughly follow a straight line sloping down and to the right.

Cross-product of Z scores

The result of multiplying a person’s Z score on one variable by the person’s Z score on another variable.

Correlation coefficient (r)

A measure of degree of linear correlation between two variables ranging from -1 (a perfect negative linear correlation) through 0 (no correlation) to +1 (a perfect positive correlation).

Direction of causality

A path of causal effect; if X is thought to cause Y then the direction of causality is from X to Y.

Correlational research design

Any research design other than a true experiment

Proportionate reduction in error (r²)

A measure of association between variables that is used when comparing associations. Also called proportion of variance accounted for.

Restriction in range

A situation in which you figure a correlation but only a limited range of the possible values on one of the variables is included in the group studied

outliers

Scores with an extreme (very high or very low) value in relation to the other scores in the distribution.

Spearman’s rho

The equivalent of a correlation coefficient for rank-ordered scores.

Correlation matrix

A common way of reporting the correlation coefficients among several variables in a research article; table in which the variables are named on the top and along the side and the correlations among them are all shown.