Correlation

Examples:

Is there a relationship between math anxiety and performance in a statistics class?

Is there a relationship between numerical skills and musical skills?

Is there a relationship between dosage and survival rate?

Is there a relationship between the degree of trauma experienced as a child and psychological problems experienced as an adult?

Is there a relationship between years of education and income?

Ask yourself -- can you think of questions in your major field/area of interest that are "relationship" questions?

When you want to study relationship or correlation between two variables, you need to measure every individual/thing/animal in the study with respect to both variables. This is bivariate (i.e. two -variable) analysis.

Scatterplot Example

A "positive relationship"

A "negative" relationship

Interpretations:

1. The closer points are to a straight (not curved) line the stronger the relationship between X and Y.
2. Often, people consider the "X" variable the independent variable and the "Y" variable, the dependent variable.
3. Magnitude of the relationship is measured with the CORRELATION COEFFICIENT -- a statistic. So where the scatterplot is the bivariate graphic and the histogram is the univariate. The correlation coefficient gives a measure of association between two variables

Correlation Coefficient (formula on pages 132-134, but see note on p. 134 just before the review exercises) it's symbol is r. A formula:

å
[(each x- average of the x's) * (each y - average of the y's)]
r=    ---------------------------------------------------------
   (Standard Deviation x)  * (Standard Deviation y)