Question

Explain the concept of correlation and how to interpret correlation coefficients of 0.3,0, and -0.95

Answer 1

Correlation coefficient (r) is a number that indicates the degree of <I>linear</I> relationship between two variables.

I. Scatter diagram (scattergram, scatterplot) is graphic representation of r. Each dot on scattergram represents two measures on one unit.

II. Reference values

A. 1 or +1 indicates perfect predictability and that both variables increase/decrease together (height in inches vs. cm. example).

B. -1 also indicates perfect predictability, but that one variable increase while the other decreases (height in inches vs. distance between head and ceiling example).

C. 0 indicates random relationship with no predictability.

D. All r's are between these points. This is only an ordinal scale.

-1_______________0_______________+1

E. However, there are some limitations.

1. The decimals cannot be converted into percentages, because it is only an ordinal scale.

2. Absolute value can never be greater than 1 (see formula).

3. Correlation does not necessarily mean causation

r = .3 indicates mild relationship with minimal predictability.

r = .95 indicates strong relationship with great predictability.