Negative correlation
Positive correlation
No correlation
A measurement used to show the strength between two variables using a value between -1 and 1; it is often symbolized in mathematical formulas as the letter r.

Quite Simply...

  • The correlation coefficient shows the strength of a relationship; the closer the correlation coefficient is to positive or negative 1, the stronger the relationship, whether it be negative or positive, between the two variables.
  • The correlation coefficient cannot be less than -1 or greater than 1.

Examples of Correlation Coefficients

  • A correlation coefficient close to zero indicates a weak linear relationship between two variables, as seen between one's type of pet and one's personality.
  • A correlation coefficient of zero would indicate that there is no correlation, or relationship, between two variables. This may be seen as the correlation coefficient between shoe size and number of books read, for example.
  • A positive correlation coefficient occurs when the values of both variables increase together, as seen between studying hard and high grades in school.
  • A negative correlation occurs when the increase of one variable corresponds with the decrease of another, as seen in less stage fright when more time was spent practicing lines in a play.
external image correlation_coefficient.gif
These are various charts showing what correlation coefficients look like on a scatterplot, beginning with a strong negative correlation and continuing through to a strong positive correlation.
external image scatter_plot.gif
Use these guidelines to determine the strength of the correlation coefficient:
Weak relationship
Moderate relationship
Strong relationship

See Also...

  • Correlational study, a type of statistical research done to determine the correlation coefficient

Go check out this game to see if you can recognize strong and weak positive and negative correlations.