# PSYCH

**Topics:**Pearson product-moment correlation coefficient, Correlation and dependence, Spearman's rank correlation coefficient

**Pages:**2 (447 words)

**Published:**November 2, 2014

In this tutorial, when we speak simply of a correlation coefficient, we are referring to the Pearson product-moment correlation. Generally, the correlation coefficient of a sample is denoted by r, and the correlation coefficient of a population is denoted by ρ or R.

How to Interpret a Correlation Coefficient

The sign and the absolute value of a correlation coefficient describe the direction and the magnitude of the relationship between two variables.

The value of a correlation coefficient ranges between -1 and 1. The greater the absolute value of a correlation coefficient, the stronger the linear relationship. The strongest linear relationship is indicated by a correlation coefficient of -1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0.

Maximum positive correlation

(r = 1.0)Strong positive correlation

(r = 0.80)Zero correlation

(r = 0)

Maximum negative correlation

(r = -1.0)Moderate negative correlation

(r = -0.43)Strong correlation & outlier

(r = 0.71)

Several points are evident from the scatterplots.

When the slope of the line in the plot is negative, the correlation is negative; and vice versa. The strongest correlations (r = 1.0 and r = -1.0 ) occur when data points fall exactly on a straight line. The correlation becomes weaker as the data points become more scattered. If the data points fall in a random pattern, the correlation is equal to zero. Correlation is affected by outliers. Compare the first scatterplot with the last scatterplot. The single outlier in the last plot greatly reduces the correlation (from 1.00 to 0.71). How to Calculate a Correlation Coefficient

If you look in different statistics textbooks, you are...

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