In my example, the p-value is so small that it is quoted as <0.001. So, the Pearson correlation does not equal (≠) 0.
There is a correlation between weight and height in the overall population.
In other words, the Pearson correlation coefficient is 0.
There is no correlation between weight and height in the overall population.
Usually, when performing the test, a two-tailed analysis is performed. The third main output from a Pearson correlation test is obviously the p-value. The other 8.67% of the variance is explained by other factors that were not measured in the experiment, such as measurement errors. We can say that 91.33% of the variability in weight is explained by the variability in height.Īnd, since it does not matter which way around the variables go on the axes, this means that the reverse is also true 91.33% of the variability in height is explained by the variability in weight. To interpret the coefficient of determination better, it is more convenient to multiply it by 100 to convert it to a percentage. R 2 is an absolute value that is always between 0 and 1. So, if you don’t have R 2 from the output of your Pearson correlation test, simply square the correlation coefficient. The coefficient of determination (R 2) indicates the amount of variance shared between the two variables.Īs the name suggests, R 2 is computed by squaring the correlation coefficient value. You should always interpret a correlation coefficient in the context of the experiment in question.įor example, a correlation coefficient of 0.2 may indicate a weak correlation in some scientific disciplines, but it actually may be a rather large correlation in other areas of science. It is very important to understand that these are broad cut-offs that do not take into account the scientific question. There have also been some attempts to apply certain cut-offs to the absolute correlation coefficients to precisely describe the magnitude of the correlation. The absolute value of the correlation coefficient indicates how strong the two variables correlate in a linear fashion. On the other hand, a negative correlation coefficient value indicates a negative correlation between the two variables so, as Variable X increases, Variable Y decreases or vice versa. To understand the direction of the linear correlation, you simply look at whether the coefficient value is negative or positive.Ī positive correlation coefficient value indicates a positive correlation between the two variables this can be seen in this example, since our r is a positive number. The correlation coefficient value can be any number between –1 and +1 and it has no units on measure. So, in this example, the correlation coefficient is 0.9557 but what does this mean? This single value can tell us two important factors about the correlation: Note, r is usually written in lower case in the literature, not upper case. The Pearson correlation coefficient, abbreviated as r, is the test statistic. Suppose I have performed a Pearson correlation test using my example data. 1 Outputs from the Pearson correlation test This relationship between variables in statistics is known as correlation.Ī Pearson correlation test is used to measure the strength and direction of this linear correlation.