Correlation Test. This value can range from 1 to 1. Pearson correlation r which measures a linear dependence between two variables x.
This is verified by the commutative property of multiplication. Corrttest r size tails the p value of the one sample test of the correlation coefficient using theorem 1 where r is the observed correlation coefficient based on a sample of the stated size. It is a corollary of the cauchy schwarz inequality that the absolute value of the pearson correlation coefficient is not bigger than 1.
Therefore the value of a correlation coefficient ranges between 1 and 1.
So to sum up a pearson correlation test measures how the direction and how strong a linear correlation is between two variables. This value can range from 1 to 1. Therefore the value of a correlation coefficient ranges between 1 and 1. The spearman rank correlation test does not carry any assumptions about the distribution of the data and is the appropriate correlation analysis when the variables are measured on a scale that is at least ordinal.
