The Pearson correlation coefficient can also be used to test whether the relationship between two variables is significant. To calculate Pearson correlation: r=[nx2(x)2][ny2(y)2]nxy(x)(y) Imagine that you're studying the relationship between newborns' weight and length. You have the weights and lengths of the 10 babies born last month at your local hospital. After you convert the imperial measurements to metric, you enter the data in a table: Follow the steps below and fill the following table: Step 1: Calculate the sums of x and y Step 2: Calculate x2 and y2 and their sums Step 3: Calculate the cross product and its sum Step 4: Calculate the Pearson Correlation r: The Pearson correlation of the sample is r. It is an estimate of rho (), the Pearson correlation of the population. Knowing r and n (the sample size), we can infer whether is significantly different from 0 . Null hypothesis (HO):=0 Alternative hypothesis (Ha): =0 Calculate the t value (a test statistic) using this formula (n=10,r is what we calculated in the previous table (step 4)): t=n21r2r We can calculate the t value: Answer of t value of Pearson Correlation calculation