This page includes Step-by-Step instructions to calculate a
correlation coefficient by
hand.
In order to find Pearson’s Sample Correlation Coefficient, r,
“by-hand” we need a formula.
Click here for formula explanation.
- We will use the table below to simplify the formula computations.
- You may find it easier to print out a copy of the chart while working
through this example.
Preliminary Step
- Find the sample mean and sample
standard deviation for the x’s and also for the y’s
listed in the table above.
(i.e. Fill in the chart below.) Hint: You may want to use a
calculator or computer for these computations. Or click here for the
Mean
and Standard Deviation Tutorial.
| Variable |
Sample Mean |
Sample Standard Deviation |
x
(temperature) |
|
|
y (water
consumption) |
|
|
Click here for solution.
Procedure 
- Either print the table above or make your own copy on a sheet of paper.
- Enter the x’s into column C1 as in the table above.
- Enter the y’s into column C2 as in the table above.
- For each row in column C3, take each individual x value and subtract the
mean of the x’s.
- For each row in column C4, take the answer from that row of C3 and divide
the answer by the standard deviation of the x’s.
- For each row in column C5, take each individual y value and subtract the
mean of the y’s.
- For each row in column C6, take the answer from that row of C5 and divide
the answer by the standard deviation of the y’s.
- For each row in column C7, multiply the answers for that row of column C4
and C6.
- Find the sum (i.e. total) of column C7.
- Correlation Coefficient, r = sum of column C7 divided by (n-1), where
n is the number of
pairs of data. Here n=7 pairs.
Compare Formula to Using the
Table.
Learn the Procedure for calculating correlation coefficients
Correlation Menu Dictionary
STATS @ MTSU