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Pearson Product-Moment Correlation Coefficient

The Pearson product-moment correlation coefficient is a statistical measurement of the correlation (linear association) between two sets of values.

The Pearson product-moment correlation coefficient for two sets of values, *x* and *y*, is given by the formula :

where *x* and *y* are the sample means of the two arrays of values.

If the value of *r* is close to +1, this indicates a strong positive correlation, and if *r* is close to -1, this indicates a strong negative correlation.

The Excel CORREL function calculates the Pearson Product-Moment Correlation Coefficient for two sets of values.

The format of the function is :

CORREL( array1, array2 )

Where array1 is a set of independent variables and array2 is a set of dependent variables. These arrays should be of equal length.

The Excel Correl function is the same as the Excel Pearson Function, except that, in earlier versions of Excel (earlier than Excel 2003), the Pearson function may exhibit some rounding errors.

Therefore, if you are using an earlier version of Excel than Excel 2003, you should use the Correl function in preference to the Pearson function. In later versions of Excel, both functions should give the same results.

A | B | |
---|---|---|

1 | x | y |

2 | 2 | 22.90 |

3 | 10 | 45.78 |

4 | 7 | 33.49 |

5 | 17 | 49.77 |

6 | 14 | 40.94 |

7 | 16 | 36.18 |

8 | 8 | 21.05 |

9 | 12 | 50.57 |

10 | 11 | 31.32 |

11 | 15 | 53.76 |

12 | 18 | 55.66 |

13 | 3 | 27.61 |

14 | 4 | 11.15 |

15 | 1 | 10.11 |

16 | 6 | 37.90 |

17 | 5 | 31.08 |

18 | 13 | 45.48 |

19 | 19 | 63.83 |

20 | 20 | 63.60 |

21 | 9 | 27.01 |

Columns A and B of the spreadsheet on the right contain two arrays of values. These are shown in the chart below:

The Pearson Product-Moment Correlation Coefficient of the values in columns A and B of the spreadsheet can be calculated using the Excel Correl function, as follows:

=CORREL( A2:A21, B2:B21 )

This gives the result **0.870035104**, which indicates a strong positive correlation between the two sets of values.

Information on interpreting the significance of the Pearson Product-Moment Correlation Coefficient is given on the University of Connecticut website

Further information and examples of the Excel Correl function can be found on the Microsoft Office website.

If you get an error from your Excel Correl function this is likely to be one of the following :

Common Errors

#N/A | - | Occurs if the supplied arrays are of different lengths |

#DIV/0! | - | Occurs if either of the supplied arrays are empty or if the standard deviation of their values equals zero |