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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.

Further information on the Pearson Product-Moment Correlation Coefficient is provided on WikipediaThe Excel Pearson function calculates the Pearson Product-Moment Correlation Coefficient for two sets of values.

The syntax of the function is:

PEARSON( array1, array2 )

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

Note that the Pearson function ignores text values and logical values that are supplied as part of an array.

The Excel Pearson function performs the same calculation as the Excel Correl Function. However, 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, you should use the Correl function in preference to the Pearson function. In more recent versions of Excel, both functions should give the same results.

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

1 | x | y |

2 | 1 | 10.11 |

3 | 2 | 22.90 |

3 | 2 | 27.61 |

4 | 3 | 27.61 |

5 | 4 | 11.15 |

6 | 5 | 31.08 |

7 | 6 | 37.90 |

8 | 7 | 33.49 |

9 | 8 | 21.05 |

10 | 9 | 27.01 |

11 | 10 | 45.78 |

12 | 11 | 31.32 |

13 | 12 | 50.57 |

14 | 13 | 45.48 |

15 | 14 | 40.94 |

16 | 15 | 53.76 |

17 | 16 | 36.18 |

18 | 17 | 49.77 |

19 | 18 | 55.66 |

20 | 19 | 63.83 |

21 | 20 | 63.60 |

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

The Pearson Product-Moment Correlation Coefficient of these values can be calculated using the Excel Pearson function, as follows:

=PEARSON( A2:A21, B2:B21 )

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

A useful table for on interpreting the significance of the Pearson Product-Moment Correlation Coefficient is provided on the University of Connecticut website

For further details and examples of the Excel Pearson function, see the Microsoft Office website.

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

Common Errors

#N/A | - | Occurs if the supplied array arguments have different lengths. |

#DIV/0! | - | Occurs if either of the supplied array arguments is empty or if the standard deviation of their values is equal to zero. |