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Table of Contents

 


 

Pearson's Product Moment Correlation Coefficient

Software Output 

Example of one bivariate comparison with a scattergram. Comparing individual income in U.S. dollars to years of education.

 

 

Pearson's Correlation

 

INCOME: A

 

   21779.0|                    *     *    

          |                 *        *  *

          |                 *     *   *  *

          |              *     *      *   

   14030.0|        *         *              

          |    *  *        *  *  *  *   

          | *           *                

          |       *        *             

          |    *         *                

    6281.0| *   *                         

           ---------------|--------------|

           4.0          12.0          20.0

 

          EDUC: B

 

Number of cases: 32

Missing: 0 C

Pearson Correlation: 0.751 D

p < (2-tailed signif.): 0.0000 E

 

 

Interpretation                                           

A   The Y axis of the scattergram.  If theory suggests cause and effect, the Y axis is commonly used for the dependent (response) variable.

B   The X axis of the scattergram.  If theory suggests cause and effect, the X axis is commonly used for the independent variable.

C   Since each observation (case) must have values for both income and education, any observations where one or both of these variables have no data will be removed from the analysis.

D   Pearson correlation coefficient representing a high positive correlation between education and income.   Interpretation: As years of education increases so does personal income.

E   There is a statistically significant association between income and education.

 

 

Correlation Matrix

 

Example of multiple bivariate comparisons displayed in a correlation matrix.  Comparing individual income, education, and months of work experience.

 

 

Correlation: Pearson (R) Coefficients

 

--------------------------------------------

    Coeff |         Correlation Matrix     |

    Cases |--------------------------------|

      p < |   INCOME |     EDUC | WORKEXP  |

--------------------------------------------

   INCOME |  1.000 A| 0.751 D| -0.160 F|

          |     32 B|    32    |    32    |

          |      . C|  0.000 E|  0.381 G|

--------------------------------------------

     EDUC |    0.751 |    1.000 |   -0.520 |

          |       32 |       32 |       32 |

          |    0.000 |        . |    0.002 |

--------------------------------------------

 WORKEXP  |   -0.160 |   -0.520 |    1.000 |

          |       32 |       32 |       32 |

          |    0.381 |    0.002 |        . |

--------------------------------------------

        2-tailed significance tests

         '.' p-value not computed

 

 

Interpretation                                                            

A   The diagonal in the matrix represents Pearson correlations between the same variable which will always be 1 since the variables are identical. The correlations above the diagonal are a mirror reflection of these below the diagonal, so you only interpret half of the matrix (in this case three correlation coefficients).

B   The number of paired observations for this comparison.

C   A statistical test is not performed when you are comparing a variable to itself.  Mathematically this will always equal zero.

D   Pearson correlation coefficient representing a high positive correlation between education and income.   Interpretation: As years of education increases so does personal income.

E   There is a statistically significant association between income and education.

F   Pearson correlation coefficient representing a very weak negative correlation between work experience and income.  Interpretation: As years of work experience increases personal income decreases.

G   There is not a statistically significant association between work experience and income.


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