Pearson’s Correlation or Correlation Coefficient

The Pearson’s correlation or correlation coefficient or simply correlationĀ  is used to find the degree of linear relationship between two continuous variables. The value for a correlation coefficient lies between 0.00 (no correlation) and 1.00 (perfect correlation). Generally, correlations above 0.80 are considered pretty high.

Remember:

  1. Correlation is interdependence of continuous variables, it does not refer to any cause and effect.
  2. Correlation is used to determine linear relationship between variables.
  3. Draw a scatter plot before performing/calculating the correlation (to check the assumptions of linearity)

Procedure in SPSS

The command for correlation is found at Analyze –> Correlate –> Bivariate i.e.

Analyze-->Correlate-->Bivariate...

The Bivariate Correlations dialog box will be there:

Correlation dialog box in spss

Select one of the variables that you want to correlate in the left hand pane of the Bivariate Correlations dialog box and shift it into the Variables pane on the right hand pan by clicking the arrow button. Now click on the other variable that you want to correlate in the left hand pane and move it into the Variables pane by clicking on the arrow button

Bivariate correlation box

Output

output from correlation test

The Correlations table in output gives the values of the specified correlation tests, such as Pearson’s correlation. Each row of the table corresponds to one of the variables similarly each column also corresponds to one of the variables.

Interpretation

In example, the cell at the bottom row of the right column represents the correlation of depression with depression having the correlation equal to 1.0. Likewise the cell at the middle row of the middle column represents the correlation of anxiety with anxiety having correlation value This in in both cases shows that anxiety is related with anxiety similarly depression is related to depression, so have perfect relationship.

The cell at middle row and right column (or cell at the bottom row at the middle column) is more interesting. This cell represents the correlation of anxiety and depression (or depression with anxiety). There are three numbers in these cells.

  1. The top number is the correlation coefficient value which is 0.310.
  2. The middle number is the significance of this correlation which is 0.018.
  3. The bottom number, 46 is the number of observations that were used to calculate the correlation coefficient. between the variable of study.

Note that the significance tells us whether we would expect a correlation that was this large purely due to chance factors and not due to an actual relation. In this case, it is improbable that we would get an r (correlation coefficient) this big if there was not a relation between the variables.

 

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2 Comments

  1. Hosea Haff says:

    Perfectly composed articles, Really enjoyed reading.

  2. Anonymous says:

    Pearson’s Correlation or Correlation Coefficient | Introduction to Statistics, Basic Statistics, Applied Statistics or Pearson’s Correlation or Correlation Coefficient | Introduction to Statistics, Basic Statistics, Applied Statistics ou say!

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