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Pearson correlation

This procedure is available in both the Analyse-it Standard and the Analyse-it Method Evaluation edition

Pearson correlation is a test to determine the degree of correlation (association) between two variables.

The requirements of the test are:

  • Two variables measured on a continuous scale.
  • Variables are from a population with a bivariate normal distribution.

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout. The dataset must contain two continuous scale variables.   

When entering new data we recommend using New Dataset to create a new 2 variables dataset ready for data entry.

Using the test

To start the test:

  1. Excel 2007:
    Select any cell in the range containing the dataset to analyse, then click Correlation on the Analyse-it tab, then click Pearson
  2. Excel 97, 2000, 2002 & 2003:
    Select any cell in the range containing the dataset to analyse, then click Analyse on the Analyse-it toolbar, click Correlation then click Pearson.

  3. Click Variable X and Variable Y and select the variables.
  4. Click Alternative hypothesis and select the alternative hypothesis to test.
  5. r ≠ 0 to test if the variables are correlated.
    r > 0 to test if the variables are positively correlated, where observations of the variables tend to increase together.
    r < 0 to test if the variables are negatively correlated, where observations of one variable tend to increase as observations in the other variable decrease.
  6. Enter Confidence interval to calculate around the Pearson r statistic. The level should be entered as a percentage between 50 and 100, without the % sign.
  7. Click OK to run the test.

The report shows the number of observations analysed, and, if applicable, how many missing cases were pairwise deleted.

The Pearson r correlation statistic and confidence interval are shown.

METHOD The confidence interval is calculated using the Fisher's Normal transformation (see [1] or [2]).

The hypothesis test is shown. The p-value is the probability of rejecting the null hypothesis, that the variables are independent, when it is in fact true. A significant p-value implies that the two variables are correlated.

METHOD The p-value is calculated using the t approximation (see [1]).

The scatter plot (see below) shows a visual assessment of the strength of association.

Further reading & references

  1. Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition)
    David J. Sheskin, ISBN 1-58488-440-1 2003; 945.
  2. Statistics with Confidence (2nd edition)

    Gardner M.J., Altman D.G. ISBN 0-7279-1375-1 2000; 89-90.