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Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

Pearson's r

The Pearson correlation is appropriate when both variables being compared are of a continuous level of measurement (interval or ratio). Use the Levels of Measurement tab to learn more about determining the appropriate level of measurement for your variables.

Assumptions

  1. Independence of cases - determined by research design
  2. Linearity - assessed through visual assessment of a scatterplot
  3. No significant outliers - identified through visual examination of scatterplot and other means
  4. Homoscedasticity - assessed through visual examination of residuals scatterplot (should be approximately rectangular in shape)

Running Pearson Correlation in SPSS

  1. Analyze > Correlate > Bivariate
  2. Move variables of interest into the "Variables" box (they must be scale variables)
  3. Select "Pearson" as the test.
  4. You may use the "Options" button to select descriptive statistics you wish to include as well.
  5. Click "OK" to run the test.

Interpreting the Output

The results will generate in a matrix. You can ignore any boxes that show a "1" as the correlation value as these are simply the variable correlated with itself. These values will form a diagonal across the matrix that can be used to help you focus on the correct values. You only need to explore the correlation values on half of the matrix. APA Style uses the bottom half.

Pearson's Output table from SPSS

 

With the release of SPSS 27, users now have the option to only produce the lower half of the table, which is in line with APA Style and makes it easier to identify the correct correlation values.

Pearson's Output table 2 from SPSS

 

Reporting Results

When reporting the results of the correlation analysis, APA Style has very specific requirements on what information should be included. Below is the key information required for reporting the Pearson Correlation results. You want to replace the red text with the appropriate values from your output.

r(degrees of freedom) = the r statisticp = p value.

Example:
A Pearson product-moment correlation was run to determine the relationship between ice cream sales and shark attacks. There was a moderate, positive correlation between ice cream sales and the number of shark attacks, which was statistically significant (r(13) = .706, p < .05).

Notes:

  • When reporting the p-value, there are two ways to approach it. One is when the results are not significant. In that case, you want to report the p-value exactly: p = .24. The other is when the results are significant. In this case, you can report the p-value as being less than the level of significance: p < .05.
  • The r statistic should be reported to two decimal places without a 0 before the decimal point: .36
  • Degrees of freedom for this test are N - 2, where "N" represents the number of people in the sample. N can be found in the correlation output.

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