Psychology Statistics For Dummies by Donncha Hanna

Author:Donncha Hanna
Language: eng
Format: epub
Publisher: Wiley
Published: 2012-08-01T16:00:00+00:00

Figure 12-19: The Kendall’s correlation table as produced by SPSS.

Writing up the results

The APA manual suggests that you should report the correlation coefficient (denoted by the symbol τ or sometimes just by r) value rounded to 2 decimal places, with the degrees of freedom in parentheses, followed by the significance level (denoted by p). The degrees of freedom for a bi-variate correlation coefficient is always n – 2, which is the sample size minus 2; in the current example it is 100 – 2 = 98. Taking the example reported in Figure 12-18, we would report the result as follows:

τ (98) = .04, p = .65

When you are reporting your result you should always report it in the statistical or numerical format and also in words. You need to describe the magnitude of the relationship, the direction of the relationship and whether it is statistically significant or not:

There was a very weak, positive, non-significant relationship between the responses of the two items; τ (98) = .04, p = 0.65

You can find the τ symbol (pronounced tau) in the symbol option under the Greek and Coptic subset in Microsoft Word.

Using Partial Correlation

Pearson’s, Kendall’s and Spearman’s correlations are all very useful when looking at the relationship between two variables. In statistics, as in life, relationships are often more complex. More than one variable is likely to be related to exam scores, distress or whether someone watches The X Factor (see the examples in the previous sections). Partial correlation is a useful technique that allows you to test the relationship between two variables while controlling for (or partialling out) the influence of other variables on the relationship. The type of partial correlation that is calculated in SPSS is based on Pearson’s correlation (see the previous section) and therefore has the same assumptions.

Performing partial correlation in SPSS

In a small country called Statsville a government official has noticed that there appears to be a very strong, positive, statistically significant correlation between ice-cream sales and the number of drownings over a 12-month period r(10) = .96, p<.001); higher monthly ice-cream sales were related to an increase in the deaths due to drowning. The local media has picked up on the finding and are asking whether ice-cream causes drowning or whether people at funerals tend to buy a lot of ice-cream. However, you have an alternative suggestion; perhaps a third variable is influencing the relationship. Where it is warm people tend to buy more ice-cream in an effort to cool down. Similarly, where it is warm more people tend to go swimming and therefore more people get into difficulties and may unfortunately drown. You suggest that temperature may be influencing the relationship. To test this hypothesis you conduct a partial correlation.

Along the top toolbar select Analyze, choose Correlate from the drop-down menu and then select the Partial option (see Figure 12-20).

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