Using the Pearson Correlation Statistic in Research

This easy tutorial will show you how to run the Pearson Correlation test in SPSS, and how to interpret the result.

Correlation is a statistical method used to assess a possible linear association between two continuous variables. In addition, It is simple both to calculate and to interpret. (Source)

Above all, Correlation describes the strength and direction of a linear relationship between two variables.  On the other hand, the Pearson correlation coefficient is appropriate for continuous variables. Finally, we can use it when we have one continuous variable and one dichotomous variable.

First of all, Pearson correlation coefficients (r) can only take values from -1 to +1. That is to say, the sign indicates whether the correlation is positive (both variables together and declining and increasing) or negative (one variable decreasing as the other increases and vice versa).

We can categorize the type of correlation by considering as one variable increases what happens to the other variable:

• Positive correlation – the other variable has a tendency to also increase;
• Negative correlation – the other variable has a tendency to decrease;
• No correlation – the other variable does not tend to either increase or decrease.

The starting point of any such analysis should be the construction and subsequent examination of a scatterplot. For examples of negative, no, and positive correlation are as follows.

Are there guidelines for interpreting Pearson’s correlation coefficient?

Yes, We proposed the following guidelines: A Pearson correlation coefficient between 0.51 and 0.99 indicates a high correlation between variables (values above 0.80 indicate an extremely high correlation. )

Assumptions of the Pearson Correlation Test

The assumptions for the Pearson correlation coefficient are as follows:

• Level of measurement: each variable should be continuous
• Related pairs: each participant or observation should have a pair of values
• Absence of outliers: not having outliers in either variable.
• Normality of variables: Variables should be approximately normally distributed.
• Linearity and Homoscedasticity: There is a linear relationship between two variables.

An Example; Pearson Correlation Test

We want to examine the relationship between math test score and level of anxiety, math test score and level of stress, and level of anxiety and level of stress.

A Pearson correlation coefficient was computed to determine the relationship between Math test score and level of anxiety, between Math test score and level of stress, and between the level of stress and level of anxiety.

Firstly, the results indicate a non-significant positive relationship between Math test score and level of anxiety, [r(37) = .233, p = .165].  In addition, there was also non-significant negative relationship between Math test score and level of stress, [r(37) = -.279, p = .094].

In contrast, there was a significant positive relationship between level of anxiety and level of stress, [r(37) = .482, p = .000].

To sum up, as the level of anxiety increases, the level of stress increases. Therefore, we fail to reject the null hypothesis that the correlation between Math test score and level of anxiety, and between Math test score and level of stress is zero. On the other hand. we reject the null hypothesis that the correlation between the level of anxiety and the level of stress is zero.

Visit our Reporting Pearson Correlation Analysis in SPSS for more details.