A comparison of the Pearson and Spearman correlation methods Learn more about Minitab. In This Topic What is correlation? Comparison of Pearson and Spearman coefficients Other nonlinear relationships.
What is correlation? A correlation coefficient measures the extent to which two variables tend to change together. The coefficient describes both the strength and the direction of the relationship.
Minitab offers two different correlation analyses: Pearson product moment correlation The Pearson correlation evaluates the linear relationship between two continuous variables.
Spearman rank-order correlation The Spearman correlation evaluates the monotonic relationship between two continuous or ordinal variables. This relationship forms a perfect line. When a relationship is random or non-existent, then both correlation coefficients are nearly zero. Note: The bivariate Pearson Correlation only reveals associations among continuous variables.
The bivariate Pearson Correlation does not provide any inferences about causation, no matter how large the correlation coefficient is. The null hypothesis H 0 and alternative hypothesis H 1 of the significance test for correlation can be expressed in the following ways, depending on whether a one-tailed or two-tailed test is requested:.
Correlation can take on any value in the range [-1, 1]. The strength can be assessed by these general guidelines [1] which may vary by discipline :. Note: The direction and strength of a correlation are two distinct properties. The strength of the nonzero correlations are the same: 0. But the direction of the correlations is different: a negative correlation corresponds to a decreasing relationship, while and a positive correlation corresponds to an increasing relationship.
However, keep in mind that Pearson correlation is only capable of detecting linear associations, so it is possible to have a pair of variables with a strong nonlinear relationship and a small Pearson correlation coefficient.
It is good practice to create scatterplots of your variables to corroborate your correlation coefficients. Statistical power analysis for the behavioral sciences 2nd ed.
Your dataset should include two or more continuous numeric variables, each defined as scale, which will be used in the analysis. Each row in the dataset should represent one unique subject, person, or unit. All of the measurements taken on that person or unit should appear in that row. If measurements for one subject appear on multiple rows -- for example, if you have measurements from different time points on separate rows -- you should reshape your data to "wide" format before you compute the correlations.
The Bivariate Correlations window opens, where you will specify the variables to be used in the analysis. All of the variables in your dataset appear in the list on the left side. To select variables for the analysis, select the variables in the list on the left and click the blue arrow button to move them to the right, in the Variables field.
A Variables : The variables to be used in the bivariate Pearson Correlation. You must select at least two continuous variables, but may select more than two. The test will produce correlation coefficients for each pair of variables in this list.
B Correlation Coefficients: There are multiple types of correlation coefficients. By default, Pearson is selected. Selecting Pearson will produce the test statistics for a bivariate Pearson Correlation. C Test of Significance: Click Two-tailed or One-tailed , depending on your desired significance test. SPSS uses a two-tailed test by default. E Options : Clicking Options will open a window where you can specify which Statistics to include i.
Basically, a Pearson product-moment correlation attempts to draw a line of best fit through the data of two variables, and the Pearson correlation coefficient, r , indicates how far away all these data points are to this line of best fit i.
A value of 0 indicates that there is no association between the two variables. A value greater than 0 indicates a positive association; that is, as the value of one variable increases, so does the value of the other variable.
A value less than 0 indicates a negative association; that is, as the value of one variable increases, the value of the other variable decreases. This is shown in the diagram below:. The closer the value of r to 0 the greater the variation around the line of best fit.
Different relationships and their correlation coefficients are shown in the diagram below:. Remember that these values are guidelines and whether an association is strong or not will also depend on what you are measuring.
No, the two variables have to be measured on either an interval or ratio scale. However, both variables do not need to be measured on the same scale e. Further information about types of variable can be found in our Types of Variable guide. If you have ordinal data, you will want to use Spearman's rank-order correlation or a Kendall's Tau Correlation instead of the Pearson product-moment correlation.
No, the two variables can be measured in entirely different units. For example, you could correlate a person's age with their blood sugar levels.
Indeed, the calculations for Pearson's correlation coefficient were designed such that the units of measurement do not affect the calculation. This allows the correlation coefficient to be comparable and not influenced by the units of the variables used. The Pearson product-moment correlation does not take into consideration whether a variable has been classified as a dependent or independent variable. It treats all variables equally.
For example, you might want to find out whether basketball performance is correlated to a person's height. You might, therefore, plot a graph of performance against height and calculate the Pearson correlation coefficient. That is, as height increases so does basketball performance.
This makes sense. This is because the Pearson correlation coefficient makes no account of any theory behind why you chose the two variables to compare. This is illustrated below:.
It is important to realize that the Pearson correlation coefficient, r , does not represent the slope of the line of best fit.
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