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Choosing a correlation test

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Choosing the test | Discussion | See also

Choosing the test

Use the table below to choose the test. See below for further details.

How many dichotomous⁺ (binary) variables?

Both variables interval or ratio?

Measures are linear? (No = monotonic^*)
Y	Pearson correlation
N	Spearman correlation

Both variables are ordinal?

Kendall correlation

Both variables can be ranked?
Y	Kendall correlation
N	Convert to frequency data and use Chi-square test for independence

Biserial Correlation Coefficient

2 x 2 table?
Y	Phi
N	Cramer's V

Data has frequency values for each category?
Y	Chi-square test for independence

⁺dichotomous = 'can have only two values' (eg. yes/no or 0/1).
^*monotonic = constantly increasing or decreasing.

Discussion

A correlation coefficient is measured between -1 and 1.

A positive indicates that if one variable increases, the other increases also. A negative coefficient indicates that if one variable increases, the other decreases.

0 indicates no relationship between the two variables.

1 or -1 indicates a linear relationships, such that if one variable is known, the second can be accurately predicted.