Zero-Order Correlation: Definition, Examples

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What is Zero-Order Correlation?

Zero-order correlation indicates nothing has been controlled for or “partialed out” in an experiment. They are any correlation between two variables (X, Y) where no factor is controlled or held constant.

• If a third factor Z is controlled for, the correlation is first-order;
• If factors Z,A are controlled for, that’s a second-order correlation.

In elementary statistics, you usually deal with zero-order correlations exclusively (although they aren’t actually labeled as such). For example, Pearson correlation (“r”) is a zero-order correlation coefficient, because it has no controlled variables. Pearson’s isn’t the only zero-order correlation though: any correlation coefficient can be zero-order as long as no variables are controlled for or held constant.

Zero-order correlations are also called gross, raw, or unpartialed correlations.

Values of Zero-Order Correlation

In general, zero-order correlations have a value between -1 and 1:

• 1: for every positive increase of 1 in one variable, there is a positive increase of 1 in the other.
• -1: for every positive increase of 1 in one variable, there is a negative decrease of 1 in the other.
• 0: there isn’t a positive or negative increase. The two variables aren’t related.

The absolute value of the zero-order correlation coefficient gives us the relationship strength. Stronger relationships have bigger numbers. For example, |-.84| = .84, which has a stronger relationship than .49.

Notation

A result such as r_1,2 is a zero-order correlation. The subscripts 1 and 2 just indicate the two variables involved in the regression. If, on the other hand, you had r_12,3, this is a partial regression; the subscript “3” indicates some aspect of the experiment (e.g. height, weight, temperature) has been controlled for. As partial or semi-partial regressions always control at least one aspect of an experiment, there is no such thing as a “zero-order” partial or semi-partial correlation

Zero Correlation

The term “zero correlation” means something different entirely; It indicates that two sets of variables are not correlated at all. In other words, Pearson’s r would return a value of zero.

Next: Partial Correlation

References

Brannick, M. Partial and Semipartial Correlation. Retrieved March 6, 2017 from: faculty.cas.usf.edu/mbrannick/regression/19%20Partial%20and%20Semi.ppt
Hardy, M. Bryman, A. (Eds.) (2009). Handbook of Data Analysis.
Rajaretnam, T. (2009). Statistics for Social Sciences. SAGE Publishing India.