## 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.