What statistical method allows you to estimate the correlation between two halves of a test?

The Spearman-Brown formula is used to estimate the reliability of a test when it is split into two halves, effectively providing a way to assess the correlation between the two halves of the test. This method is particularly relevant in psychometrics for determining the split-half reliability of an instrument, which is a measure of how consistently different parts of a test yield similar results.

By administering the same test to a group and then dividing the scores into two halves, the Spearman-Brown formula helps in adjusting the correlation obtained from these halves to predict what the correlation would be if the test had a different length. This adjustment allows psychometricians to infer the stability and consistency of the test items as they relate to each other when split, thereby giving insight into the overall reliability of the test.

In contrast, the other statistical methods listed serve different purposes. The Pearson correlation measures the linear correlation between two continuous variables, not specifically designed for split-half reliability. The point-biserial correlation is used when one variable is continuous and the other is binary, and Kendall's tau is a non-parametric measure of correlation between two ordinal variables. These methods do not specifically address the analysis of test halves.