What is the appropriate method for calculating reliability for a coding category assessed on a continuous scale?

Calculating reliability for a coding category assessed on a continuous scale is effectively done using the intraclass correlation coefficient (ICC). The ICC is particularly suited for evaluating the consistency or agreement of measurements made by multiple raters or measurements taken across different times. When the data is continuous, the ICC quantifies how much variation in the data can be attributed to the true differences between subjects rather than measurement error, thus providing a robust measure of reliability.

In situations where the data involves continuous scores, the ICC accounts for both the variance within subjects and between subjects, making it ideal for assessing the degree to which different coders or instruments produce similar results. This is crucial in research contexts where consistent coding is necessary for the validity of the conclusions drawn from the data.

The other methods listed, while important in other contexts, are not appropriate for this specific case. Kappa coefficients are more suited for categorical data, measuring agreement between raters rather than the reliability of continuous data. Variance simply measures the spread of scores but does not provide a reliability estimate. Split-half reliability, while useful for tests or assessments that can be divided into two halves for estimating consistency, is also not designed to handle the intricacies of continuous data as effectively as the intraclass correlation.