Box 1.

Spearman–Brown reliability.

Unit-level, or Spearman–Brown reliability is defined as the proportion of the total variance in measured organisational-level scores, which is attributable to true variation between organisations (organisation-level variance) and can be estimated using the formula below. The term within-organisation variance used here is also sometimes known as the residual variance; n is the mean achieved sample size per organisation. $$\text{Reliability}=\frac{\text{betweenorganisationvarianceinmeasuredscores}}{\text{betweenorganisationvariance}+(\frac{\text{withinorganisationvariance}}{\text{n}})}$$ Spearman–Brown reliability is the intraclass correlation coefficient when the number of observations or the sample size within each organisation is 1. $$\text{ICC}=\frac{\text{betweenorganisationvarianceinmeasuredscores}}{\text{betweenorganisationvariance}+\text{withinorganisationvariance}}$$ By rearranging the above formula, unit-level reliability can therefore be estimated from the intraclass correlation coefficient and sample size as follows: $$\text{Reliability}=\frac{\mathrm{ICC}\times n}{1+(n-1)\times \mathrm{ICC}}$$