Figure 2.

Required sample size (number of organisations) to detect a true population correlation where measurement (Spearman–Brown) reliability is less than 100%. In this figure, R is the true correlation in the population. Where reliability is less than 1.0, required sample sizes are calculated assuming that the measurement reliability of both characteristics and performance measures considered for the correlation study is at the stated level. This calculation was made by multiplying the true correlation by the square root of the reliability of each measure and calculating the required sample size for this attenuated correlation. Note that the required sample size axis is on a log scale. For measures of healthcare organisation quality which are used for ‘high stakes’ applications (such as for pay-for-performance or public reporting schemes), the measurement reliability is typically required to be between 0.7 and 0.9.¹¹