Background: Cronbach's alpha is widely used as the preferred index of reliability for medical postgraduate examinations. A value of 0.8-0.9 is seen by providers and regulators alike as an adequate demonstration of acceptable reliability for any assessment. Of the other statistical parameters, Standard Error of Measurement (SEM) is mainly seen as useful only in determining the accuracy of a pass mark. However the alpha coefficient depends both on SEM and on the ability range (standard deviation, SD) of candidates taking an exam. This study investigated the extent to which the necessarily narrower ability range in candidates taking the second of the three part MRCP(UK) diploma examinations, biases assessment of reliability and SEM.
Methods: a) The interrelationships of standard deviation (SD), SEM and reliability were investigated in a Monte Carlo simulation of 10,000 candidates taking a postgraduate examination. b) Reliability and SEM were studied in the MRCP(UK) Part 1 and Part 2 Written Examinations from 2002 to 2008. c) Reliability and SEM were studied in eight Specialty Certificate Examinations introduced in 2008-9.
Results: The Monte Carlo simulation showed, as expected, that restricting the range of an assessment only to those who had already passed it, dramatically reduced the reliability but did not affect the SEM of a simulated assessment. The analysis of the MRCP(UK) Part 1 and Part 2 written examinations showed that the MRCP(UK) Part 2 written examination had a lower reliability than the Part 1 examination, but, despite that lower reliability, the Part 2 examination also had a smaller SEM (indicating a more accurate assessment). The Specialty Certificate Examinations had small Ns, and as a result, wide variability in their reliabilities, but SEMs were comparable with MRCP(UK) Part 2.
Conclusions: An emphasis upon assessing the quality of assessments primarily in terms of reliability alone can produce a paradoxical and distorted picture, particularly in the situation where a narrower range of candidate ability is an inevitable consequence of being able to take a second part examination only after passing the first part examination. Reliability also shows problems when numbers of candidates in examinations are low and sampling error affects the range of candidate ability. SEM is not subject to such problems; it is therefore a better measure of the quality of an assessment and is recommended for routine use.