Quantum mechanics

Statistical power

Gaussian

Statistics

Multivariate statistics

Multivariate normal distribution

Power (physics)

Physics

Mathematics

Coverage probability

Type I and type II errors

Sample size determination

Confidence interval

Standard deviation

Normal distribution

Heteroscedasticity

Univariate

Journal of Cataract & Refractive Surgery

Purpose: To provide a reference for study design comparing intraocular lens (IOL) power calculation formulas, to show that the standard deviation (SD) of the prediction error (PE) is the single most accurate measure of outcomes, and to provide the most recent statistical methods to determine P values for type 1 errors. Setting: Baylor College of Medicine, Houston, Texas, and University of Southern California, Los Angeles, California, USA. Design: Retrospective consecutive case series. Methods: Two datasets comprised of 5200 and 13 301 single eyes were used. The SDs of the PEs for 11 IOL power calculation formulas were calculated for each dataset. The probability density functions of signed and absolute PE were determined. Results: None of the probability distributions for any formula in either dataset was normal (Gaussian). All the original signed PE distributions were not normal, but symmetric and leptokurtotic (heavy tailed) and had higher peaks than a normal distribution. The absolute distributions were asymmetric and skewed to the right. The heteroscedastic method was much better at controlling the probability of a type I error than older methods. Conclusions: (1) The criteria for patient and data inclusion were outlined; (2) the appropriate sample size was recommended; (3) the requirement that the formulas be optimized to bring the mean error to zero was reinforced; (4) why the SD is the single best parameter to characterize the performance of an IOL power calculation formula was demonstrated; and (5) and using the heteroscedastic statistical method was the preferred method of analysis was shown.

Review and recommendations for univariate statistical analysis of spherical equivalent prediction error for IOL power calculations