Evaluating and reporting astigmatism for individual and aggregate data

J Cataract Refract Surg. 1998 Jan;24(1):57-65. doi: 10.1016/s0886-3350(98)80075-8.


Purpose: To demonstrate the proper method for evaluating and reporting astigmatism for individual and aggregate data.

Setting: University of Texas Medical School and Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA.

Methods: The surgically induced refractive change (SIRC) was determined for three data sets of patients who have had keratorefractive (photorefractive keratectomy) or cataract surgery. To make changes in refraction comparable, vertex distances for the refractions and keratometric index of refraction were considered. Doubledangle plots and single-angle plots were then used to display the data. Polar values (cylinder and axis) were converted to a Cartesian (x and y) coordinate system to determine the mean value of the induced astigmatism for each data set.

Results: Doubled-angle plots clearly demonstrated the trends of induced astigmatism for each data set, and the mean value for induced astigmatism agreed exactly with the intuitive appearance of the plot.

Conclusions: Converting astigmatism data to a Cartesian coordinate system allowed the correct computation of descriptive statistics such as mean values, standard deviations, and correlation coefficients. Using doubled-angle plots to display the data provides the investigator with the best method of recognizing trends in the data.

MeSH terms

  • Astigmatism / diagnosis*
  • Astigmatism / etiology
  • Cataract Extraction / adverse effects
  • Cornea / pathology*
  • Humans
  • Keratotomy, Radial / adverse effects
  • Lasers, Excimer
  • Mathematics
  • Middle Aged
  • Photorefractive Keratectomy / adverse effects
  • Postoperative Complications / diagnosis