Slope of psychometric functions and termination rule analysis for low contrast acuity charts

Abstract

Purpose: To assess whether the slopes of psychometric functions for measuring low contrast letter acuity were different from those for measuring high contrast letter acuity.

Methods: Ten participants, wearing their best spectacle correction, were assessed monocularly. Stimuli were logarithmic progression charts, generated on a computer monitor, with nine rows of five randomised Sloan letters generated in either high contrast format (Weber contrast 99.2%) or low contrast format (Weber contrast 18.7%). For each participant, psychometric functions were generated by probit analysis of the data on each of 16 attempts at a low contrast chart and 16 attempts at a high contrast chart. Each of these probit fits yielded an estimate of Probit Size which provided information about how steep or flat the psychometric function was, along with an estimate of Probit Acuity Threshold.

Results: Probit Size was significantly larger (p < 0.001) for low contrast charts than for high contrast charts, indicating that psychometric functions were flatter for low contrast charts. Mean Probit Sizes in logMAR were 0.099 (SEM 0.022) for low contrast charts and 0.071 (SEM 0.009) for high contrast charts if a guess rate of 1/26 was assumed, or were 0.086 (SEM 0.019) for low contrast charts and 0.064 for high contrast charts if a guess rate of 1/10 was assumed. Monte Carlo analysis showed that these means were likely to be biased estimates, with true Probit Size probably being larger (i.e. slightly flatter fits) by 0.016-0.019 logMAR. As expected, Probit Acuity Thresholds were poorer for low contrast charts than for high contrast charts (p < 0.001).

Conclusion: Our Monte Carlo modelling showed that such differences in acuity psychometric functions would be expected to give greater intra-subject variability in low contrast letter-by-letter acuity thresholds than for high contrast letter-by-letter acuity thresholds, and that this difference would depend on the termination rule used when measuring acuity. Likewise the variation in letter-by- letter acuity thresholds with termination rule will be different for high and low contrast charts. For low contrast and high contrast Sloan letter charts in a standard logarithmic format, a termination rule of four mistakes on a row, will give close to optimum sensitivity-to-change.

Keywords: low contrast acuity; probit analysis; psychometric function slope; termination rule.