June 2015
Volume 56, Issue 7
ARVO Annual Meeting Abstract  |   June 2015
Slope of the psychometric function for low contrast logMAR charts.
Author Affiliations & Notes
  • Andrew Carkeet
    Optometry and Vision Science, QUT, Kelvin Grove, QLD, Australia
    QUT, IHBI, Kelvin Grove, QLD, Australia
  • Ian L Bailey
    School of Optometry, UC Berkeley, Berkeley, CA
  • Footnotes
    Commercial Relationships Andrew Carkeet, None; Ian Bailey, None
  • Footnotes
    Support None
Investigative Ophthalmology & Visual Science June 2015, Vol.56, 3887. doi:
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      Andrew Carkeet, Ian L Bailey; Slope of the psychometric function for low contrast logMAR charts. . Invest. Ophthalmol. Vis. Sci. 2015;56(7 ):3887.

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      © ARVO (1962-2015); The Authors (2016-present)

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Data from acuity charts can be analysed by fitting psychometric functions. While psychometric functions are traditionally used to yield acuity thresholds, the slopes of such psychometric functions can be used to predict the variability of such visual acuity thresholds. This repeated-measures research examined whether high contrast and low contrast acuity charts yield different slopes for their psychometric functions.


Ten participants, 6 female & 4 male, mean age 43 years (SD 18 years), took part in this research. Participants were tested with their preferred eye and wearing their best spectacle correction. Stimuli were Sloan letters presented on an LCD computer monitor, with 9 rows of letters arranged in randomized letter sequences with a standard logMAR chart format. The background had a luminance of 235 cd m-2 and the high and low contrasts were 99.2% and 18.7% Weber contrast. Each participant read 32 charts, 16 at low contrast and 16 at high contrast. For each chart, responses were analysed by probit analysis to generate thresholds and slopes for the psychometric functions.


For our participants, the mean high and low contrast visual acuity thresholds (logMAR) were -0.189 0.076 and -0.027 0.079 respectively. Probit sizes were used as a measure of the slopes of the psychometric functions, with smaller probit sizes indicating steeper slopes. Low contrast acuity charts yielded flatter psychometric functions than high contrast acuity charts, indicating a more gradual transition between seeing and non-seeing for the low contrast charts. The difference was statistically significant (F1,9=12.8, p=0.006). The estimates of slope differed slightly, according to whether a lower asymptote of 0.1 (1 in 10 guess rate) or 0.0385 (1 in 26 guess rate) was selected for probit fits. (F1,9=74.1, p<0.001). Probit sizes and inter-subject standard deviations are shown in Table 1.


These results indicate that visual acuity measurements are intrinsically more variable with low contrast charts. Previous research has shown that low levels of optical blur also flatten the psychometric function for visual acuity. Monte Carlo modelling based on the probit values shows that stopping patients reading down a low contrast acuity chart, after they’ve made three or more mistakes on a 5-letter row, gives close to optimal precision of acuity measurements.  

Table 1. Mean probit sizes (logMAR) with inter subject standard deviations.
Table 1. Mean probit sizes (logMAR) with inter subject standard deviations.


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