# How do I calculate a recognition rate

## Ophthalmology Clinic

Michael Bach and Guntram Kommerell

Preliminary manuscript, final version appeared in: Clinical monthly sheets for ophthalmology (1998; 212: 190-195), Ferdinand Enke-Verlag
Subsequent extensions: Column 7 in Tab. 1 (April 24, 2002)

### Summary

When determining visual acuity, the ophthalmologist should be aware of the scientific basis, even if, for practical reasons, in many cases he can choose a method that does not meet strict theoretical requirements.

Psychometric function. In the European standard EN ISO 8596 (as well as in the formerly valid DIN 58220), the Landolt ring is prescribed for measuring visual acuity, which is to be offered in 8 different orientations. As the size of the Landolt ring decreases, the hit rate drops from 100% to the guess probability (chance probability) of 12.5%. This gradual transition is described by the "psychometric function". In the form of a curve, the psychometric function has a steepest point (= turning point). It lies in the middle between 100 and 12.5, i.e. with a hit rate of 56.25%. This steepest point (approximated by 5 of 8 Landolt rings) was chosen as the threshold because the visual acuity read there is least affected by random fluctuations.

Forced choice. The test person must be stopped when naming the Landolt ring orientation to "forced choice"; a statement like "I can't see anything" must not be accepted.

"Normal" visual acuity. It cannot be assigned to a specific number, such as 1.0; when tested in accordance with the standards, young test subjects with healthy eyes achieve values ​​of around 2.0, while old test subjects 0.5 can be "normal".

Visual acuity averaging. Only with logarithmic, not arithmetic, scaling of the visual acuity are there approximately the same levels corresponding to the sensitivity level. Therefore visual acuity values ​​must not be averaged arithmetically. On the other hand, it is correct to average geometrically or first logarithmize the visual acuity values, then average and finally delogarithmize the value obtained.

"Minimum Angle of Resolution" superfluous. MAR is the reciprocal of visual acuity. The recently chosen marking of the resolving power with log (MAR) is superfluous, because log (MAR) has the same statistical properties as log (visual acuity). In addition, log (MAR) is not clear because the value decreases as the eyesight increases.

Computer-aided procedures. They make it easier to follow EN ISO 8596. For example, with the "Freiburg Visus Test", the examiner does not have to remember whether 5 correct answers have already been given for each level, and he does not have to ensure that the Landolt ring is offered a maximum of 8 times per level becomes.

### introduction

The aim of this article is to present the scientific basis for determining visual acuity, on which EN ISO 8596 (European Standard, CEN (European Committee for Standardization) 1996) is based. The EN ISO largely corresponds to the formerly valid DIN 54220. When determining visual acuity, the ophthalmologist should be aware of the scientific basis, even if, for practical reasons, in many cases he can choose a method that does not meet strict theoretical requirements.

All of the following considerations follow from the conception of visual acuity as a psychophysical threshold: A physical measure (the optotype size) is related to perception, and a threshold is defined at a suitable point. According to EN ISO, visual acuity is measured with Landolt rings. It results from the formula (e.g. Paliaga 1993)

Visual acuity = 1 / gap of the smallest recognized Landolt ring [minutes of arc].

### Logarithmic gradation of visual acuity

The gradation between the individual visual acuity values ​​corresponds to the sensitivity level only if it is scaled logarithmically (Ferris et al. 1982; Paliaga 1993). Why this is so can best be made clear with two examples: For a patient who only has a visual acuity of 0.1, an increase of 0.1 to 0.2 is a big gain, because the visual acuity has doubles and the patient can now read a sign from twice as far. For a patient with visual acuity 0.8, however, an increase of 0.1 to 0.9 is practically insignificant, because visual acuity has only improved by a factor of 0.908 = 1.125. These examples show that the visual acuity should not be scaled in arithmetically equal intervals, but geometrically with a constant factor, i.e. logarithmically.