Table 1 Entropy, information gain and number of classes from visual acuity tests.
From: Quantification of expected information gain in visual acuity and contrast sensitivity tests
Snellen | ETDRS | \(q\mathrm{VA}\) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
# Mistakes | Whole chart | VA alone | VA + Range | |||||||||
3 | 4 | 5 | 15 | 45 | 90 | 15 | 45 | 90 | ||||
Simulation 1 | H(Y) (bits) | 3.5 | 6.1 | 6.1 | 6.0 | 5.9 | 6.1 | 6.1 | 6.1 | 10.7 | 11.6 | 11.7 |
H(Y|X) (bits) | 1.6 | 3.5 | 3.5 | 3.6 | 3.4 | 3.8 | 2.9 | 2.4 | 7.8 | 7.2 | 6.5 | |
IG (bits) | 1.8 | 2.5 | 2.5 | 2.5 | 2.5 | 2.3 | 3.2 | 3.7 | 3.0 | 4.4 | 5.2 | |
N(Y|X) | 3.6 | 5.7 | 5.7 | 5.6 | 5.6 | 5.0 | 9.1 | 12.7 | 7.9 | 20.5 | 37.2 | |
# Optotypes | 24.7 | 41.4 | 45.5 | 51.8 | 70 | 15 | 45 | 90 | 15 | 45 | 90 | |
IG/Optotype(bits) | 0.07 | 0.06 | 0.06 | 0.05 | 0.04 | 0.16 | 0.07 | 0.04 | 0.20 | 0.10 | 0.06 | |
IG/log2(# Optotype)(bits) | 0.40 | 0.47 | 0.46 | 0.44 | 0.40 | 0.60 | 0.58 | 0.56 | 0.76 | 0.79 | 0.80 | |
Simulation 2 | H(Y) (bits) | 3.0 | 5.5 | 5.5 | 5.5 | 5.3 | 5.6 | 5.5 | 5.5 | 10.1 | 10.4 | 10.3 |
H(Y|X) (bits) | 1.6 | 3.5 | 3.5 | 3.6 | 3.4 | 3.7 | 2.8 | 2.3 | 7.7 | 7.2 | 6.5 | |
IG (bits) | 1.5 | 2.1 | 2.0 | 1.9 | 1.9 | 1.9 | 2.8 | 3.3 | 2.3 | 3.3 | 3.9 | |
N(Y|X) | 2.8 | 4.2 | 4.0 | 3.8 | 3.8 | 3.8 | 6.8 | 9.5 | 5.1 | 9.6 | 14.6 | |
# Optotypes | 23.8 | 44.7 | 48.4 | 55.1 | 70 | 15 | 45 | 90 | 15 | 45 | 90 | |
IG/Optotype(bits) | 0.06 | 0.05 | 0.04 | 0.03 | 0.03 | 0.13 | 0.06 | 0.04 | 0.16 | 0.07 | 0.04 | |
IG/log2(# Optotype)(bits) | 0.32 | 0.38 | 0.36 | 0.33 | 0.32 | 0.49 | 0.50 | 0.50 | 0.60 | 0.59 | 0.60 | |
