Cohen’s U1, U2, and U3

Computing Cohen’s (1988) U1, U2, and U3 from d (Table 2.2.1, p. 22)

U3 = function(x) pnorm(x)
U2 = function(x) pnorm(x/2)
U1 = function(x) (2*U2(x) - 1) /U2(x)
cohenTab = data.frame(d = c(seq(0.0, 2.0, 0.1),
                            seq(2.2, 4.0, 0.2)))
cohenTab$U1 = U1(cohenTab$d) * 100
cohenTab$U2 = U2(cohenTab$d) * 100
cohenTab$U3 = U3(cohenTab$d) * 100
cohenTab

d	U1	U2	U3
0.0	0.0	50.0	50.0
0.1	7.7	52.0	54.0
0.2	14.8	54.0	57.9
0.3	21.3	56.0	61.8
0.4	27.4	57.9	65.5
0.5	33.0	59.9	69.1
0.6	38.2	61.8	72.6
0.7	43.0	63.7	75.8
0.8	47.4	65.5	78.8
0.9	51.6	67.4	81.6
1.0	55.4	69.1	84.1
1.1	58.9	70.9	86.4
1.2	62.2	72.6	88.5
1.3	65.3	74.2	90.3
1.4	68.1	75.8	91.9
1.5	70.7	77.3	93.3
1.6	73.1	78.8	94.5
1.7	75.4	80.2	95.5
1.8	77.4	81.6	96.4
1.9	79.4	82.9	97.1
2.0	81.1	84.1	97.7
2.2	84.3	86.4	98.6
2.4	87.0	88.5	99.2
2.6	89.3	90.3	99.5
2.8	91.2	91.9	99.7
3.0	92.8	93.3	99.9
3.2	94.2	94.5	99.9
3.4	95.3	95.5	99.9663
3.6	96.3	96.4	99.9841
3.8	97.0	97.1	99.9928
4.0	97.7	97.7	99.9968