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Recreate arc sine Conversion Table A-16

John Quensen

June 3, 2017

Introduction

Table A-16 in the appendix of Snedecore and Cochran (1967) was my introduction to the arc sine conversion of percentages to angles. The table was actually reprinted from Bliss (1937), and tabulated values of arc sine(sqrt(percentage/100)). For example, the tabulated value for 15% is 22.79. Angles in R are in radians, not degrees. Thus the arc_sine function in this package does not return the values in Table A-16, but rather the corresponding angle in radians. For example, arc_sine(15) = 0.3976994. To get the angle in degrees, you can convert from radians to degrees with the function rad2deg. Thus rad2deg(arc_sine(15)) = 22.786498.

Just for kicks, the following code reproduces Table A-16:

part1 <- matrix(data = NA, nrow = 10, ncol = 10)
for (i in 1:10) {
  for (j in 1:10) {
    x <- rad2deg(arc_sine(((i-1)/10)+((j-1)/100)))
    part1[i,j] <- formatC(x, digits = 2, format = "f")
  }
}
col1 <- seq(from = 0, to = 0.9, by = 0.1)
part1 <- data.frame(col1, part1)
colnames(part1) <- c("%", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9")

part2 <- matrix(data = NA, nrow = 98, ncol = 10)
for (i in 1:98) {
  for (j in 1:10) {
    x <- rad2deg(arc_sine(i+((j-1)/10)))
    part2[i,j] <-formatC(x, digits = 2, format = "f")
  }
}
col1 <- seq(from = 1, to = 98, by = 1)
part2 <- data.frame(col1, part2)
colnames(part2) <- c("%", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9")

part3 <- matrix(data = NA, nrow = 11, ncol = 10)
for (i in 1:11) {
  for (j in 1:10) {
    m <- 99 + ((i-1)/10)
    n <- ((j-1)/100)
    if((m+n) <= 100) {
      x <- rad2deg(arc_sine(m+n))
       part3[i,j] <- formatC(x, digits = 2, format = "f")
    }
  }
}
col1 <- round(seq(from = 99, to = 100, by = 0.1), 1)
part3 <- data.frame(col1, part3)
colnames(part3) <- c("%", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9")

a16 <- rbind(part1, part2, part3)

knitr::kable(a16, align = "l", caption = "Table of Angles Corresponding to Percentages, after Bliss(1937).")

Table of Angles Corresponding to Percentages, after Bliss(1937).
%	0	1	2	3	4	5	6	7	8	9
0.0	0.00	0.57	0.81	0.99	1.15	1.28	1.40	1.52	1.62	1.72
0.1	1.81	1.90	1.99	2.07	2.14	2.22	2.29	2.36	2.43	2.50
0.2	2.56	2.63	2.69	2.75	2.81	2.87	2.92	2.98	3.03	3.09
0.3	3.14	3.19	3.24	3.29	3.34	3.39	3.44	3.49	3.53	3.58
0.4	3.63	3.67	3.72	3.76	3.80	3.85	3.89	3.93	3.97	4.01
0.5	4.05	4.10	4.14	4.17	4.21	4.25	4.29	4.33	4.37	4.41
0.6	4.44	4.48	4.52	4.55	4.59	4.62	4.66	4.70	4.73	4.76
0.7	4.80	4.83	4.87	4.90	4.93	4.97	5.00	5.03	5.07	5.10
0.8	5.13	5.16	5.20	5.23	5.26	5.29	5.32	5.35	5.38	5.41
0.9	5.44	5.47	5.50	5.53	5.56	5.59	5.62	5.65	5.68	5.71
1.0	5.74	6.02	6.29	6.55	6.80	7.03	7.27	7.49	7.71	7.92
2.0	8.13	8.33	8.53	8.72	8.91	9.10	9.28	9.46	9.63	9.80
3.0	9.97	10.14	10.30	10.47	10.63	10.78	10.94	11.09	11.24	11.39
4.0	11.54	11.68	11.83	11.97	12.11	12.25	12.38	12.52	12.66	12.79
5.0	12.92	13.05	13.18	13.31	13.44	13.56	13.69	13.81	13.94	14.06
6.0	14.18	14.30	14.42	14.54	14.65	14.77	14.89	15.00	15.12	15.23
7.0	15.34	15.45	15.56	15.68	15.79	15.89	16.00	16.11	16.22	16.32
8.0	16.43	16.54	16.64	16.74	16.85	16.95	17.05	17.15	17.26	17.36
9.0	17.46	17.56	17.66	17.76	17.85	17.95	18.05	18.15	18.24	18.34
10.0	18.43	18.53	18.63	18.72	18.81	18.91	19.00	19.09	19.19	19.28
11.0	19.37	19.46	19.55	19.64	19.73	19.82	19.91	20.00	20.09	20.18
12.0	20.27	20.36	20.44	20.53	20.62	20.70	20.79	20.88	20.96	21.05
13.0	21.13	21.22	21.30	21.39	21.47	21.56	21.64	21.72	21.81	21.89
14.0	21.97	22.06	22.14	22.22	22.30	22.38	22.46	22.54	22.63	22.71
15.0	22.79	22.87	22.95	23.03	23.11	23.18	23.26	23.34	23.42	23.50
16.0	23.58	23.66	23.73	23.81	23.89	23.97	24.04	24.12	24.20	24.27
17.0	24.35	24.43	24.50	24.58	24.65	24.73	24.80	24.88	24.95	25.03
18.0	25.10	25.18	25.25	25.33	25.40	25.47	25.55	25.62	25.70	25.77
19.0	25.84	25.91	25.99	26.06	26.13	26.21	26.28	26.35	26.42	26.49
20.0	26.57	26.64	26.71	26.78	26.85	26.92	26.99	27.06	27.13	27.20
21.0	27.27	27.35	27.42	27.49	27.56	27.62	27.69	27.76	27.83	27.90
22.0	27.97	28.04	28.11	28.18	28.25	28.32	28.39	28.45	28.52	28.59
23.0	28.66	28.73	28.79	28.86	28.93	29.00	29.06	29.13	29.20	29.27
24.0	29.33	29.40	29.47	29.53	29.60	29.67	29.73	29.80	29.87	29.93
25.0	30.00	30.07	30.13	30.20	30.26	30.33	30.40	30.46	30.53	30.59
26.0	30.66	30.72	30.79	30.85	30.92	30.98	31.05	31.11	31.18	31.24
27.0	31.31	31.37	31.44	31.50	31.56	31.63	31.69	31.76	31.82	31.88
28.0	31.95	32.01	32.08	32.14	32.20	32.27	32.33	32.39	32.46	32.52
29.0	32.58	32.65	32.71	32.77	32.83	32.90	32.96	33.02	33.09	33.15
30.0	33.21	33.27	33.34	33.40	33.46	33.52	33.58	33.65	33.71	33.77
31.0	33.83	33.90	33.96	34.02	34.08	34.14	34.20	34.27	34.33	34.39
32.0	34.45	34.51	34.57	34.63	34.70	34.76	34.82	34.88	34.94	35.00
33.0	35.06	35.12	35.18	35.24	35.30	35.37	35.43	35.49	35.55	35.61
34.0	35.67	35.73	35.79	35.85	35.91	35.97	36.03	36.09	36.15	36.21
35.0	36.27	36.33	36.39	36.45	36.51	36.57	36.63	36.69	36.75	36.81
36.0	36.87	36.93	36.99	37.05	37.11	37.17	37.23	37.29	37.35	37.41
37.0	37.46	37.52	37.58	37.64	37.70	37.76	37.82	37.88	37.94	38.00
38.0	38.06	38.12	38.17	38.23	38.29	38.35	38.41	38.47	38.53	38.59
39.0	38.65	38.70	38.76	38.82	38.88	38.94	39.00	39.06	39.11	39.17
40.0	39.23	39.29	39.35	39.41	39.47	39.52	39.58	39.64	39.70	39.76
41.0	39.82	39.87	39.93	39.99	40.05	40.11	40.16	40.22	40.28	40.34
42.0	40.40	40.45	40.51	40.57	40.63	40.69	40.74	40.80	40.86	40.92
43.0	40.98	41.03	41.09	41.15	41.21	41.27	41.32	41.38	41.44	41.50
44.0	41.55	41.61	41.67	41.73	41.78	41.84	41.90	41.96	42.02	42.07
45.0	42.13	42.19	42.25	42.30	42.36	42.42	42.48	42.53	42.59	42.65
46.0	42.71	42.76	42.82	42.88	42.94	42.99	43.05	43.11	43.17	43.22
47.0	43.28	43.34	43.39	43.45	43.51	43.57	43.62	43.68	43.74	43.80
48.0	43.85	43.91	43.97	44.03	44.08	44.14	44.20	44.26	44.31	44.37
49.0	44.43	44.48	44.54	44.60	44.66	44.71	44.77	44.83	44.89	44.94
50.0	45.00	45.06	45.11	45.17	45.23	45.29	45.34	45.40	45.46	45.52
51.0	45.57	45.63	45.69	45.74	45.80	45.86	45.92	45.97	46.03	46.09
52.0	46.15	46.20	46.26	46.32	46.38	46.43	46.49	46.55	46.61	46.66
53.0	46.72	46.78	46.83	46.89	46.95	47.01	47.06	47.12	47.18	47.24
54.0	47.29	47.35	47.41	47.47	47.52	47.58	47.64	47.70	47.75	47.81
55.0	47.87	47.93	47.98	48.04	48.10	48.16	48.22	48.27	48.33	48.39
56.0	48.45	48.50	48.56	48.62	48.68	48.73	48.79	48.85	48.91	48.97
57.0	49.02	49.08	49.14	49.20	49.26	49.31	49.37	49.43	49.49	49.55
58.0	49.60	49.66	49.72	49.78	49.84	49.89	49.95	50.01	50.07	50.13
59.0	50.18	50.24	50.30	50.36	50.42	50.48	50.53	50.59	50.65	50.71
60.0	50.77	50.83	50.89	50.94	51.00	51.06	51.12	51.18	51.24	51.30
61.0	51.35	51.41	51.47	51.53	51.59	51.65	51.71	51.77	51.83	51.88
62.0	51.94	52.00	52.06	52.12	52.18	52.24	52.30	52.36	52.42	52.48
63.0	52.54	52.59	52.65	52.71	52.77	52.83	52.89	52.95	53.01	53.07
64.0	53.13	53.19	53.25	53.31	53.37	53.43	53.49	53.55	53.61	53.67
65.0	53.73	53.79	53.85	53.91	53.97	54.03	54.09	54.15	54.21	54.27
66.0	54.33	54.39	54.45	54.51	54.57	54.63	54.70	54.76	54.82	54.88
67.0	54.94	55.00	55.06	55.12	55.18	55.24	55.30	55.37	55.43	55.49
68.0	55.55	55.61	55.67	55.73	55.80	55.86	55.92	55.98	56.04	56.10
69.0	56.17	56.23	56.29	56.35	56.42	56.48	56.54	56.60	56.66	56.73
70.0	56.79	56.85	56.91	56.98	57.04	57.10	57.17	57.23	57.29	57.35
71.0	57.42	57.48	57.54	57.61	57.67	57.73	57.80	57.86	57.92	57.99
72.0	58.05	58.12	58.18	58.24	58.31	58.37	58.44	58.50	58.56	58.63
73.0	58.69	58.76	58.82	58.89	58.95	59.02	59.08	59.15	59.21	59.28
74.0	59.34	59.41	59.47	59.54	59.60	59.67	59.74	59.80	59.87	59.93
75.0	60.00	60.07	60.13	60.20	60.27	60.33	60.40	60.47	60.53	60.60
76.0	60.67	60.73	60.80	60.87	60.94	61.00	61.07	61.14	61.21	61.27
77.0	61.34	61.41	61.48	61.55	61.61	61.68	61.75	61.82	61.89	61.96
78.0	62.03	62.10	62.17	62.24	62.31	62.38	62.44	62.51	62.58	62.65
79.0	62.73	62.80	62.87	62.94	63.01	63.08	63.15	63.22	63.29	63.36
80.0	63.43	63.51	63.58	63.65	63.72	63.79	63.87	63.94	64.01	64.09
81.0	64.16	64.23	64.30	64.38	64.45	64.53	64.60	64.67	64.75	64.82
82.0	64.90	64.97	65.05	65.12	65.20	65.27	65.35	65.42	65.50	65.57
83.0	65.65	65.73	65.80	65.88	65.96	66.03	66.11	66.19	66.27	66.34
84.0	66.42	66.50	66.58	66.66	66.74	66.82	66.89	66.97	67.05	67.13
85.0	67.21	67.29	67.37	67.46	67.54	67.62	67.70	67.78	67.86	67.94
86.0	68.03	68.11	68.19	68.28	68.36	68.44	68.53	68.61	68.70	68.78
87.0	68.87	68.95	69.04	69.12	69.21	69.30	69.38	69.47	69.56	69.64
88.0	69.73	69.82	69.91	70.00	70.09	70.18	70.27	70.36	70.45	70.54
89.0	70.63	70.72	70.81	70.91	71.00	71.09	71.19	71.28	71.37	71.47
90.0	71.57	71.66	71.76	71.85	71.95	72.05	72.15	72.24	72.34	72.44
91.0	72.54	72.64	72.74	72.85	72.95	73.05	73.15	73.26	73.36	73.46
92.0	73.57	73.68	73.78	73.89	74.00	74.11	74.21	74.32	74.44	74.55
93.0	74.66	74.77	74.88	75.00	75.11	75.23	75.35	75.46	75.58	75.70
94.0	75.82	75.94	76.06	76.19	76.31	76.44	76.56	76.69	76.82	76.95
95.0	77.08	77.21	77.34	77.48	77.62	77.75	77.89	78.03	78.17	78.32
96.0	78.46	78.61	78.76	78.91	79.06	79.22	79.37	79.53	79.70	79.86
97.0	80.03	80.20	80.37	80.54	80.72	80.90	81.09	81.28	81.47	81.67
98.0	81.87	82.08	82.29	82.51	82.73	82.97	83.20	83.45	83.71	83.98
99.0	84.26	84.29	84.32	84.35	84.38	84.41	84.44	84.47	84.50	84.53
99.1	84.56	84.59	84.62	84.65	84.68	84.71	84.74	84.77	84.80	84.84
99.2	84.87	84.90	84.93	84.97	85.00	85.03	85.07	85.10	85.13	85.17
99.3	85.20	85.24	85.27	85.30	85.34	85.38	85.41	85.45	85.48	85.52
99.4	85.56	85.59	85.63	85.67	85.71	85.75	85.79	85.83	85.86	85.90
99.5	85.95	85.99	86.03	86.07	86.11	86.15	86.20	86.24	86.28	86.33
99.6	86.37	86.42	86.47	86.51	86.56	86.61	86.66	86.71	86.76	86.81
99.7	86.86	86.91	86.97	87.02	87.08	87.13	87.19	87.25	87.31	87.37
99.8	87.44	87.50	87.57	87.64	87.71	87.78	87.86	87.93	88.01	88.10
99.9	88.19	88.28	88.38	88.48	88.60	88.72	88.85	89.01	89.19	89.43
100.0	90.00	NA	NA	NA	NA	NA	NA	NA	NA	NA

References

Bliss, C. J. 1937. Plant Protection, No. 12, Leningrad.

Snedecore, G. W., and W. G. Cochran. 1967. Statistical Methods. Sixth Edition. The Iowas State University Press, Ames, Iowa, USA.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.