Dreams: Statistical Analysis

To find an h score from two percentages, simply look up both percentages in this table and find the difference between their corresponding X's. For instance, scores of 50% and 25% yield an h of 1.571 - 1.047 = .524.

%	X
0	0.000
1	0.200
2	0.284
3	0.348
4	0.403
5	0.451
6	0.495
7	0.536
8	0.574
9	0.609
10	0.644
11	0.676
12	0.707
13	0.738
14	0.767
15	0.795
16	0.823
17	0.850
18	0.876
19	0.902
20	0.927
21	0.952
22	0.976
23	1.000
24	1.024

%	X
25	1.047
26	1.070
27	1.093
28	1.115
29	1.137
30	1.159
31	1.181
32	1.203
33	1.224
34	1.245
35	1.266
36	1.287
37	1.308
38	1.328
39	1.349
40	1.369
41	1.390
42	1.410
43	1.430
44	1.451
45	1.471
46	1.491
47	1.511
48	1.531
49	1.551

%	X
50	1.571
51	1.591
52	1.611
53	1.631
54	1.651
55	1.671
56	1.691
57	1.711
58	1.731
59	1.752
60	1.772
61	1.793
62	1.813
63	1.834
64	1.855
65	1.875
66	1.897
67	1.918
68	1.939
69	1.961
70	1.982
71	2.004
72	2.026
73	2.049
74	2.071

%	X
75	2.094
76	2.118
77	2.141
78	2.165
79	2.190
80	2.214
81	2.240
82	2.265
83	2.292
84	2.319
85	2.346
86	2.375
87	2.404
88	2.434
89	2.465
90	2.498
91	2.532
92	2.568
93	2.606
94	2.647
95	2.691
96	2.739
97	2.793
98	2.858
99	2.941

You can also find X and h by using a mathematical formula. The formula is: X is the anticosine (using radians) of 1 - 2P, where P is a number from 0 to 1 (not 0 to 100). h is simply the difference between the two X's:

h = cos^-1(1-2P_a) - cos^-1(1-2P_b)

In Excel, assuming the two proportions are in cells A2 & B2, the formula would be: =ACOS(1-(2*A2))-ACOS(1-(2*B2))

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