This is a statistical analysis of John Benneth's experiment on 50 samples (25 placebos) as described at http://www.marius.net/protocol.html . The simple probability refers to the chance of getting exactly n positive hits by random guessing. It is calculated using Excel's hypergeometric function. The cumulative probabability refers to the chance of getting at least n hits and is obtained by summing simple probabilities from n to 25. The numerical error is of the order of 1.0E-09, i.e one chance in a billion.
Number of hits Simple probability Cumulative probability
0 7.91073E-15 1
1 4.94421E-12 1
2 7.11966E-10 1
3 4.18478E-08 0.999999999
4 1.26589E-06 0.999999957
5 2.23304E-05 0.999998692
6 0.000248115 0.999976361
7 0.001827952 0.999728246
8 0.009254006 0.997900294
9 0.033017379 0.988646288
10 0.084524489 0.95562891
11 0.157173637 0.871104421
12 0.213930784 0.713930784
13 0.213930784 0.5
14 0.157173637 0.286069216
15 0.084524489 0.128895579
16 0.033017379 0.04437109
17 0.009254006 0.011353712
18 0.001827952 0.002099706
19 0.000248115 0.000271754
20 2.23304E-05 2.36388E-05
21 1.26589E-06 1.30846E-06
22 4.18478E-08 4.25647E-08
23 7.11966E-10 7.16918E-10
24 4.94421E-12 4.95212E-12
25 7.91073E-15 7.91073E-15

ChartObject Probabilities for John 
Benneth's experiment on 50 samples (25 placebos).


"Some remarks on the Memory of Water Controversy"


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