Torah puzzle

Results are suspiciously close

(page 1)

Criticism

(according to Gil Kalai)

Imagine the following situation. A researcher claims a new effect manifesting itself via outcomes of a measurement. If the effect exists (and is strong enough), then the outcomes are positive in the mean. If the effect does not exist, then the outcomes are negative in the mean.

The researcher conducts a series of 27 measurements. The outcomes (sorted for convenience) are:

-4.40 1.15 3.91
-3.84 1.37 4.30
-3.53 1.46 4.45
-1.84 1.73 5.02
-0.85 2.36 5.65
-0.58 2.53 6.33
0.13 2.83 7.23
0.19 3.36
0.58 3.40
0.66 3.47

The sum of outcomes 47.1 shows clearly that they are positive in the mean. However, the new effect being very unexpected, we ask the researcher to conduct another series. Well, he performs 26 more measurements, getting the following (sorted) outcomes:

-2.14 0.10 3.91
-2.00 0.35 4.70
-1.89 0.43 4.87
-1.64 0.72 7.37
-1.35 0.74 12.30
-0.93 1.24 13.15
-0.78 1.61
-0.68 2.32
-0.63 2.79
-0.51 3.23

their sum being 47.3 . Are you convinced now?

The second series is intended to increase our conviction. Instead, however, it arouses a suspiction: why the second sum 47.3 is so close to the first sum 47.1 ? Should we trust the data?..

The said above outlines an argument against [WRR94] published in:

Gil Kalai,
On the paper of Witztum, Rips and Rosenberg on equidistant letter sequences in the Book of Genesis,
available online: www.ma.huji.ac.il/~kalai/w/w.html

However, my presentation is simplified. The work of G. Kalai contains more thorough statistical examination of the argument, and some other interesting arguments.

To page 2 ---> Are the above numbers the outcomes of [WRR94]? In which sense?
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