The model we described has three parameters (N,f,a), governing the number of points in
each point set, the fraction of points that are moved closer, and the amount they are moved
We use the model in the following way. We choose values for the three parameters.
We generate at random a collection of point sets uniformly distributed in the unit square and a collection
of point sets in accordance with the model specification. The collection has a suffiently large number
of point sets, say 10,000. Clearly, one collection satisfies the Null hypothesis and the other collection
satisfies the Alternative hypothesis.
In a simple Torah code experiment, the ELSs in a monkey text corresponds to
a point set that is uniformly distributed in the unit square. And one point set from the
collection generated according to the model corresponds to the ELSs from the Torah text.
Our first investigation is to explore a variety of test statistics in which we sample a
point set generated according to the model and perform a test of hypothesis on it to see if
we are able to reject the Null hypothesis in favor of the Alternative hypothesis. We will
perform this test with each point set generated under the model against the point sets generated
under the Null hypothesis. We will do so with a variety of test statistics
at a variety of different significance levels.
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