Testing Basics Edit

When a pet is realeased, it is possible to obtain unique DNA with a certain probility. These probabilities are only shown in percent, and for a basic pet the probability changes from 0% to 1% at level 24. It is currently not known if fractional probabilities are employed or not. Knowing this would influence the optimal level when to release a basic pet.

So the null-hypothesis H_0 is that "fractional probabilities are employed", and this must be tested by releasing a number n of pets at level 23 and observing if they yield unique DNA or not. In the first case, H_0 is affirmed, but in the second case, a chance remains that H_0 is true even though no unique DNA was observed ("error of second kind").

Assuming that fractional probabilities are employed, it is also not known what kind of rounding is used: cutting off decimal places (0.99% becomes 0%) or rounding to nearest (0.51% becomes 1%).

The latter is the worse case, so let p=0.005 be the estimated probability that a pet gives unique DNA when released at level 23. That means (1-p)^n is the probability no unique DNA was observed even though H_0 is true.

To limit the error of second kind, we want (1-p)^n < a for an a we chose, or n > ln a / ln (1-p).

This shows that we need about n=600 tests with a remaining 5% probability (a=0.05) for an error of second kind, and n=920 for 1% (a=0.01).

If the other kind of rounding is used, the numbers are a lot better.

Another possible test Edit

As this test needs a large number of pet released at level 23, with potentially no unique DNA gain, a different test may also be interesting: Release pets at level 24. If no fractional probabilities are employed, this is the optimal cutoff point for unique DNA. If they are employed, the data about level 24 pets can still be used to estimate the probability for unique DNA at that level, and in that way can determine the kind of rounding in use. Which could reduce the number of tests for level 23 drastically.

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