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OPTION 1  Hardy Weinberg Exact Tests
(adapted from the original Genepop v3.1b documentation)

Three distinct tests are available, all concerned with the same null hypothesis Ho (= random union of gametes). The difference between them is the construction of the rejection zone. For the Probability-test (sub-option 3), the probability of the observed sample is used to define the rejection zone, and the P-value of the test corresponds to the sum of the probabilities of all tables (with the same allelic counts) with the same or lower probability. This is the "exact HW test" of Haldane (1954), Weir (1990b), Guo and Thompson (1992) and others. When the alternative hypothesis (H1) of interest is heterozygote excess or deficiency, more powerful tests than the probability-test can be used (see Rousset and Raymond, 1995). One of them, the score test (U test), is available here, either for H1 = heterozygote deficiency (sub-option 1) or H1 = heterozygote excess (sub-option 2). The multi-samples version of these two tests are accessible through sub-options 4 or 5.

Two distinct algorithms are available:

  1. The complete enumeration method, as described by Louis and Dempster (1987). This procedure was written in Quick Basic by Michel Raymond and Francois Rousset from a Fortran listing provided by E. J. Louis (Inst. Mol. Med., Oxford, UK). For the web version, this method has been converted to C. This program works for less than five alleles. As an exact P-value is calculated by complete enumeration, no standard error is computed.

  2. A Markov chain method to estimate without bias the exact P-value of this test (Guo and Thompson, 1992). This procedure was written in Pascal Michel Raymond and Francois Rousset, following the algorithm of Guo and Thompson (1992), plus minor modifications. We have also converted this method into C.
Details on the Markov chain method used to estimate the P-value can be found in Guo and Thompson (1992). The web form prompts you for three numbers:
  1. the dememorization number. Enter 1000 if you have no other idea (i.e. the default option). Values below 100 or above 32,767 are not allowed.
  2. the number of batches (B). We suggest 100 for a first trial (i.e. the default option for sub-options 1-3) or 20 for sub-options 4-5. Values below 10 or above 32,767 are not allowed.
  3. The number of iterations per batch (C). We suggest 1000 for a first trial (i.e. the default option). Values below 400 or above 2,147,483,647 (32,767 for sub-options 4 and 5) are not allowed.

Two important results are provided for each test by this option:

  1. the P-value associated with Ho (i.e. HW equilibrium) and
  2. the standard error (S.E.) of this estimate.

If S.E. is too large (say S.E. > 0.01), it is wise sometimes to run the analysis again, and increase the number of batches (if you tried 100 for the first trial, use 200 next, with C = 1000). How close the estimate is to the true value depends on the product BxC: the larger, the better.

Results are returned via your web browser which you can then save to you local machine. You may also choose to have them emailed to you.

Please report any problems or bugs that you encounter with the web version of this option to Eleanor Morgan

Last Modified on January 18, 2000 by Eleanor Morgan
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