Statistical Hypothesis Testing


Theories (Models) in Science must make predictions of observable events
. . -that we did not previous know about
. . -and must be testable predictions
In Biology, the one theory we have which meets the above test is Mendel's Hypothesis,

  • which predicts the outcome of genetics experiments before they are set up,
  • but it explains evolution
    . . -as well as Kepler's "Laws of Planetary Motion" explain gravity.



    Chi-square Test

    Used to test the "goodness of fit" of observed data (grouped into classes)
    to expected (theoretical, predicted) data.


    Expected values from Mendel's Hypothesis (Punnett Analysis)

  • exp(offspring) = pr(phenotypes) * obs(litter size)
  • obs(offspring) = counts of creatures by phenotype


    Expected values from binomial expansion

  • {pr(AA) = p2, pr(Aa) = 2pq, pr(aa) = q2} ... in F-1 generation
  • q = pr(allele "a") ... in P-1 generation
  • p = 1 - q
    . . -= pr(allele "A") ... in P-1 generation


    offspring
    genotype count phenotype prob exp obs
    AA 1 type A 25% 4.5 .
    Aa 2 hybrid 50% 9.0 .
    aa 1 type a 25% 4.5 .
    total 4 100% 18.0 18

    Record obs data; calculate dev, dev2/exp

  • dev = obs - exp
  • X2 = SUM( dev2 / exp )


    offspring
    phenotype prob exp obs dev X2
    type A 25% 4.5 4 -0.5 .056
    hybrid 50% 9.0 8 -1.0 .111
    type a 25% 4.5 6 +1.5. .500
    total 100% 18.0 18 .667 ns



    Total dev2/exp contribution to X2 is compared to the tablulated "critical values" (c.v.) to determine significance

  • if less than c.v.
    . . -Eureka! there is no evidence to reject genetics explanation!
  • if greater than c.v.
    . . -Eureka, data cannot be explained by genetics explanation.


    critical values, X2
    # phenotypes df 5% 1%
    monohybrid
    dominance
    1 5.024 6.635
    monohybrid
    no dominance
    2 5.991 9.210
    dihybrid
    dominance
    3 7.815 11.345
    dihybrid
    no dominance
    8 15.507 20.090



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    © 2004 Prof. LaFrance, Ancilla College