# 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% monohybriddominance 1 5.024 6.635 monohybridno dominance 2 5.991 9.210 dihybriddominance 3 7.815 11.345 dihybridno dominance 8 15.507 20.090