BIOL 373 Lecture Notes - Lecture 14: Biostatistics, Random Effects Model, John Tukey
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Tests for the effects of > 1 factor on the population means. X : mean of all ij group means. X i : mean of all groups under i: ex: mean. X 1 : mean of all groups where i=1. Factor a ss = bn a i=1 ( x i x )2: where n is #individuals within each group, b is number of options under i (=1 with one null and one alternative hypothesis) b a. Cell ss = n i=1 j=1 ( x i j x )2. These formulas allow for the calculation of: total ss, error ss, interactions ss. Example: left vs right claw sizes of fiddler crabs. Divide msfactor by random variation in the theoretic population variation due. F= factor+random variation random variation: mserror measures random variation o. Msfactor = variation due to factor + random variation variation due. Mserror random variation random variation. Levels of each factor are chosen at random.
