Download Elementary Statistics. A Workbook by K. Hope and G. P. Meredith (Auth.) PDF

By K. Hope and G. P. Meredith (Auth.)

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First of all there is the general mean μ (Greek mu) of all persons in the population, then there is the deviation A from that mean which is caused by the experimental treatment of the group to which the person belongs {A can be a constant or it can be a value of a variable), and finally there is a value e drawn from the distribution of errors whose variance is estimated 40 ELEMENTARY 8ΤΑΤΙ8Ή€5 by the Within G r o u p M . S . : In a factorial design there are several treatment effects. F o r example, in a 2 χ 2 design we have an effect A for one factor, an effect Β for the other factor, and an effect AB for the interaction of the two treatments: X= μ-^Α + Β-^{ΑΒ)-^€, The importance of additivity should be evident from the number of plus signs in these equations.

These weights provide us with a way of testing whether the factor of sex is interacting with the factor of teaching method. It may be, for example, that the new method suits girls but not boys, and the female experimental group does better than the female control group, while for boys there is n o diflference. T o put it another way, is the difference between the girls' means, 7 — 3 = 4, significantly greater t h a n the difference between the boys' means, 3 — 1 = 2 ? The lambdas for an interaction term are always derivable by multiplying the lambdas for the interacting factors.

It is one thing to be unable to detect differences. It is quite another to confidently assert that there are n o differences to be detected. If the JP ratio is somewhere near the 1 0 % level, we should do well to suspend decision and bring in a verdict of not proven. The conventional 5 % level is not a rigid frontier between two clearly distinguishable outcomes of experiments. It is an arbitrary boundary erected across the middle of a no-man's-land. A small experiment which produces a difference between means or variances at the 15 % level may be regarded by the experimenter as sufficiently encouraging to warrant a n experiment with larger numbers.

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