Re: A * Titans * fight II: Jack Tomsky versus R. A. Fisher

*********
Two sample parameters comparison (observed p1^ and
p2^)___H0: p1 = p2 ___H1: p1=/ p2.

Let be W (data| H0) a complete, unbiased, known
statistics, of the continuous parameter p. The
confidence interval for the difference D= |p1-p2| is

__|p1^ - p2^| - W(1-a) <= D <= |p1^ - p2^| - W(a)

when the difference |p1-p2| of the two parameters. By
a= alpha is noted the significance level.

Because the above C. I. doesn’t degenerate in a
single point, consequently W(a) = W(1-a), ONE CAN
NEVER BE SURE OF THE TWO PARAMETER´S EQUALITY, say
D=0.
Furthermore, for significative tests, the absolute
difference on parameters (at alpha significance
level) must be greater than D.

Luis Amaral Afonso [The moderator



According to Afonso's definition of the W statistic, W must be between zero and one. Thus, both ends of his confidence interval are less than or equal to |p1^ - p2^|.

This means that D is always <= |p1^ - p2^|. In the particular case where we observe p1^ = p2^, it follows that D <= 0. Since D by definition can't be negative, D = 0. It follows that the hypothesis H: p1 = p2 is true and must be accepted.

Thus, based on Afonso's complete and unbiased formulas, he has proved that whenever we observe p1^ = p2^, the null hypothesis H: p1 = p2 must be true.

Good work!

Jack (moderator)
.

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