advanced stat ex 3 part iii Cohen "the earth is round"

What probability (denoted by p or sig) is given at the conclusion of a null hypothesis significance test? hint: it is not the probability that the null hypothesis is true). What conditional probability is NOT denoted by sig or p?

sig = P (D/Ho) but we really want P (Ho/D).

From the fact that a test for schizophrenia is over 95% accurate [P(a positive diagnosis of schizophrenia/that you actually have the disease)], why can't we conclude that you are over 95% likely to actually have schizophrenia, if you receive a diagnosis of schizophrenia on this test (see example discussed on pages 998 and 999 in Cohen)?

-When Cohen does the math, he accounts for the fact that schizophrenia only occurs in 2% of the population and that the probability of the test being wrong and you being normal is 3%. The overall conditional probability of false positives, then becomes about 60% or, -it is the error of inverse probability, p(Ho | D) does NOT equal p(D|Ho), p (D|Ho) = 95%, but p (Ho|D) = [ p(D|Ho) * p(Ho)] / p(D)

How is a conditional probability different from a simple probability?

-conditional probability is the probability of an event A given that another (B) has occurred -Simple probability; is the likelihood of an event

Why does Cohen say that the null hypothesis is always false?

Because in the real world, A and B are always different for some decimal place. The means differ or r is never equal to 0

So, if p or sig (on SPSS) is below .05, what can we conclude? What can we not conclude—even though we often do?

If p or sig is below .05 then we conclude the data is unlikely. We cannot conclude that Ho is unlikely.

What alternative statistical concepts does Cohen recommend instead of significance tests?

Use exploratory data analysis & effect size measures

Why does Cohen say that the probability of a type I error is always zero?

because the null hypothesis is always false