Whats the power of a Test ?
1 - ß
Propability to reject H0 if its False
What is the Family-Wise-Error-Rate?
A control for the type l error
The propability that at least one true null hypothesis is rejected
V: number of false positives ( null True but rejected)
P(V > 0)
The more null hypothesis are true => the more likely I will reject a true one
Whats the False discovery rate ?
A control for type l error
the proportion of true null hypotheses under the rejected ones
R : num rejections / V : num false positives ( null True but rejected)
E(V/R l R > 0) * P( R > 0)
Order p-values increasingly
select all pvalues where
Whats the Per-comparison-Error-Rate ?
A type l error comtrol
V: number of false positives ( null True but rejected) / m : total number of H0
E(V) / m
Order Type l error controls.
PCER <= FDR <= FWER
How can the controls be applied ?
Either changing the pvalue by multiplying with m: p*m <= alpha
Adjusting alpha with m: p <= alpha/m
Why do we need to correct for multiple testing ?
Under the assumption that all null Hypothsesis are true
p-values are uniformly distributed
=> with p-value 0.05 some true Hypothesis are automatically rejected
=> this needs to be acounted for
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