R - Errors and Power

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Type I and Type II errors

                              Real World
Null Hypothesis        True              False
Accept         Correct Decision        Type II Error (β)
Reject         Type I Error (α)        Correct Decision

Power

Power is the probability of correctly rejecting a false null hypothesis
  • E.g. the probability that:
    • given there is a difference between the population means
    • the sample means will be significantly different
  • The probability of failing to reject a false null hypothesis is β
Power = 1 - β


When designing an experiment you know the chance of finding a significant effect.


Questions

Power is:

  • The probability that the null hypothesis is true
  • The probability that the null hypothesis is false
  • The probability a false null hypothesis will be rejected
  • The probability a true null hypothesis will be rejected


If the power of an experiment is low then:

  • The experiment will likely be inconclusive
  • Any significant findings obtained are suspect
  • The results are skewed.

power.* function

# Find the sample size
power.t.test(power=0.9,sd=2,sig.level=0.05,delta=3)
# Find the power of the test
power.t.test(n=2,sd=2,sig.level=0.05,delta=3)


PWR package

  • pwr.p.test: test for one proportion (ES=h)
  • pwr.2p.test: test for two proportions (ES=h)
  • pwr.t.test: one sample and two samples (equal sizes) t tests for means (ES=d)
  • pwr.t2n.test: two samples (different sizes) t test for means (ES=d)
  • pwr.anova.test: test for one-way balanced anova (ES=f)
  • pwr.r.test: correlation test (ES=r)
  • pwr.f2.test: test for the general linear model

....

Pwr package

 install.packages("pwr")
 library("pwr")