R - Errors and Power

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")