## An R Companion for the Handbook of Biological Statistics

Salvatore S. Mangiafico

# Power Analysis

### Packages used in this chapter

The following commands will install these packages if they are not already installed:

if(!require(pwr)){install.packages("pwr")}

Introduction

Parameters

How it works

See the Handbook for information on these topics.

### Examples

#### Power analysis for binomial test

### --------------------------------------------------------------
### Power analysis, binomial test, pea color, p. 43
### --------------------------------------------------------------

P0 = 0.75
P1 = 0.78
H  = ES.h(P0,P1)               # This calculates effect size

library(pwr)

pwr.p.test(
h=H,
n=NULL,                  # NULL tells the function to
sig.level=0.05,          #     calculate this
power=0.90,              # 1 minus Type II probability
alternative="two.sided")

n = 2096.953                 # Somewhat different than in Handbook

#     #     #

#### Power analysis for unpaired t-test

### --------------------------------------------------------------
### Power analysis, t-test, student height, pp. 43
44
### --------------------------------------------------------------

M1  = 66.6                      # Mean for sample 1
M2  = 64.6                      # Mean for sample 2
S1  =  4.8                      # Std dev for sample 1
S2  =  3.6                      # Std dev for sample 2

Cohen.d = (M1 - M2)/sqrt(((S1^2) + (S2^2))/2)

library(pwr)

pwr.t.test(
n = NULL,                  # Observations in _each_ group
d = Cohen.d,
sig.level = 0.05,          # Type I probability
power = 0.80,              # 1 minus Type II probability
type = "two.sample",       # Change for one- or two-sample
alternative = "two.sided"
)

Two-sample t test power calculation

n = 71.61288

NOTE: n is number in *each* group 71.61288

#     #     #

How to do power analyses

Methods are shown in the previous examples.