Chapter07_power {DanielBiostatistics10th} R Documentation

## Chapter 7 (Power Curve)

### Description

Functions for Chapter 7, Hypothesis Testing.

### Usage

power_z(
x,
null.value,
sd,
n,
alternative = c("two.sided", "less", "greater"),
sig.level = 0.05
)


### Arguments

 x numeric vector, mean parameter(s) \mu_1 in the alternative hypothesis null.value numeric scalar, mean parameter \mu_0 in the null hypothesis sd numeric scalar, population standard deviation \sigma n integer scalar, sample size n alternative character scalar, alternative hypothesis, either 'two.sided' (default), 'greater' or 'less' sig.level numeric scalar, significance level (i.e., Type-I-error rate), default .05

### Details

Function power_z() calculates the powers at each element of the alternative parameters \mu_1, for one-sample z-test

• H_0: \mu = \mu_0 vs. H_A: \mu \neq \mu_0, if alternative = 'two.sided'

• H_0: \mu \leq \mu_0 vs. H_A: \mu > \mu_0, if alternative = 'greater'

• H_0: \mu \geq \mu_0 vs. H_A: \mu < \mu_0, if alternative = 'less'

### Value

Function power_z() returns a 'power_z' object, which inherits from 'power.htest' class.

### References

Wayne W. Daniel, Biostatistics: A Foundation for Analysis in the Health Sciences, Tenth Edition. Wiley, ISBN: 978-1-119-62550-6.

### Examples

library(DanielBiostatistics10th)

# Page 272, Example 7.9.1
(p791 = power_z(seq.int(from = 16, to = 19, by = .5), null.value = 17.5, sd = 3.6, n = 100L))
# Page 275, Table 7.9.1
autoplot(p791) + labs(title = 'Page 275, Figure 7.9.2')

# Page 276, Example 7.9.2
(p792 = power_z(seq.int(from = 50, to = 70, by = 5), null.value = 65, sd = 15, n = 20L,
sig.level = .01, alternative = 'less'))
autoplot(p792) + labs(title = 'Page 277, Figure 7.9.4')

# Page 278, Example 7.10.1
(n_d7101 <- uniroot(f = function(x) {
power_z(55, null.value = 65, sd = 15, n = x, sig.level = .01, alternative = 'less')$power - .95 }, interval = c(0, 50))$root)
power_z(55, null.value = 65, sd = 15, n = ceiling(n_d7101), sig.level = .01, alternative = 'less')


[Package DanielBiostatistics10th version 0.1.10 Index]