Type II error, also known as a false negative, occurs when you fail to reject the null hypothesis when it’s actually false. In hypothesis testing, this error is denoted as β (beta). To calculate Type II error in R, you need to know the effect size (difference between the null and alternative hypotheses), sample size, standard deviation, and the desired significance level (alpha).

Here’s an example code to calculate Type II error in R:

# Install and load required packages
if (!require(pwr))
install.packages("pwr")
library(pwr)

# Parameters
effect_size <-
0.5 # The difference between null and alternative hypotheses
sample_size <- 100 # The number of observations in each group
sd <- 15 # The standard deviation
alpha <- 0.05 # The significance level

# Calculate Type II Error
pwr_result <-
pwr.t.test(
n = sample_size,
d = effect_size / sd,
sig.level = alpha,
type = "two.sample",
alternative = "two.sided"
)
type_II_error <- 1 - pwr_result$power

# Print Type II Error
print(type_II_error)

In this example, we are using the pwr package to calculate the power of the test, and then subtracting it from 1 to obtain the Type II error (β). Remember to adapt the parameters according to your specific problem.

Output

> # Print Type II Error
> print(type_II_error)
[1] 0.9436737

Another example code to calculate Type II error in R

To calculate the Type II error in R, you need to perform a power analysis, which requires several inputs such as sample size, effect size, significance level, and power. Here is an example of how to do it:

# define the sample size
n <- 50

# define the effect size
d <- 0.5

# define the significance level
alpha <- 0.05

# define the power
power <- 0.8

# calculate the critical t-value for the given 
# significance level and degrees of freedom
df <- n - 1
t_crit <- qt(1 - alpha/2, df)

# calculate the non-centrality parameter
ncp <- d * sqrt(n) / sqrt(1 + d^2 / (2*(n-1)))

# calculate the Type II error rate
1 - pt(t_crit, df, ncp, lower.tail=FALSE)

In this example, we first defined the sample size, effect size, significance level, and power. We then calculated the critical t-value using the qt function, which returns the t-value corresponding to the given significance level and degrees of freedom. We then calculated the non-centrality parameter using the formula ncp = d * sqrt(n) / sqrt(1 + d^2 / (2*(n-1))), which represents the distance between the null hypothesis and the alternative hypothesis in terms of standard errors. Finally, we used the pt function to calculate the probability of observing a t-value greater than the critical t-value under the alternative hypothesis, which represents the Type II error rate.