R Jackknife Test for Equal Dispersions: Approximate p-value Calculation

To find the approximate p-value for the Jackknife test to compare the hypothesis of equal dispersions versus the alternative that the dispersions are different at α = 0.05 in R, you can follow these steps:

1. Install and load the 'lawstat' package in R if you haven't done so already. You can use the following commands:

install.packages('lawstat')
library(lawstat)

2. Create two vectors, Y and X, containing the given data. Y should have 10 values, and X should have 5 values. In R, you can create these vectors using the following commands:

Y <- c(0.8, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
X <- c(1.15, 0.88, 0.9, 0.74, 1.21)

3. Use the jackknife_var function to compute the Jackknife variances and obtain the approximate p-value. The code is as follows:

jackknife_var(Y, X)$p.value

4. The function jackknife_var will return an approximate p-value for the Jackknife test. If the p-value is less than 0.05, you can reject the hypothesis of equal dispersions and conclude that the dispersions are different. If the p-value is greater than or equal to 0.05, you fail to reject the hypothesis, indicating that the dispersions may be equal.

Remember to ensure that you have properly imported and set up the data in the R environment. If you encounter any issues, make sure to execute the commands in the correct order and check if the 'lawstat' package is installed.