bootEd was created for teaching simple bootstrap intervals to undergraduate students in introductory statistics courses. Specifically, this package was created so that teachers can emphasize assumptions pertaining to pivotal quantities, which the percentile, basic, and studentized bootstrap intervals rely on. The importance of discussing these assumptions is further discussed in the corresponding article.
To install and load bootEd, use the following code:
install.packages("devtools")
devtools::install_github("tottyn/bootEd")
library(bootEd)Each function in bootEd requires that the user specify the vector of data and a function to apply to the data. The function can be a base R function, such as mean or median, or a user-defined summary function. For example, to construct a bootstrap interval for the mean using the percentile method we use the following code:
percentile(sample = rnorm(100, mean = 3, sd = 0.5), parameter = "mean")And the output is:
## The percentile bootstrap interval for the mean is: (2.902389, 3.096528).
##
## Assumptions: the shifted sampling distribution of the statistic of interest is symmetric
## and it does not depend on any unknown parameters, such as the underlying population variance.
The bootstrap distribution is itself symmetric, but the assumption pertains to the shifted sampling distribution, which we are estimating. Since our sample size is large, the Central Limit Theorem (CLT) indicates that the sampling distribution of the sample mean will be approximately bell-shaped (i.e. symmetric). However, the CLT also implies that its variance will depend on the variance of the underlying population, an unknown parameter. Therefore, there will be some differences in the spread of the shifted sampling distributions when the samples come from populations with different variances. However, since the sample size is large, these differences will likely be small (see the article for more details). Therefore, the shifted bootstrap distribution can be expected to approximate the shifted sampling distribution moderately well.
Each of the functions in the package returns the desired interval, a prompt about its assumptions, and plots for visualizing the bootstrap distribution. By including the prompt, a discussion about how reasonable the assumptions are is elicited and students can learn to consider the assumptions of these methods before applying them. It is important to discuss these assumptions because there are non-trivial differences in the performance of these methods when their assumptions are or are not reasonable.
These functions can also be used to perform simulations. See examples.Rmd for more examples and breaking_assumptions.Rmd for the code used to generate the results in the article.
bootEd is released under the following Code of Conduct. Please submit an issue for any questions and concerns.
Davison, A., & Hinkley, D. (1997). Bootstrap Methods and their Application (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511802843
Efron, B., & Tibshirani, R.J. (1994). An Introduction to the Bootstrap (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9780429246593