# Bootstrapping

`Bootstrapping.Rmd`

## Bootstrapping and confidence intervals

Since I first discovered confidence intervals (CIs) back in the 1980s, and then discovered bootstrapping probably in the late 90s or early naughties, the advantages they have respectively over traditional null hypothesis significance testing (NHST) and over splitting analytic methods into parametric and non-parametric in a very clumsy way have been utterly persuasive for me. However, with a few exceptions both were late to be implemented into SPSS which has been the dominant statistical software used by psychologists and psychotherapy researchers until recently.

R, mainly through the excellent `boot`

package offered me
a way to bring the two together and I have leant on that for many papers
for probably 15 years now. However, `boot::boot()`

is not
always the friendliest of R functions and coupling it into the tidverse
way of doing things in R isn’t always easy as `boot`

is
firmly in the “base R” tradition.

From the start of thinking about this CECPfuns package I wanted to pull together the various bootstrap functions, often very clumsy ones, and make sure I had the latest versions to hand and tested and documented so I would remember how they worked and what I’d done inside them fairly easily. As I started to think of making CECPfuns fairly public I realised that these function should help non-statisticians and relative R newcomers to use bootstrapping to get confidence intervals for typical therapy data analyses research. At the moment the functions in the package are:

- getBootCICorr()
- getBootCIalpha()
- getBootCImean()
- getBootCICSC()

Each, I think, has sufficient information for people to use them in
their help files and each has pretty extensive trapping of improbable or
impossible inputs so I hope their error messages and warnings will be
protective (`boot::boot()`

is brilliant but not always
transparently helpful when I try to something stupid with it!)

Over the next few months more bootstrap functions for the sample statistics we use a lot will be added and I will add these sections to this vignette.

- Background on confidence intervals for those not (fully) happy they understand the ideas including some simple theory about the relationships between CIs and NHST. What CIs are and what they are not.
- A bit on the distinction between parametric statistical tests and non-parametric tests, how they relate to distibutions of continuous variables, and why the traditional way of choosing between them is problematical.
- An introduction to bootstrapping. Why we don’t need it to get a confidence interval around a proportion and why it’s useful for most other sample statistics that aren’t simple counts.
- Worked examples of CIs and bootstrapped CIs for commonly meaningful analyses of therapy data.