# boot.ttest2: Bootstrap t-test for 2 independent samples In Rfast: A Collection of Efficient and Extremely Fast R Functions

## Description

Bootstrap t-test for 2 independent samples.

## Usage

 `1` ```boot.ttest2(x, y, B = 999) ```

## Arguments

 `x` A numerical vector with the data. `y` A numerical vector with the data. `B` The number of bootstrap samples to use.

## Details

Instead of sampling B times from each sample, we sample √{B} from each of them and then take all pairs. Each bootstrap sample is independent of each other, hence there is no violation of the theory.

## Value

A vector with the test statistic and the bootstrap p-value.

## Author(s)

Michail Tsagris and Christina Chatzipantsiou

R implementation and documentation: Michail Tsagris <mtsagris@uoc.gr> and Christina Chatzipantsiou <chatzipantsiou@gmail.com>.

## References

B.L. Welch (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.

Efron Bradley and Robert J. Tibshirani (1993). An introduction to the bootstrap. New York: Chapman \& Hall/CRC.

Chatzipantsiou C., Dimitriadis M., Papadakis M. and Tsagris M. (2019). Extremely efficient permutation and bootstrap hypothesis tests using R. To appear in the Journal of Modern Applied Statistical Methods.

https://arxiv.org/ftp/arxiv/papers/1806/1806.10947.pdf

```ttest2, exact.ttest2, ftest ```

## Examples

 ```1 2 3 4 5``` ```tic <- proc.time() x <- rexp(40, 4) y <- rbeta(50, 2.5, 7.5) system.time( a <- boot.ttest2(x, y, 9999) ) a ```

### Example output

```Loading required package: Rcpp