# BCa Bootstrap Independent-Samples Test and CI for Two Standard Deviations

### Description

Obtains an independent-samples confidence interval and (optionally) performs an independent-samples hypothesis test for the ratio of two population standard deviations, using the BCa bootstrap method.

### Usage

1 2 3 |

### Arguments

`x` |
a numeric vector of observations of the variable (stacked case) or a numeric vector of data values representing the first of the two samples (unstacked case). |

`y` |
a vector of corresponding population identifiers (stacked case) or a numeric vector of data values representing the second of the two samples (unstacked case). |

`stacked` |
a logical value (default TRUE) indicating whether the data are stacked. |

`variable` |
an optional string that gives the name of the variable under consideration; ignored if stacked is TRUE. |

`null.hyp` |
the null-hypothesis value; if omitted, no hypothesis test is performed. |

`alternative` |
a character string specifying the alternative hypothesis; must be one of "two.sided" (default), "greater", or "less". |

`conf.level` |
the confidence level (between 0 and 1); default is 0.95. |

`type` |
a character string specifying the type of CI; if user supplied, must be one of "two-sided", "upper-bound", or "lower-bound"; defaults to "two-sided" if alternative is "two.sided", "upper-bound" if alternative is "less", and "lower-bound" if alternative is "greater". |

`R` |
the number of bootstrap replications; default is 9999. |

### Value

A list with class "boot.two" containing the following components:

`Stacked ` |
a logical indicating whether the data are stacked (TRUE) or not (FALSE). |

`Boot.values ` |
the point estimates for the ratio of the standard deviations obtained from the bootstrap. |

`Confidence.limits ` |
the confidence limit(s) for the confidence interval. |

`Parameter ` |
the parameter under consideration, here standard deviation. |

`Header ` |
the main title for the output. |

`Variable ` |
the name of the variable under consideration or NULL |

`Pop.1 ` |
the first population. |

`Pop.2 ` |
the second population. |

`n.1 ` |
the sample size for the first population. |

`n.2 ` |
the sample size for the second population. |

`Statistic ` |
the name of the statistic, here ratio.sd. |

`Observed.1 ` |
the observed point estimate for the standard deviation of the first population. |

`Observed.2 ` |
the observed point estimate for the standard deviation of the second population. |

`Observed ` |
the observed point estimate for the ratio of the two standard deviations. |

`Replications ` |
the number of bootstrap replications. |

`Mean ` |
the mean of the bootstrap values. |

`SE ` |
the standard deviation of the bootstrap values. |

`Bias ` |
the difference between the mean of the bootstrap values and the observed value. |

`Percent.bias ` |
the percentage bias: 100*|Bias/Observed|. |

`Null ` |
the null-hypothesis value or NULL. |

`Alternative ` |
the alternative hypothesis or NULL. |

`P.value ` |
the P-value or a statement like P < 0.001 or NULL. |

`p.value ` |
the P-value or NULL. |

`Level ` |
the confidence level. |

`Type ` |
the type of confidence interval. |

`Confidence.interval ` |
the confidence interval. |

### Author(s)

Neil A. Weiss

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# Elmendorf tear strengths, in grams, for independent samples of
# Brand A and Brand B vinyl floor coverings.
data("elmendorf")
str(elmendorf)
attach(elmendorf)
# Note that the data are stacked.
# 90% confidence interval for the ratio of the population standard
# deviations of tear strength for Brands A and B.
boot.ratio.sd.bca(STRENGTH, BRAND, conf.level = 0.90)
# 95% (default) confidence interval for the ratio of the population
# standard deviations of tear strength for Brands A and B, and a
# two-tailed hypothesis test with null hypothesis 1 (i.e., the
# population standard deviations are equal).
boot.ratio.sd.bca(STRENGTH, BRAND, null.hyp = 1)
detach(elmendorf) # clean up
``` |