README.md
In familial: Statistical Tests of Familial Hypotheses

familial

An R package for familial inference. Briefly, this package provides tests for hypotheses of the form

$\mathrm{H}_0:\mu(\lambda)=\mu_0\text{ for some }\lambda\in\Lambda\quad\text{vs.}\quad\mathrm{H}_1:\mu(\lambda)\neq\mu_0\text{ for all }\lambda\in\Lambda,$

where $\{\mu(\lambda):\lambda\in\Lambda\}$ is a family of centers, e.g., that induced by the Huber loss function with parameter $\lambda$ . In contrast to classic statistical tests such as the $t$ or sign tests for the mean or median, familial tests do not depend on a single (sometimes arbitrarily chosen) center.

Presently, familial supports tests of the Huber family of centers, which includes the mean and median. Testing is carried out using a Bayesian approach whereby the posterior probabilities of the competing hypotheses $\mathrm{H}_0$ and $\mathrm{H}_1$ are from the Bayesian bootstrap. One- and two-sample tests are supported, as are directional tests. Methods for visualizing output are provided.

To install the latest stable version from CRAN, run the following code:

install.packages('familial')

To install the latest development version from GitHub, run the following code:

devtools::install_github('ryan-thompson/familial')

The center.test() function performs a test of centers, with the default being the Huber family of centers.

library(familial)
set.seed(1)

# One-sample test with point null
x <- MASS::galaxies
center.test(x, mu = 21000)

## -----------------------------------------------
## familial test of centers with huber family
## -----------------------------------------------
## mu = 21000 
## posterior probabilities: 
##    H0    H1 
## 0.542 0.458 
## optimal decision: indeterminate

# One-sample test with interval null
center.test(x, mu = c(20500, 21500))

## -----------------------------------------------
## familial test of centers with huber family
## -----------------------------------------------
## mu = 20500 21500 
## posterior probabilities: 
##    H0    H1 
## 0.959 0.041 
## optimal decision: H0

# Two-sample test
x <- MASS::cabbages[MASS::cabbages$Cult == 'c39', 'HeadWt']
y <- MASS::cabbages[MASS::cabbages$Cult == 'c52', 'HeadWt']
center.test(x, y)

## -----------------------------------------------
## familial test of centers with huber family
## -----------------------------------------------
## mu = 0 
## posterior probabilities: 
##    H0    H1 
## 0.008 0.992 
## optimal decision: H1

# Two-sample paired directional test
x <- MASS::anorexia[MASS::anorexia$Treat == 'FT', 'Postwt']
y <- MASS::anorexia[MASS::anorexia$Treat == 'FT', 'Prewt']
center.test(x, y, paired = T, alternative = 'greater')

## -----------------------------------------------
## familial test of centers with huber family
## -----------------------------------------------
## mu = 0 
## posterior probabilities: 
##    H0    H1 
## 0.006 0.994 
## optimal decision: H1

See the package vignette or reference manual.