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,](https://latex.codecogs.com/png.image?%5Cdpi%7B110%7D&space;%5Cbg_white&space;%0A%5Cmathrm%7BH%7D_0%3A%5Cmu%28%5Clambda%29%3D%5Cmu_0%5Ctext%7B%20for%20some%20%7D%5Clambda%5Cin%5CLambda%5Cquad%5Ctext%7Bvs.%7D%5Cquad%5Cmathrm%7BH%7D_1%3A%5Cmu%28%5Clambda%29%5Cneq%5Cmu_0%5Ctext%7B%20for%20all%20%7D%5Clambda%5Cin%5CLambda%2C%0A ” _0:()=_0_1:()_0, “)
where is a family of centers, e.g., that induced by the Huber loss function with parameter . In contrast to classic statistical tests such as the 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 and 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:
::install_github('ryan-thompson/familial') devtools
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
<- MASS::galaxies
x 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
<- MASS::cabbages[MASS::cabbages$Cult == 'c39', 'HeadWt']
x <- MASS::cabbages[MASS::cabbages$Cult == 'c52', 'HeadWt']
y 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
<- MASS::anorexia[MASS::anorexia$Treat == 'FT', 'Postwt']
x <- MASS::anorexia[MASS::anorexia$Treat == 'FT', 'Prewt']
y 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.