agnostic.t.test: Agnostic Student's t-Test

In vcoscrato/agnostic: Agnostic hyothesis testing

Description

Performs t-tests under the agnostic perspective.

Usage

agnostic.t.test(x, y = 0, alternative = "two.sided", alpha = 0.05,
  beta = 0.05, paired = FALSE)

Arguments

x	A vector of data.
y	A vector of data or a constant.
alternative	A character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
alpha	Desired type I probability of error.
beta	Desired tupe II probability of error.
paired	Boolean indicating if x and y are paired data vectors.

Value

A list containing the decision, the limits of the critical region and the test statistic value for the test.

Examples

#One sample test
agnostic.t.test(rnorm(10), 0)

#Two sample paired test
agnostic.t.test(rnorm(20, mean = 1), rnorm(20), paired = TRUE)

#Simulation example (this should take some seconds to run)
library(tidyr)
library(ggplot2)

n=10
mu.grid=seq(-2,2,length.out = 50)
B=5000
decision=matrix(NA,length(mu.grid),B)
for(i in 1:length(mu.grid))
{
  #print(i/length(mu.grid))
  for(b in 1:B)
  {
    decision[i,b]=agnostic.t.test(x=rnorm(n,mean = mu.grid[i]), alternative = "two.sided")$decision
  }
}

decisions.names=c("Agnostic","Reject H0","Accept H0")
probability.decisions=t(apply(decision,1,function(x)
{
  return(apply(as.matrix(decisions.names),1,function(y)
  {
    mean(x==y)
  }))
}))
colnames(probability.decisions)=decisions.names
probability.decisions=cbind(mu.grid,as.data.frame(probability.decisions))
probability.decisions=gather(probability.decisions,"Decision","Probability",
Agnostic:`Accept H0`)

theme = theme_set(theme_minimal(base_size = 26))
theme = theme_update(legend.position="top", legend.title=element_blank(),
panel.grid.major.x=element_blank())

ggplot()+geom_line(data=probability.decisions,aes(x=mu.grid,y=Probability,
linetype=Decision,color=Decision),size=2)+
geom_hline(yintercept = 0.05)+xlab(expression(mu))+geom_vline(xintercept = 0)+
ylab("Probability of each decision")

vcoscrato/agnostic documentation built on April 4, 2020, 11:27 a.m.