Added bootstrap hypothesis test for means

.Rbuildignore

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+^.*\.Rproj$
+^\.Rproj\.user$

.gitignore

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+.Rproj.user
+.Rhistory
+.RData
+.Ruserdata

DESCRIPTION

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+Package: bootstrapr
+Type: Package
+Title: What the Package Does (Title Case)
+Version: 0.1.0
+Author: Who wrote it
+Maintainer: The package maintainer <yourself@somewhere.net>
+Description: More about what it does (maybe more than one line)
+    Use four spaces when indenting paragraphs within the Description.
+License: What license is it under?
+Encoding: UTF-8
+LazyData: true

NAMESPACE

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+exportPattern("^[[:alpha:]]+")

R/bootstrap_mean.R

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+bootstrap.mean.test = function(x, y = NULL, alternative = c("two.sided", "less", "greater"), mu = 0, conf.level = 0.95, bootstrap_samples = 1000000) {
+    ## Select the alternative chosen
+    alternative = match.arg(alternative)
+
+    ## Make sure argument mu is correct
+    if(!missing(mu) && (length(mu) != 1 || is.na(mu))) {
+        stop("'mu' must be a single number")
+    }
+
+    ## Make sure confidence interval is between 0 and 1
+    if(!missing(conf.level) && (length(conf.level) != 1 || !is.finite(conf.level) || conf.level < 0 || conf.level > 1)) {
+        stop("'conf.level' must be a single number between 0 and 1")
+    }
+
+    if (is.null(y)) {
+        dname = deparse(substitute(x))
+    } else {
+        dname = paste(deparse(substitute(x)), "and", deparse(substitute(y)))
+    }
+
+    ## Take out missing values
+    x = x[!is.na(x)]
+    if (!is.null(y)) {
+        y = y[!is.na(y)]
+    }
+
+    ## Check to see if we have enough observations and enough variation in data
+    nx = length(x)
+    mx = mean(x)
+    vx = var(x)
+   if (is.null(y)) {
+        if (nx < 2) {
+            stop("not enough 'x' observations")
+        }
+	    stderr = sqrt(vx / nx)
+        if (stderr < 10 * .Machine$double.eps * abs(mx)) {
+            stop("data are essentially constant")
+        }
+    } else {
+	    ny = length(y)
+        if(nx < 2) {
+            stop("not enough 'x' observations")
+        }
+	    if(ny < 2) {
+            stop("not enough 'y' observations")
+        }
+	    my = mean(y)
+	    vy = var(y)
+	    stderrx = sqrt(vx / nx)
+	    stderry = sqrt(vy / ny)
+	    stderr = sqrt(stderrx^2 + stderry^2)
+        if(stderr < 10 * .Machine$double.eps * max(abs(mx), abs(my))) {
+            stop("data are essentially constant")
+        }
+    }
+
+
+    ## Preallocate the vectors
+    bootstrap_replicants = numeric(bootstrap_samples)
+    bootstrap_means = numeric(bootstrap_samples)
+    ## If it's a one sample bootstrap test
+    if (is.null(y)) {
+        observed_difference = mx - mu
+        ## Simulate null hypothesis by shifting x to have a new mean of mu
+        x_shifted = x - mx + mu
+        for (i in 1:bootstrap_samples) {
+            ## Resample under the null hypothesis the difference between the means of mu
+            bootstrap_xshifted = sample(x_shifted, nx, replace = T)
+            bootstrap_replicants[i] = mean(bootstrap_xshifted) - mu
+            ## Resample original x for confidence interval 
+            bootstrap_x = sample(x, nx, replace = T)
+            bootstrap_means[i] = mean(bootstrap_x)
+        }
+        method = "One Sample Bootstrap Test"
+        estimate = setNames(mx, "mean of x")
+        
+    } else { ## If it's a two sample bootstrap test
+        observed_difference = mx - my - mu
+        ## Under the null hypothesis the difference in means between x and y is mu
+        pooled_mean = mean(c(x, y)) + mu
+        x_shifted = x - mx + pooled_mean
+        y_shifted = y - my + pooled_mean
+        for (i in 1:bootstrap_samples) {
+            ## Resample under null hypothesis the difference of means
+            bootstrap_xshifted = sample(x_shifted, nx, replace = T)
+            bootstrap_yshifted = sample(y_shifted, ny, replace = T)
+            bootstrap_replicants[i] = mean(bootstrap_xshifted) - mean(bootstrap_yshifted) - mu
+            ## Resample original data for confidence interval
+            bootstrap_x = sample(x, nx, replace = T)
+            bootstrap_y = sample(x, ny, replace = T)
+            bootstrap_means[i] = mean(bootstrap_x) - mean(bootstrap_y)
+        }
+        method = "Two Sample Bootstrap Test"
+        estimate = c(mx,my)
+        names(estimate) = c("mean of x","mean of y")
+    }
+
+    if (alternative == "two.sided") {
+        pval = sum(abs(bootstrap_replicants) >= abs(observed_difference)) / bootstrap_samples
+        lower_bound = quantile(bootstrap_means, (1 - conf.level) / 2)
+        upper_bound = quantile(bootstrap_means, conf.level + (1 - conf.level) / 2)
+    } else if (alternative == "less") {
+        pval = sum(bootstrap_replicants <= observed_difference) / bootstrap_samples
+        lower_bound = -Inf
+        upper_bound = quantile(bootstrap_means, conf.level)
+    } else if (alternative == "greater") {
+        pval = sum(bootstrap_replicants >= observed_difference) / bootstrap_samples
+        lower_bound = quantile(bootstrap_means, 1 - conf.level)
+        upper_bound = Inf
+    }
+    cint = c(lower_bound, upper_bound)
+    names(mu) = if(!is.null(y)) "difference in means" else "mean"
+    attr(cint,"conf.level") = conf.level
+    rval = list(p.value = pval, conf.int = cint, estimate = estimate, null.value = mu,
+	       alternative = alternative, method = method, data.name = dname)
+    class(rval) = "htest"
+    return(rval)
+}

bootstrapr.Rproj

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+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX
+
+AutoAppendNewline: Yes
+StripTrailingWhitespace: Yes
+
+BuildType: Package
+PackageUseDevtools: Yes
+PackageInstallArgs: --no-multiarch --with-keep.source

man/bootstrap.mean.test.Rd

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+\name{bootstrap.mean.test}
+\alias{bootstrap.mean.test}
+\title{Bootstrap Test for Means}
+\description{Performs one and two sample bootstrap tests for means on vectors of data}
+\usage{
+bootstrap.mean.test(x, ...)
+
+## Default method:
+bootstrap.mean.test(x, y = NULL, alternative = c("two.sided", "less", "greater"), mu = 0, conf.level = 0.95, bootstrap_samples = 1e+06)
+}
+\arguments{
+  \item{x}{a (non-empty) numeric vector of data values.}
+  \item{y}{an optional (non-empty) numeric vector of data values.}
+  \item{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.}
+  \item{mu}{a number indicating the true value of the mean (or difference in means if you are performing a two sample test).}
+  \item{conf.level}{confidence level of the interval.}
+  \item{bootstrap_samples}{the number of bootstrap replicants to generate. Influences the accuracy of the p-value and confidence interval}
+}
+\details{
+alternative = "greater" is the alternative that x has a larger mean than y.
+
+If the input data are effectively constant (compared to the larger of the two means) an error is generated.
+}
+\value{
+A list with class \code{"htest"} containing the following components:
+  \item{p.value}{the p-value for the test.}
+  \item{conf.int}{a confidence interval for the mean appropriate to the
+    specified alternative hypothesis.}
+  \item{estimate}{the estimated mean or difference in means depending on
+    whether it was a one-sample test or a two-sample test.}
+  \item{null.value}{the specified hypothesized value of the mean or mean
+    difference depending on whether it was a one-sample test or a
+    two-sample test.}
+  \item{alternative}{a character string describing the alternative
+    hypothesis.}
+  \item{method}{a character string indicating what type of t-test was
+    performed.}
+  \item{data.name}{a character string giving the name(s) of the data.}
+}
+\references{
+Gould, Rob. Bootstrap Hypothesis Test. PDF.
+http://www.stat.ucla.edu/~rgould/110as02/bshypothesis.pdf
+
+Myung, Jay. Bootstrap Hypothesis Testing. PDF.
+http://faculty.psy.ohio-state.edu/myung/personal/course/826/bootstrap_hypo.pdf
+
+}
+\author{
+Brandon Rozek (brozek@mail.umw.edu)
+}
+
+\seealso{
+  \code{\link{t.test}}
+}
+\examples{
+x = rnorm(200, 2, 5)
+y = rnorm(200, 2, 5)
+# One sample test
+bootstrap.mean.test(x, mu = 1)
+
+# Two sample test
+bootstrap.mean.test(x, y)
+}
+
+\keyword{htest}