| t.test {stats} | R Documentation |
Student's t-Test
Description
Performs one and two sample t-tests on vectors of data.
Usage
t.test(x, ...)## Default S3 method:t.test(x, y = NULL, alternative = c("two.sided", "less", "greater"), mu = 0, paired = FALSE, var.equal = FALSE, conf.level = 0.95, ...)## S3 method for class 'formula't.test(formula, data, subset, na.action = na.pass, ...)Arguments
x | a (non-empty) numeric vector of data values. |
y | an optional (non-empty) numeric vector of data values. |
alternative | a character string specifying the alternativehypothesis, must be one of |
mu | a number indicating the true value of the mean (ordifference in means if you are performing a two sample test). |
paired | a logical indicating whether you want a pairedt-test. |
var.equal | a logical variable indicating whether to treat thetwo variances as being equal. If |
conf.level | confidence level of the interval. |
formula | a formula of the form |
data | an optional matrix or data frame (or similar: see |
subset | an optional vector specifying a subset of observationsto be used. |
na.action | a function which indicates what should happen whenthe data contain |
... | further arguments to be passed to or from methods.For the |
Details
alternative = "greater" is the alternative thatx has alarger mean thany. For the one-sample case: that the mean is positive.
Ifpaired isTRUE then bothx andy mustbe specified and they must be the same length. Missing values aresilently removed (in pairs ifpaired isTRUE). Ifvar.equal isTRUE then the pooled estimate of thevariance is used. By default, ifvar.equal isFALSEthen the variance is estimated separately for both groups and theWelch modification to the degrees of freedom is used.
If the input data are effectively constant (compared to the larger of thetwo means) an error is generated.
If the data contain infinite values,t.test() no longer errors andreturns a still not very useful result. Note thatwilcox.test() isrobust against outliers and hencedeals more usefully with suchInf values inx ory.
Value
A list with class"htest" containing the following components:
statistic | the value of the t-statistic. |
parameter | the degrees of freedom for the t-statistic. |
p.value | the p-value for the test. |
conf.int | a confidence interval for the mean appropriate to thespecified alternative hypothesis. |
estimate | the estimated mean or difference in means depending onwhether it was a one-sample test or a two-sample test. |
null.value | the specified hypothesized value of the mean or meandifference depending on whether it was a one-sample test or atwo-sample test. |
stderr | the standard error of the mean (difference), used asdenominator in the t-statistic formula. |
alternative | a character string describing the alternativehypothesis. |
method | a character string indicating what type of t-test wasperformed. |
data.name | a character string giving the name(s) of the data. |
See Also
Examples
## Two-sample t-testt.test(1:10, y = c(7:20)) # P = .00001855t.test(1:10, y = c(7:20, 200)) # P = .1245 -- NOT significant anymore## Traditional interfacewith(mtcars, t.test(mpg[am == 0], mpg[am == 1]))## Formula interfacet.test(mpg ~ am, data = mtcars)## One-sample t-test## Traditional interfacet.test(sleep$extra)## Formula interfacet.test(extra ~ 1, data = sleep)## Paired t-test## The sleep data is actually paired, so could have been in wide format:sleep2 <- reshape(sleep, direction = "wide", idvar = "ID", timevar = "group")## Traditional interfacet.test(sleep2$extra.1, sleep2$extra.2, paired = TRUE)## Formula interfacet.test(Pair(extra.1, extra.2) ~ 1, data = sleep2)