t.test
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, ...)
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 alternative hypothesis, must be one of |
mu | a number indicating the true value of the mean (or difference in means if you are performing a two sample test). |
paired | a logical indicating whether you want a paired t-test. |
var.equal | a logical variable indicating whether to treat the two 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 observations to be used. |
na.action | a function which indicates what should happen when the data contain |
... | further arguments to be passed to or from methods. |
Details
alternative = "greater"
is the alternative that x
has a larger mean than y
. For the one-sample case: that the mean is positive.
If paired
is TRUE
then both x
and y
must be specified and they must be the same length. Missing values are silently removed (in pairs if paired
is TRUE
). If var.equal
is TRUE
then the pooled estimate of the variance is used. By default, if var.equal
is FALSE
then the variance is estimated separately for both groups and the Welch modification to the degrees of freedom is used.
If the input data are effectively constant (compared to the larger of the two means) an error is generated.
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 the specified alternative hypothesis. |
estimate | the estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test. |
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. |
stderr | the standard error of the mean (difference), used as denominator in the t-statistic formula. |
alternative | a character string describing the alternative hypothesis. |
method | a character string indicating what type of t-test was performed. |
data.name | a character string giving the name(s) of the data. |
See Also
Examples
require(graphics) t.test(1:10, y = c(7:20)) # P = .00001855 t.test(1:10, y = c(7:20, 200)) # P = .1245 -- NOT significant anymore ## Classical example: Student's sleep data plot(extra ~ group, data = sleep) ## Traditional interface with(sleep, t.test(extra[group == 1], extra[group == 2])) ## Formula interface t.test(extra ~ group, data = sleep) ## Formula interface to one-sample test t.test(extra ~ 1, data = sleep) ## Formula interface to paired test ## The sleep data are actually paired, so could have been in wide format: sleep2 <- reshape(sleep, direction = "wide", idvar = "ID", timevar = "group") t.test(Pair(extra.1, extra.2) ~ 1, data = sleep2)
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Licensed under the GNU General Public License.