t.test {stats}  R Documentation 
Performs one and two sample ttests on vectors of data.
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, ...)
x 
a (nonempty) numeric vector of data values. 
y 
an optional (nonempty) 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 ttest. 
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. 
alternative = "greater"
is the alternative that x
has a
larger mean than y
. For the onesample 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.
A list with class "htest"
containing the following components:
statistic 
the value of the tstatistic. 
parameter 
the degrees of freedom for the tstatistic. 
p.value 
the pvalue 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 onesample test or a twosample test. 
null.value 
the specified hypothesized value of the mean or mean difference depending on whether it was a onesample test or a twosample test. 
stderr 
the standard error of the mean (difference), used as denominator in the tstatistic formula. 
alternative 
a character string describing the alternative hypothesis. 
method 
a character string indicating what type of ttest was performed. 
data.name 
a character string giving the name(s) of the data. 
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 onesample 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)