Description Usage Arguments Details Value Null Hypothesis Test Assumptions Confidence Intervals Author(s) References See Also Examples
Performs a onesample, twosample, or a Welch modified twosample ttest based on user supplied summary information. Output is identical to that produced with t.test
.
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mean.x 
a single number representing the sample mean of 
s.x 
a single number representing the sample standard deviation of 
n.x 
a single number representing the sample size of 
mean.y 
a single number representing the sample mean of 
s.y 
a single number representing the sample standard deviation of 
n.y 
a single number representing the sample size of 
alternative 
is a character string, one of 
mu 
is a single number representing the value of the mean or difference in means specified by the null hypothesis. 
var.equal 
logical flag: if 
conf.level 
is the confidence level for the returned confidence interval; it must lie between zero and one. 
... 
Other arguments passed onto 
If y
is NULL
, a onesample ttest is carried out with x
. If y
is not NULL
, either a standard or Welch modified twosample ttest is performed, depending on whether var.equal
is TRUE
or FALSE
.
A list of class htest
, containing the following components:

the tstatistic, with names attribute 

is the degrees of freedom of the tdistribution associated with statistic. Component 

the pvalue for the test 

is a confidence interval (vector of length 2) for the true mean or difference in means. The confidence level is recorded in the attribute 

is a vector of length 1 or 2, giving the sample mean(s) or mean of differences; these estimate the corresponding population parameters. Component 

is the value of the mean or difference in means specified by the null hypothesis. This equals the input argument 
alternative 
records the value of the input argument alternative: 
data.name 
is a character string (vector of length 1) containing the names x and y for the two summarized samples. 
For the onesample ttest, the null hypothesis is that the mean of the population from which x
is drawn is mu
. For the standard and Welch modified twosample ttests, the null hypothesis is that the population mean for x
less that for y
is mu
.
The alternative hypothesis in each case indicates the direction of divergence of the population mean for x
(or difference of means for x
and y
) from mu
(i.e., "greater"
, "less"
, or "two.sided"
).
The assumption of equal population variances is central to the standard twosample ttest. This test can be misleading when population variances are not equal, as the null distribution of the test statistic is no longer a tdistribution. If the assumption of equal variances is doubtful with respect to a particular dataset, the Welch modification of the ttest should be used.
The ttest and the associated confidence interval are quite robust with respect to level toward heavytailed nonGaussian distributions (e.g., data with outliers). However, the ttest is nonrobust with respect to power, and the confidence interval is nonrobust with respect to average length, toward these same types of distributions.
For each of the above tests, an expression for the related confidence interval (returned component conf.int
) can be obtained in the usual way by inverting the expression for the test statistic. Note that, as explained under the description of conf.int
, the confidence interval will be halfinfinite when alternative is not "two.sided"
; infinity will be represented by Inf
.
Alan T. Arnholt <arnholtat@appstate.edu>
Kitchens, L.J. 2003. Basic Statistics and Data Analysis. Duxbury.
Hogg, R. V. and Craig, A. T. 1970. Introduction to Mathematical Statistics, 3rd ed. Toronto, Canada: Macmillan.
Mood, A. M., Graybill, F. A. and Boes, D. C. 1974. Introduction to the Theory of Statistics, 3rd ed. New York: McGrawHill.
Snedecor, G. W. and Cochran, W. G. 1980. Statistical Methods, 7th ed. Ames, Iowa: Iowa State University Press.
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# 95% Confidence Interval for mu1  mu2, assuming equal variances
round(tsum.test(mean.x = 53/15, mean.y = 77/11, s.x=sqrt((222  15*(53/15)^2)/14),
s.y = sqrt((560  11*(77/11)^2)/10), n.x = 15, n.y = 11, var.equal = TRUE)$conf, 2)
# One Sample ttest
tsum.test(mean.x = 4, s.x = 2.89, n.x = 25, mu = 2.5)

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