tsum.test {BSDA}  R Documentation 
Summarized ttest
Description
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
.
Usage
tsum.test(
mean.x,
s.x = NULL,
n.x = NULL,
mean.y = NULL,
s.y = NULL,
n.y = NULL,
alternative = "two.sided",
mu = 0,
var.equal = FALSE,
conf.level = 0.95
)
Arguments
mean.x 
a single number representing the sample mean of 
s.x 
a single number representing the sample standard deviation for

n.x 
a single number representing the sample size for 
mean.y 
a single number representing the sample mean of 
s.y 
a single number representing the sample standard deviation for

n.y 
a single number representing the sample size for 
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. 
Details
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
.
Value
A list of class htest
, containing the following components:
statistic 
the tstatistic, with names attribute 
parameters 
is the degrees of freedom of the tdistribution associated
with statistic. Component 
p.value 
the pvalue for the test. 
conf.int 
is
a confidence interval (vector of length 2) for the true mean or difference
in means. The confidence level is recorded in the attribute

estimate 
vector of length 1 or 2, giving the sample mean(s) or mean
of differences; these estimate the corresponding population parameters.
Component 
null.value 
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 
a character string (vector of length 1) containing the names x and y for the two summarized samples. 
Null Hypothesis
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"
).
Author(s)
Alan T. Arnholt
References
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.
See Also
Examples
tsum.test(mean.x=5.6, s.x=2.1, n.x=16, mu=4.9, alternative="greater")
# Problem 6.31 on page 324 of BSDA states: The chamber of commerce
# of a particular city claims that the mean carbon dioxide
# level of air polution is no greater than 4.9 ppm. A random
# sample of 16 readings resulted in a sample mean of 5.6 ppm,
# and s=2.1 ppm. Onesided onesample ttest. The null
# hypothesis is that the population mean for 'x' is 4.9.
# The alternative hypothesis states that it is greater than 4.9.
x < rnorm(12)
tsum.test(mean(x), sd(x), n.x=12)
# Twosided onesample ttest. The null hypothesis is that
# the population mean for 'x' is zero. The alternative
# hypothesis states that it is either greater or less
# than zero. A confidence interval for the population mean
# will be computed. Note: above returns same answer as:
t.test(x)
x < c(7.8, 6.6, 6.5, 7.4, 7.3, 7.0, 6.4, 7.1, 6.7, 7.6, 6.8)
y < c(4.5, 5.4, 6.1, 6.1, 5.4, 5.0, 4.1, 5.5)
tsum.test(mean(x), s.x=sd(x), n.x=11 ,mean(y), s.y=sd(y), n.y=8, mu=2)
# Twosided standard twosample ttest. The null hypothesis
# is that the population mean for 'x' less that for 'y' is 2.
# The alternative hypothesis is that this difference is not 2.
# A confidence interval for the true difference will be computed.
# Note: above returns same answer as:
t.test(x, y)
tsum.test(mean(x), s.x=sd(x), n.x=11, mean(y), s.y=sd(y), n.y=8, conf.level=0.90)
# Twosided standard twosample ttest. The null hypothesis
# is that the population mean for 'x' less that for 'y' is zero.
# The alternative hypothesis is that this difference is not
# zero. A 90% confidence interval for the true difference will
# be computed. Note: above returns same answer as:
t.test(x, y, conf.level=0.90)