tsum.test {BSDA} | R Documentation |
Summarized t-test
Description
Performs a one-sample, two-sample, or a Welch modified two-sample t-test
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 one-sample t-test is carried out with
x
. If y is not NULL
, either a standard or Welch modified
two-sample t-test is performed, depending on whether var.equal
is
TRUE
or FALSE
.
Value
A list of class htest
, containing the following components:
statistic |
the t-statistic, with names attribute |
parameters |
is the degrees of freedom of the t-distribution associated
with statistic. Component |
p.value |
the p-value 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 one-sample t-test, the null hypothesis is
that the mean of the population from which x
is drawn is mu
.
For the standard and Welch modified two-sample t-tests, 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: McGraw-Hill.
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. One-sided one-sample t-test. 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)
# Two-sided one-sample t-test. 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)
# Two-sided standard two-sample t-test. 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)
# Two-sided standard two-sample t-test. 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)