tsum.test {PASWR} | R Documentation |
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
.
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)
mean.x |
a single number representing the sample mean of x |
s.x |
a single number representing the sample standard deviation for x |
n.x |
a single number representing the sample size for x |
mean.y |
a single number representing the sample mean of y |
s.y |
a single number representing the sample standard deviation for y |
n.y |
a single number representing the sample size for y |
alternative |
is a character string, one of "greater" , "less" or
"two.sided" , or just the initial letter of each, indicating the specification
of the alternative hypothesis. For one-sample tests, alternative refers to the true
mean of the parent population in relation to the hypothesized value mu .
For the standard two-sample tests, alternative refers to the difference between
the true population mean for x and that for y , in relation to mu .
For the one-sample and paired t-tests, alternative refers to the true mean of the
parent population in relation to the hypothesized value mu . For the standard
and Welch modified two-sample t-tests, alternative refers to the difference between
the true population mean for x and that for y , in relation to mu .
For the one-sample t-tests, alternative refers to the true mean of the parent population
in relation to the hypothesized value mu . For the standard and Welch modified
two-sample t-tests, alternative refers to the difference between the true population
mean for x and that for y , in relation to mu . |
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 TRUE , the variances of the parent populations
of x and y are assumed equal. Argument var.equal should be supplied
only for the two-sample tests. |
conf.level |
is the confidence level for the returned confidence interval; it must lie between zero and one. |
"two.sided"
, and var.equal
determine the type of test. If y
is NULL
, a one-sample t-test is
carried out with x
.NULL
, either a standard or
Welch modified two-sample t-test is performed, depending on whether var.equal
is TRUE
or FALSE
.
A list of class htest
, containing the following components:
statistic |
the t-statistic, with names attribute "t" |
parameters |
is the degrees of freedom of the t-distribution
associated with statistic.
Component parameters has names attribute "df" . |
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 conf.level . When alternative
is not "two.sided" , the confidence interval will be half-infinite,
to reflect the interpretation of a confidence interval as the set of all
values k for which one would not reject the null hypothesis that
the true mean or difference in means is k . Here infinity will be
represented by Inf . |
estimate |
vector of length 1 or 2, giving the sample mean(s)
or mean of differences; these estimate the corresponding population
parameters. Component estimate has a names attribute describing its elements. |
null.value |
|
alternative |
records the value of the input argument alternative:
"greater" , "less" or "two.sided" . |
data.name |
a character string (vector of length 1) containing the names x and y for the two summarized samples. |
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"
).
The assumption of equal population variances is central to the standard two-sample t-test. This test can be misleading when population variances are not equal, as the null distribution of the test statistic is no longer a t-distribution. If the assumption of equal variances is doubtful with respect to a particular dataset, the Welch modification of the t-test should be used.
The t-test and the associated confidence interval are quite robust with respect to level toward heavy-tailed non-Gaussian distributions (e.g., data with outliers). However, the t-test is non-robust with respect to power, and the confidence interval is non-robust 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 half-infinite when
alternative is not "two.sided"
; infinity will be represented by Inf
.
Alan T. Arnholt
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.
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) # Example 8.13 from PASWR tsum.test(mean.x=4, s.x=2.89, n.x=25, mu=2.5) # Example 9.8 from PASWR