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 |
|---|---|
| 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. |
A list of class htest, containing the following components:
the t-statistic, with names attribute "t"
is the degrees of freedom of the t-distribution associated
with statistic. Component parameters has names attribute
"df".
the p-value 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
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.
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.
the value of the mean or difference in means specified by
the null hypothesis. This equals the input argument mu. Component
null.value has a names attribute describing its elements.
records the value of the input argument alternative:
"greater" , "less" or "two.sided".
a character string (vector of length 1) containing the names x and y for the two summarized samples.
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.
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").
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)#> [1] -4.72 -2.22 #> attr(,"conf.level") #> [1] 0.95# Example 8.13 from PASWR tsum.test(mean.x=4, s.x=2.89, n.x=25, mu=2.5)#> #> One-sample t-Test #> #> data: Summarized x #> t = 2.5952, df = 24, p-value = 0.01588 #> alternative hypothesis: true mean is not equal to 2.5 #> 95 percent confidence interval: #> 2.807067 5.192933 #> sample estimates: #> mean of x #> 4 #># Example 9.8 from PASWR