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.

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
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.- 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.

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.

```
tsum.test(mean.x=5.6, s.x=2.1, n.x=16, mu=4.9, alternative="greater")
#> Warning: argument 'var.equal' ignored for one-sample test.
#>
#> One-sample t-Test
#>
#> data: Summarized x
#> t = 1.3333, df = 15, p-value = 0.1012
#> alternative hypothesis: true mean is greater than 4.9
#> 95 percent confidence interval:
#> 4.679649 NA
#> sample estimates:
#> mean of x
#> 5.6
#>
# 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)
#> Warning: argument 'var.equal' ignored for one-sample test.
#>
#> One-sample t-Test
#>
#> data: Summarized x
#> t = -0.82396, df = 11, p-value = 0.4275
#> alternative hypothesis: true mean is not equal to 0
#> 95 percent confidence interval:
#> -0.9214139 0.4194488
#> sample estimates:
#> mean of x
#> -0.2509825
#>
# 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)
#>
#> One Sample t-test
#>
#> data: x
#> t = -0.82396, df = 11, p-value = 0.4275
#> alternative hypothesis: true mean is not equal to 0
#> 95 percent confidence interval:
#> -0.9214139 0.4194488
#> sample estimates:
#> mean of x
#> -0.2509825
#>
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)
#>
#> Welch Modified Two-Sample t-Test
#>
#> data: Summarized x and y
#> t = -0.85278, df = 11.303, p-value = 0.4115
#> alternative hypothesis: true difference in means is not equal to 2
#> 95 percent confidence interval:
#> 1.127160 2.384203
#> sample estimates:
#> mean of x mean of y
#> 7.018182 5.262500
#>
# 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)
#>
#> Welch Two Sample t-test
#>
#> data: x and y
#> t = 6.1281, df = 11.303, p-value = 6.617e-05
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#> 1.127160 2.384203
#> sample estimates:
#> mean of x mean of y
#> 7.018182 5.262500
#>
tsum.test(mean(x), s.x=sd(x), n.x=11, mean(y), s.y=sd(y), n.y=8, conf.level=0.90)
#>
#> Welch Modified Two-Sample t-Test
#>
#> data: Summarized x and y
#> t = 6.1281, df = 11.303, p-value = 6.617e-05
#> alternative hypothesis: true difference in means is not equal to 0
#> 90 percent confidence interval:
#> 1.242424 2.268940
#> sample estimates:
#> mean of x mean of y
#> 7.018182 5.262500
#>
# 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)
#>
#> Welch Two Sample t-test
#>
#> data: x and y
#> t = 6.1281, df = 11.303, p-value = 6.617e-05
#> alternative hypothesis: true difference in means is not equal to 0
#> 90 percent confidence interval:
#> 1.242424 2.268940
#> sample estimates:
#> mean of x mean of y
#> 7.018182 5.262500
#>
```