Student's T-Test Based on Sample Statistics for Performing T-Tests From Summary Statistics

Performs one and two sample t-tests based on user supplied summary information instead of data as in t.test().

Usage

tTestA(
  mx,
  sx,
  nx,
  my = NULL,
  sy = NULL,
  ny = NULL,
  alternative = c("two.sided", "less", "greater"),
  mu = 0,
  paired = FALSE,
  var.equal = FALSE,
  conf.level = 0.95,
  ...
)

Arguments

mx: a single number representing the sample mean of x.
sx: a single number representing the sample standard deviation of x.
nx: a single number representing the sample size of x.
my: an optional single number representing the sample mean of y.
sy: an optional single number representing the sample standard deviation of y.
ny: an optional single number representing the sample size of y.
alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
mu: a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
paired: logical; paired tests are not supported. Use a one-sample test on the differences instead.
var.equal: a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.
conf.level: confidence level of the interval.
...: further arguments to be passed to or from methods.

Value

A list with class "htest" containing the following components:

statistic: the value of the t-statistic.
parameter: the degrees of freedom for the t-statistic.
p.value: the p-value for the test.
conf.int: a confidence interval for the mean appropriate to the specified alternative hypothesis.
estimate: the estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test.
null.value: the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test.
alternative: a character string describing the alternative hypothesis.
method: a character string indicating what type of t-test was performed.
data.name: a character string giving the name(s) of the data.

Details

alternative = "greater" is the alternative that x has a larger mean than y.

The option paired is not supported here, as the variance of the differences can't be calculated on the base of the variances of the two samples. However, for calculating the paired test we can simply supply the mean and standard deviation of the differences and use the one-sample test with mu = 0.

If var.equal is TRUE then the pooled estimate of the variance is used. By default, if var.equal is FALSE then the variance is estimated separately for both groups and the Welch modification to the degrees of freedom is used.

If the input data are effectively constant (compared to the larger of the two means) an error is generated.

Examples


## Classical example: Student's sleep data
mx <- 0.75
my <- 2.33
sx <- 1.789010
sy <- 2.002249
nx <- ny <- 10
tTestA(mx=mx, my=my, sx=sx, sy=sy, nx=nx, ny=ny)
#> 
#> 	Welch Two Sample t-test
#> 
#> data:  mx and my
#> t = -1.8608, df = 17.776, p-value = 0.07939
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#>  -3.3654835  0.2054835
#> sample estimates:
#> mean of x mean of y 
#>      0.75      2.33 
#> 

# compare to
with(sleep, t.test(extra[group == 1], extra[group == 2]))
#> 
#> 	Welch Two Sample t-test
#> 
#> data:  extra[group == 1] and extra[group == 2]
#> t = -1.8608, df = 17.776, p-value = 0.07939
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#>  -3.3654832  0.2054832
#> sample estimates:
#> mean of x mean of y 
#>      0.75      2.33 
#> 

# use the one sample test for the differences instead of paired=TRUE option
x <- with(sleep, extra[group == 1])
y <- with(sleep, extra[group == 2])

tTestA(mx=mean(x-y), sx=sd(x-y), nx=length(x-y))
#> 
#> 	One Sample t-test
#> 
#> data:  mean(x - y)
#> t = -4.0621, df = 9, p-value = 0.002833
#> alternative hypothesis: true mean is not equal to 0
#> 95 percent confidence interval:
#>  -2.4598858 -0.7001142
#> sample estimates:
#> mean of x 
#>     -1.58 
#> 

# compared to 
t.test(x, y, paired = TRUE)
#> 
#> 	Paired t-test
#> 
#> data:  x and y
#> t = -4.0621, df = 9, p-value = 0.002833
#> alternative hypothesis: true mean difference is not equal to 0
#> 95 percent confidence interval:
#>  -2.4598858 -0.7001142
#> sample estimates:
#> mean difference 
#>           -1.58 
#>