One Sample T Tests
The R function t.test
(on-line
help) does t tests and confidence intervals.
The example done on the confidence intervals page also does a test, although the default test is not necessarily the one you want.
Other arguments to the t.test
function are mu
,
which specifies hypothesized value under H0 other
than zero, and alternative
, which allows for upper-tailed,
lower-tailed, or two-tailed tests (as can be seen from the example above,
the default is two-tailed).
Here are the one-tailed tests
Here is one with a different null hypothesis
The arguments mu
and alternative
are used
similarly for two-sample tests.
Power Calculations
Normal Reference Distribution
These are the examples done in the slides for the class (slides 186–194, deck 2).
does the upper-tailed test and
does the two-tailed test.
Comments
The R functions pnorm
and qnorm
(on-line
help) do the DF and inverse DF of the normal distribution.
The R keyword for
(on-line
help) indicates a loop. In this example, the first curve
command draws the first power curve for sample size n[1]
,
and the second curve
command draws the remaining power curves for sample sizes n[2]
,
through n[length(n)]
.
The R function curve
(on-line
help) draws curves. In the first argument x
is a free
variable ranging between the values of the from
and to
arguments.
The
(on-line
help for topic plotmath
) explains what
xlab = expression((theta - theta[0]) / tau)does.
Student T Reference Distribution
These are the examples done in the slides for the class (slides 195–201, deck 2).
does the upper-tailed test and
does the two-tailed test.
Comments
The R functions pt
and qt
(on-line
help) do the DF and inverse DF of the t distribution.