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.
