Hints and/or comments about Problem 24
- This problem is similar to Problems 11 and 12. If you didn't get
those completely right, you may want to check out the correct answers
here and try to understand
where you went wrong before.
- Be sure to report all p-values using 2 significant digits.
(E.g., 0.29, 0.040, and 0.000051 all have 2 significant digits.)
- For the ordinary F test, give the value of the test statistic
along with the p-value. For the studentized range test, you don't have
to show any work if you don't want to. For Welch's
F test,
to improve your partial credit in
the event that you get the wrong answer, give the unrounded degrees of
freedom value in addition to the integer value that you used. Also,
giving the values of the numerator and denominator of the test
statistic can help to show that you did part of the computations
correctly.
For the Alexander-Govern test, give the value of the test statistic
in addition to the p-value.
For the Welch-Sidák test, give the value of the t statistic, along with the
proper degrees of freedom, obtained from each pair of samples. Be sure
to obtain the df by rounding to the nearest integer. Then
use the tables to make a statement about the p-value. (E.g., with the
tables I gave you, the best you can do
is put p-value < 0.01,
0.01 < p-value < 0.05,
or p-value > 0.05.
- As a check of your work, you should have that the p-values based on
tests that adjust for heteroscedasticity are appreciably smaller than
the standard tests which are based on an assumption of equal variances.
In fact, the conservative procedure based on pairwise Welch tests and
Boole's inequality (which I didn't ask you to do for this problem)
yields a smaller p-value than the ordinary F test and the
studentized range test do.