On Sun, 19 Dec 1999, Joe Ward wrote in part:
> (Reminder: when using a t-table, the p-values usually involve ONE-TAIL and
> when using the F-table, the p-values involve TWO-TAILS )
Re t: Well, that depends in part on how the table in question was set
up, and in part on the investigator's intent. _I_ always use
the t table for TWO-sided hypotheses, unless there's a good
reason to argue for a one-sided hypothesis.
And the t-tests in Minitab (e.g.) are by default TWO-sided;
the confidence intervals are two-sided and cannot be made
one-sided except by physically substituting (in a file editor)
"infinity" (or "- infinity") for one end of the interval reported.
Re F: Two-sided? Only when the hypothesis in question is of the kind
usually specified for an ANOVA, that certain means are equal.
In terms of the formal null hypothesis even of ANOVA, that one
variance estimate is equal to another, the test (and the p-value
returned by a statistical package) is ONE-sided. One doesn't
reject the null in ANOVA if the mean square between is
significantly less than the mean square within. (This is of
course equivalent to a two-sided test in the metric of the
subgroup means; but the F distribution was devised for the
comparison of variance estimates.)
> Example: The critical-value of t for probability of p = .05 at t(18)
> = 1.734;
> The critical-value of F for probability of p = .10 at
> F(1,18) = (1.734)^2 = 3.01
This sort of language is one of the reasons I really don't like to use
the term "critical value". It is much clearer, to my way of thinking,
to say that the 95th percentile of t(18) = 1.734. In terms of "critical
values", this is the critical value for a (two-sided) significance level
of 0.10 (or 10%, if you prefer); OR for a one-sided significance level
of 0.05. Similarly, the 90th percentile of F(1,18) = 1.734^2 = 3.01,
which is the critical value for a ONE(!)-sided test of the hypothesis
that E(MS between) < or = E(MS within) [against the one-sided alternative
that E(MSB) > E(MSW)].
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
