To: sbaker@odu.edu
From: Thomas Meyer
tmeyer@ph.vccs.edu
276 656-0283
Patrick Henry Community College
Subject: Statistics - w/ Dr.Spencer Baker - Homework Assignment #4, Ch 12 - Problem 12, page 307.
Date: March 26, 2004
Question:
Discuss the relative advantages and disadvantages of testing a directional vs. a
nondirectional null hypothesis.
Answer:
In a one-tail test (sometimes called a directional test) we reject the null hypothesis only if the result comes out in the direction we specify. One tailed-tests are therefore more often found in the studies under which variable relationships have already become well known, and one-tailed tests are less often found in the studies in which variables and their relationships are less well known. The ability to detect an actual treatment effect is higher in a one-tail test.
A two-tail test (sometimes called a non-directional test or hypothesis)
has half of its rejection region in each tail of the sampling distribution.
Hence the critical values are larger. By rejection region we mean that the
portion of the null hypothesis sampling distribution is so extreme that samples
this deviant would occur only alpha percent of the time if the null hypothesis
is true. Having a larger rejection critical value makes it more difficult
to reject the null hypothesis, and to demonstrate statistical significance
sufficient to warrant rejecting the null hypothesis.
The two-tail test also removes the uncertainty about whether the researcher
specified the direction in which the outcome was to go before conducting the
test. Whereas in a one-tail test, it is possible to wonder if such a
direction was in fact specified before the outcome ensued. Perhaps the
difficulty with using the two-tail test is that we are less likely to detect a
true treatment effect, and thereby more likely to fail to reject the null
hypothesis when it is in fact false (commit type II error).
There is some criticism of using either or both of these measures. Sample size effects the size of rejection areas. The avenues taken if statistical tests are unused include use of confidence interval, the reporting of effect sizes, and the use of Bayesian statistics.
filename: StatHW3Ch12Prob12page306TomMeyer.doc
Tom Meyer
Thomas Meyer