One and TwoTailed Tests
Prerequisites
Binomial
Distribution, Introduction
to Hypothesis Testing, Statistical
Significance
A probability computed considering differences
in only one direction such as the statistic is larger than the parameter
is called a onetailed probability. For example,
if a parameter is 0 and the statistic is 12, a onetailed probability (the
positive tail) would be the probability of a statistic being ≥ to 12. A
probability computed considering differences in both direction (statistic
either larger or smaller than the parameter) is called twotailed probability.
For example, if a parameter is 0 and the statistic is 12, a twotailed probability
would be the he probability of being either ≤ 12 or ≥12.
You should always decide whether you are going to
use a onetailed or a twotailed probability before looking at
the data. Statistical tests that compute onetailed probabilities
are called onetailed tests; those that
compute twotailed probabilities are called twotailed
tests. Twotailed tests are much more common
than onetailed tests in scientific research because an outcome
signifying that something other than chance is operating is usually
worth noting. Onetailed tests are appropriate when it is not
important to distinguish between no effect and an effect in the
unexpected direction. For example, consider an experiment designed
to test the efficacy of treatment for the common cold. The researcher
would only be interested in whether the treatment was better than
a placebo control. It would not be worth
distinguishing between the case in which the treatment was worse
than a placebo and the case in which it was the same because in
both cases the drug would be worthless.
Some have argued that a onetailed test is justified
whenever the researcher predicts the direction of an effect. The
problem with this argument is that if the effect comes out strongly
the in the nonpredicted direction, the researcher is not justified
in concluding that the effect is not zero. Since this is unrealistic,
onetailed tests are usually viewed skeptically if justified on
this basis alone.
