as i have stated in another forum ... there exists a need (in my view) to
do some revamping of our typical 2 by 2 table that we use to layout the
matrix of errors and correct decisions in hypothesis testing ... but that
is another story
however, i think that we definitely need some standardization and revamping
when it comes to using terms like 1 and 2 tailed tests ...
first, there is the issue of the null hypothesis ... and how our research
hypothesis relates to the null ... and here, i would like to standardized
the terminology as "directionality" ...
thus, if the null (happened to be) is that mu = 50 ... and your research
prediction is that the new method should be better than the old method
(which yields 50) ... then your research hypothesis is a DIRECTIONAL ONE
... new method BETTER than old method .... if you think that the new method
will produce DIFFERENT results than the old ... then it is a NON
directional research hypothesis
while there are various ways to frame the null ... and also to frame the
research hypothesis, the general rule should be: use some variation of the
term "direction" when referring to your predictions AS THEY RELATE TO THE
NULL HYPOTHESIS
do NOT use in any way shape or form, the language of 1 or 2 tailed ... in
connection with your predictions ... related to the null!
now, after the null is formed ... and some particular TEST STATISTIC is
found to be used to test that null hypothesis ... invariably we will be
faced with making a decision (the test statistic will really tell you what
to do here) as to which DISTRIBUTION WILL BE USED FOR FINDING CRITICAL
VALUES (t, F, normal, etc.) AND whether or not we should be using the upper
end of that distribution ONLY, the lower end of that distribution ONLY
(which would be rather strange), or BOTH upper and lower ends of that
distribution. that is ... the form of the test statistic says whether there
would be any meaning (with respect to providing evidence against the null)
by using CVs at one end or both ends of THAT distribution
thus, the test statistic you use to test the null will tell you where to be
looking ON the distribution of interest ... for example, if you use the
chis square TEST to test a relationship in a 2 by 2 table of frequency data
... then you use the UPPER END ... (lower end values make NO sense with
respect to the null)
however, if you were using a chi square test to test some null value about
the population variance ... the test statistic calls for having both a
lower and upper critical value ... thus, you are in BOTH ends of the
distribution ... that is, rejection at both ends MAKES sense with respect
to some specified null
some test statistics function by having you use ONE end of a statistical
distribution ... some function by having you use BOTH ends of the
statistical distribution
thus, i would suggest that we STANDARDIZE THE USE OF THE TERM ... 1 or 2
tailed ... to mean ONLY whether the test statistic has a natural functional
use of having you look up CVs at one or both ends ... on which you will
then make your decisions with respect to the null
so, if i have decided to use a chi square test on a 2 by 2 contingency
table ... then the test really wants me to use the upper end of the chi
square distribution ... and therefore it is quite appropriate to refer to
this as a ONE TAILED TEST ... not because of our research hypothesis in
relation to the null ... but merely based on the fact that the test
statistic "begs" you to only use the upper end (in this case)
however, this still raises the issue of what to call the situation where
(though some have claimed this not to be legitimate ... i happen not to
agree) the test statistic that is used quite naturally provides for clear
interpretation when we reject at EITHER end ... like in the simple t test
case ... where both - and + CVs are there ... and rejection of the null
either way has meaning ... BUT, the researcher has been able to argue
persuasively that ... only ONE end of this distribution ... or only one WAY
for the test statistic to travel in this instance ... is of legitimate
concern (now, that is up to HIM/HER to make this case ... the test
statistic certainly can't and obviously ... the distribution we use has NO
say in any of this)?
I STILL WOULD NOT CALL THIS A 1 TAILED TEST!
i would offer up terms like ... uni directional test ... using only one end
of the t distribution ... (for example)
to summarize:
the term (or some variation of it) "direction" should be used when
referring to the notion of how the research hypothesis or prediction ...
relates to the null
the term "tail" ... either 1 tailed or 2 tailed ... should ONLY be used in
connection with what the test statistic that you have decided to use ...
naturally asks you to do with respect to deciding on critical values ...
when we do a simple ANOVA ... this should be called a 1 tailed test ... no
matter what your research predictions are ... when we use chi square on a
contingency table ... it should be called a 1 tailed test ... no matter how
you think the direction of the relationship should go
when we use a studentized range statistic ... Q ... it is a 1 tailed test
... no matter which way your predictions say that the ordering of the means
should go
but, when we use a t test (for means for example) ... we should call this a
TWO TAILED test ... always ...
whether the researcher opts for ... funneling alpha all at one end ... or
subdividing it up in 1/2 ... partly at one end and partly at the other end
... that is entirely a different matter ... but should NOT be dubbed "1 or
2 tailed" ...
we need to be clear on the use of terms ... and, in this area ... there
CLEARLY is serious confusion about what 1 or 2 tailed tests MEAN ... at
least the myriad of "opines" on the list with respect to this suggest that
can't we fix this? if not for us ... for students who have to learn this
stuff?
_________________________________________________________
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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