Date: Wed, 19 May 2010 12:36:31 -0400
Reply-To: Art@DrKendall.org
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: Art Kendall <Art@DrKendall.org>
Organization: Social Research Consultants
Subject: Re: Significant difference in "wrong" direction
In-Reply-To: <77B1A99F61865243991312E886F7B1F30B6B4249@FSWEXC01.fsw.leidenuniv.nl>
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To elaborate on this good advice.<br>
The null hypothesis is that one should stay with the {prevailing,
status quo, default} decision about a {theory, practice, policy}. In an
Anglo-American justice analog, the defendant null hypothesis is
presumed innocent {true, useful} unless there is sufficient evidence
otherwise. In some other justice systems failure to reach the criterion
would mean the charge is "not proven".<br>
<br>
The number of tails determines what is sufficient evidence.<br>
<br>
Remember statistical "significance" only tells us the a {difference,
relation} is statistically distinguishable from randomness. It is
necessary but not sufficient for a decsion to go with the alternative
{theory, practice, policy}.<br>
<br>
Art Kendall<br>
Social Research Consultants<br>
<br>
On 5/19/2010 10:32 AM, Ginkel, Joost van wrote:
<blockquote
cite="mid:77B1A99F61865243991312E886F7B1F30B6B4249@FSWEXC01.fsw.leidenuniv.nl"
type="cite">
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<div dir="ltr" align="left">
<div dir="ltr" align="left"><span class="245000314-19052010"><font
color="#0000ff" face="Arial" size="2">Dear Allan,</font></span></div>
<div dir="ltr" align="left"><span class="245000314-19052010"></span> </div>
<div dir="ltr" align="left"><span class="245000314-19052010"><font
color="#0000ff" face="Arial" size="2">Technically, the one-sided
p-value you get represents the probability that you find this mean
difference A - B or larger. Now if the mean of B is larger than A, you
get a negative difference and you want to know the probability that
that you find this negative difference or larger. If the results were
in the direction you would expect and SPSS would report a p-value of,
say, 0.04, the one-sided p-value would be 0.02. However, when the mean
difference goes in opposite direction, you have to look at the other
side of the distribution. Thus, in that case your p-value would become
1-0.02 = 0.98. This is probably not new to most statisticians.</font></span></div>
<div dir="ltr" align="left"><span class="245000314-19052010"><font
face="Arial"><font color="#0000ff"><font size="2">About the
philosophical part: what you should do depends entirely on the context,
I think. For example, if one medicine cures people more slowly than a
placebo although you expect it to cure people faster, then that would
be a reason to say: well, this medicine does more harm than good, so
the null-hypothesis should be rejected but not in the way you would
have wanted. Thus, say in the discussion that if you had done a
two-sided test or a one-sided test in the opposite direction, the
result would have been significant and that this implies that this
medicine is actually harmful. On the other hand, if you suspect a soda
manufacturer of fraude, for example, <span class="611423014-19052010">by
putting </span>less soda in each bottle on average than what the
bottle says, and now it turns out that there is actually more in each
bottle than what the bottle says, the manufacturer doesn't have to be
sued. So stick to your original one-sided alternative hypothesis that
the manufacturer puts less soda in the bottle.<span
class="611423014-19052010"> To summarize: I would look at the context.</span></font></font></font></span></div>
<div dir="ltr" align="left"><span class="245000314-19052010"></span> </div>
<div dir="ltr" align="left"><span class="245000314-19052010"><font
color="#0000ff" face="Arial" size="2">Best regards,</font></span></div>
<div dir="ltr" align="left"><span class="245000314-19052010"></span> </div>
<div dir="ltr" align="left"><span class="245000314-19052010"><font
color="#0000ff" face="Arial" size="2">Joost van Ginkel</font></span></div>
</div>
<div> </div>
<!-- Converted from text/rtf format -->
<p><span lang="en-us"><font face="Arial" size="2">Joost R.</font> <font
face="Arial" size="2">va</font><font face="Arial" size="2">n Ginkel,
PhD</font></span> <br>
<span lang="en-us"><font face="Arial" size="2">Leiden University</font></span>
<br>
<span lang="en-us"><font face="Arial" size="2">Faculty of Social and
Behavioural Sciences</font></span> <br>
<span lang="en-us"><font face="Arial" size="2">PO Box 9555</font></span>
<br>
<span lang="en-us"><font face="Arial" size="2">2300 RB Leiden</font></span>
<br>
<span lang="en-us"><font face="Arial" size="2">The Netherlands</font></span>
<br>
<span lang="en-us"><font face="Arial" size="2">Tel: +31-(0)71-527 3620</font></span>
<br>
<span lang="en-us"><font face="Arial" size="2">Fax: +31-(0)71-527 1721</font></span>
</p>
<div> </div>
<br>
<div class="OutlookMessageHeader" dir="ltr" align="left" lang="en-us">
<hr tabindex="-1"><font face="Tahoma" size="2"><b>From:</b> SPSSX(r)
Discussion [<a class="moz-txt-link-freetext" href="mailto:SPSSX-L@LISTSERV.UGA.EDU">mailto:SPSSX-L@LISTSERV.UGA.EDU</a>] <b>On Behalf Of </b>Allan
Lundy, PhD<br>
<b>Sent:</b> 19 May 2010 15:56<br>
<b>To:</b> <a class="moz-txt-link-abbreviated" href="mailto:SPSSX-L@LISTSERV.UGA.EDU">SPSSX-L@LISTSERV.UGA.EDU</a><br>
<b>Subject:</b> Significant difference in "wrong" direction<br>
</font><br>
</div>
<br>
Dear Listers,<br>
Like most statisticians, if I am predicting a result in a particular
direction (mean of Group A larger than that of Group B, for example), I
use a 1-tailed significance level. For example, in SPSS t-test output,
if it reports p= .080 in a 2-tailed test, I simply count that as p=
.040. However, from time to time, and again with a current client, I
get an embarrassing result: like the above but in the "wrong"
direction; that is, with the Group B mean larger. What does one do in
this case? Obviously the hypothesis was not supported, but it has
always seemed to me that such a result is meaningful -- not only is
there is no effect as predicted, but there is evidence for an effect in
the opposite direction. I have generally treated this conservatively
and reported this as a kind of super-rejection of the hypothesis. I
figure that if you are using a 1-tailed test, it should apply just as
much to harm you as help you. Of course, in a sense, this violates the
presumption behind the concept of the 1-tailed test -- that is, there
is not supposed to be any chance of getting a result in the far-left
tail of a 1-tailed distribution. How to handle this must be a profound
philosophical question in statistics, but I don't think I have ever
seen this addressed in writing. Anybody know of anything on this? Any
thoughts of your own?<br>
Thanks!<br>
Allan<br>
<br>
<br>
<x-sigsep>
<p><font color="#0000ff" face="Mistral" size="6">Allan Lundy, PhD<br>
</font><b><i>Research Consulting<br>
</i></b><a class="moz-txt-link-abbreviated" href="mailto:Allan.Lundy@comcast.net">Allan.Lundy@comcast.net</a><br>
<br>
<b>Business & Cell</b> (any time): 215-820-8100<br>
Home (8am-10pm, 7 days/week): 215-885-5313<br>
Address: 108 Cliff Terrace, Wyncote, PA 19095<br>
Visit my Web site at <a moz-do-not-send="true"
href="http://www.dissertationconsulting.net/">www.dissertationconsulting.net</a>
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