[tips] The Dress

[Rick Stevens]

Psychology addressing the pressing issues.

"Surveying more than 13,000 people — the largest published study of The
Dress to date — he finds that early risers tend to see the frock as gold
and white, whereas night owls are slightly more likely to see it as blue
and black."

https://www.buzzfeed.com/virginiahughes/science-of-the-dress?utm_term=.ou38j5D1G#.dr0re5bR3


Rick Stevens
School of Behavioral and Social Sciences
University of Louisiana at Monroe

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RE:[tips] Teaching stats and Critical Values Tables

[Mike Palij]

On: Sat, 8 Apr 2017 00:42:52 +, , Lenore Frigo wrote:

For those of you who teach lower-division introduction to
research methods (or have an opinion on what we SHOULD
be teaching at that level):

In teaching students how to interpret statistical results,
such as a t-test, do you think it's important to have them
find the critical value on a table and proceed from there,
or just start with a "print out" of the results that would
already include the actual p value?


Though not immediately obviously, the question you ask
turns out to be far more complex because of a variety of
factors.  I try to identify some of these in the points below:

(1)  The information that you have provicded does not make
clear whether you students understand the concept of a
sampling distribution of a statistics and why one is looking
to determine whether the value of an obtained statistic is
is consistent or not with the null hypothesis.  Presumably,
in the case of the t-test you are mostly concerned with
rejecting the null hypothesis (in contrast to situations where
you are doing a variation of goodnees of fit between, say,
some criterion value and your obtained value, for example
comparing the mean IQ of a sample to a value of 100
[the value of the population mean]).  If you teach the
goodness of fit chi-square for a frequency distribution,
the emphasis is on NOT rejecting the null (which might
claim that sample frequency distribution is consistent
with a normal distribution).

(2) There are phiilosophical (metaphysical?) issues involves
as well depending upon whether one considers oneself to
be either a Fisherian/Neofisherian when it comes to
statistical inference or one subscribes to the model promoted
by the Neyman-Pearson approach (which includes concepts
such as Type II errors, statistical power, and so on). As Gerd
Gigerenzer argued so long ago, most psychologist were taught
a mash-up of these two inference frameworks which has resulted
in neither being used corrested.  With respect to the use of a
table of "critical value" or probabilities (p-values), the position
that one subscribes partlyy determines what one does.
Consider the following situation:

(a) A researcher that take a Fisherian approach to statistical
testing will conduct their research and after the data is in,
analyze it to determine whether test results are either consistent
with the null hypothesis (e.g., p(obtain test value) > .05) or
inconsistent with it (i.e., p(obtained test value)  < .05). Here
a table or some other source of critical test values or the
probability of the of the obtained test rest if the null hypothesis
is true plays a critical role because one is in essence just
deciding whether the obtained value should lead one to reject
the null hypothesis or fail to reject it.  One might go on to do
some additional analyses but the most critical question that
one is interested in should have been answered.

(b) In the Neyman-Pearson approach, we need to distinguish
between whether one is an "a priorist" or a "post hoc" practioner.
The distinction between the two is illustrated in the following:

(i) The proper way to do a statistical analysis in the Neyman-Pearson
framework requires one to identify what population distributions
are involved in the null and alternative hypotheses.  In addition,
if one is going to conduct a two-sample between-subjects
experiment (NOTE: the tense implies that all this is done before
any data is collected), and one will use an independent groups
t-tests as the tool of analysis, there the following consideration
or decision one must make:

- What is the Type I Error rate that one will use? Typically,
we use alpha - .05 but, if we expect to be doing several test,
we may wish to use a Bonferroni correction so that the
overall Type I error rte is equal to .05 but this means that
the individual tests will use an alpha < .05 (examination of
a table of Bonferroni t-test values corrected for the number
of tests done will identify the relevant critical values but these
usually assume that one divides the Type I error equally
over each test, so, if one is doing 3 t-tests, the the per comparison
alpha will be .05/3 = 0.01667; however, a research can decide
to assign a Type I error rate = .02 to two tests and .01 to the
third test for whatever reason [researchers do the darnedest
things] but I have not seen any tables like this which means
that one has to get the critical values either through hand calculation
or some software program if one really is going to focus on the
value of the test statistic instead of its p-value)..

- What is the Effect Size (ES) that one is trying to detect?
The ES in the independent groups t-test situation represents the
standarding distance between the populations means of the
distributions specified in the alternative hypothesis.  This
difference, represented by delta in the population and d in the
sample, is required to figure out other aspects of the test but
it also represents what one 

RE: [tips] Teaching stats and Critical Values Tables

[Keefer, Robert P.]

I agree with all these comments.  One additional point; I always use the table 
to point out that as N approaches infinity, the t distribution approaches 
normality (since I’ve already hammered on z=1.96 for a two-tailed normal 
distribution cut off of .05).

bob k.

From: Michael Scoles [mailto:micha...@uca.edu]
Sent: Saturday, April 8, 2017 6:32 AM
To: Teaching in the Psychological Sciences (TIPS) 
Subject: Re: [tips] Teaching stats and Critical Values Tables

Looking at a table shows them that more conservative decisions require greater 
evidence, and that the reliability of that evidence is related to sample size 
(or degrees of freedom).


On Fri, Apr 7, 2017 at 10:07 PM, Jim Clark 
> wrote:
Hi

I second Stuart's process assuming prior familiarity with hypothesis testing. 
Understand the distribution. If preceded by normal distribution, generalize 
from that to distribution that is more spread out because SD is varying as well 
as numerator; also varies with df. Then use table to determine critical values 
with associated ps. Finally, p values from printout.

Jim

-Original Message-
From: Stuart McKelvie [mailto:smcke...@ubishops.ca]
Sent: 7-Apr-17 9:15 PM
To: Teaching in the Psychological Sciences (TIPS) 
>
Subject: RE:[tips] Teaching stats and Critical Values Tables

Dear Tipsters,

My response to Lenore's question is that they must learn to use the table, but 
that should only be the natural outcome of understanding the distribution of t 
and how it arises in repeated sampling.

So - understanding first, table second and printout third. But of course, after 
you understand, the printout is all you need.

Stuart


-Original Message-
From: Frigo, Lenore 
[mailto:lfr...@shastacollege.edu]
Sent: April-07-17 8:43 PM
To: Teaching in the Psychological Sciences (TIPS)
Subject: [tips] Teaching stats and Critical Values Tables

For those of you who teach lower-division introduction to research methods (or 
have an opinion on what we SHOULD be teaching at that level):

In teaching students how to interpret statistical results, such as a t-test, do 
you think it's important to have them find the critical value on a table and 
proceed from there, or just start with a "print out" of the results that would 
already include the actual p value?

Currently I have them work with the table, but it seems old-fashioned and 
unnecessarily cumbersome. On the other hand, using the table forces them to 
perhaps have a bit more conceptual understanding of what they are doing.

All input and opinions most welcome,
-Lenore

Lenore Frigo
lfr...@shastacollege.edu


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--
Michael T. Scoles, Ph.D.
Associate Professor of Psychology & Counseling
University of Central Arkansas
Conway, AR 72035
501-450-5418

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