Interesting point. Yes, if the Ss do something other than a random guess
the binomial model would be violated. The question then becomes what
would they do if they are uncertain? I suspect that they would fall back
on visual inspection...which piece appears to be different than the others
(less green pepper, more browned, etc) Such information is probably
relevant often enough that "guessing" would be well above 1/3.
Using blindfolded Ss will deal with that problem, and gets us back to
the question that Dennis is asking. I'm guessing that rather than going
through some sort of a systematic process (e.g. binary decision for the
first piece, progress to second piece only if first piece was judged
"same".....) Ss will in fact do something more like guessing. Only they
will condition their guesses such that if they picked slice A as different
on the previous trial they will first consider slices B and C on the
current trial (they will actually avoid selecting the same slice position
on sequential trials). Furthermore they will try to equalize the number
of position choices they make across the experiment so that they choose
each of A, B, and C three times and one of those a fourth time.
This leads to: trials are not independent.
The question remains, are the trials not independent in any way that
matters for the purposes of binomial probabilities? Off the top of my
head, I'm not sure. I am aware of, through secondary sources, studies
where any amount of guessing about random events (eg coin tosses) results
in a lower number of correct outcomes than simply making the same choice
every time....that is always choosing "tails" will be superior to making
choices between "heads" and "tails" on different trials.
This suggests that, at the very least, the correct value for p is less
than 1/3.
Michael
On Fri, 23 Feb 2001, dennis roberts wrote:
> a concern i have in this situation ... and why i posed the question is as
> follows
>
> since it is a taste test ... Ss will taste the pizzas ... so, the notion of
> just selecting ONE and saying it is different seems not a reasonble scenario
>
> so, what would a resonable guessing scenario be? one might be that ...
> after tasting and retasting ... the S says to himself/herself ... i just
> cannot make a choice ... i really don't know the difference ... BUT, he/she
> has to make a choice ... those are the rules ...
>
> so, if that were the case ... let's say that the strategy he/she adopts is
> to flip a mental coin ... if it is heads, call the first pizza SAME ...
> and, if tails ... call it DIFFERENT ...
>
> now, if the first turns up heads ... then there is another piece to do the
> mental flip for ... so the second piece gets the second flip ... assume it
> too is heads ... and is therefore called SAME ...
>
> then, there is NO random choice for the third ... it has to be DIFFERENT
> ... the third slice decision in this case is NOT independent of the second ...
>
> but, what if the first slice mental flip came up TAILS ... then for it, it
> is called the different one ... but automatically and out of the control of
> the S are the decisions for the other two ... they are both SAMES
>
> i claim that in this situation ... the decisions for all three are NOT
> independent decisions ... therefore, it does not satisfy one of the
> conditions for the binomial to be a correct model ...
> ========
> if the strategy were to simply flip a three sided coin ... with sides pizza
> slice 1, 2, or 3 ... whichever one the mental flip lands on ... the OTHER
> two are fixed choices and out of the control of the S ...
>
> some of the choices DEPEND on what has already transpired
>
>
>
> At 03:00 PM 2/23/01 -0600, Mike Granaas wrote:
> >On Fri, 23 Feb 2001, dennis roberts wrote:
> >
> ><snip some details of the experiment>
> >>
> >> but, what is really the p for success? q for failure?
> >>
> >> is this situation of n=10 ... really a true binomial case where p for
> >> success is 1/3 under the assumption that simple guessing were the way in
> >> which tasters made their decisions?
> >
> >It's late on friday so I could be missing something, but it seems
> >reasonable that p = 1/3 in this case. If the taster were to simply walk
> >into the room and point at the middle piece of pizza each trial they
> >should be right 1 time in 3. (Unless there is some experimental
> >manipulation that keeps the odd piece in one position more frequently than
> >would be expected...but I think you specified counterbalancing in your
> >question.)
> >
> >>
> >> (as an aside, what would it mean for tasters in this situation to be making
> >> their decisions purely based on chance?)
> >
> >I would interpret it as meaning that the tasters couldn't tell the two
> >pizza brands apart. They did no better than someone who didn't taste the
> >pizza and so were unable to discriminate between to two brands. The
> >obivious explanations are that the pizza brands really are the same in all
> >ways that matter for taste discrimination, or the tasters were not very
> >good at the task.
> >
> >Michael
> >
> >>
> >> _________________________________________________________
> >> dennis roberts, educational psychology, penn state university
> >> 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
> >> http://roberts.ed.psu.edu/users/droberts/drober~1.htm
> >>
> >>
> >>
> >> =================================================================
> >> Instructions for joining and leaving this list and remarks about
> >> the problem of INAPPROPRIATE MESSAGES are available at
> >> http://jse.stat.ncsu.edu/
> >> =================================================================
> >>
> >
> >*******************************************************************
> >Michael M. Granaas
> >Associate Professor [EMAIL PROTECTED]
> >Department of Psychology
> >University of South Dakota Phone: (605) 677-5295
> >Vermillion, SD 57069 FAX: (605) 677-6604
> >*******************************************************************
> >All views expressed are those of the author and do not necessarily
> >reflect those of the University of South Dakota, or the South
> >Dakota Board of Regents.
> >
> >
>
> ==============================================================
> dennis roberts, penn state university
> educational psychology, 8148632401
> http://roberts.ed.psu.edu/users/droberts/drober~1.htm
>
*******************************************************************
Michael M. Granaas
Associate Professor [EMAIL PROTECTED]
Department of Psychology
University of South Dakota Phone: (605) 677-5295
Vermillion, SD 57069 FAX: (605) 677-6604
*******************************************************************
All views expressed are those of the author and do not necessarily
reflect those of the University of South Dakota, or the South
Dakota Board of Regents.
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
