Anova with continuous variable
jun...@gmail.com
Lets take for example the following experiment (which is similar to
mine but with some other variable...)
Someone has to taste a meal is estimate how spicy it is.
It is always the same meal, but the quantity of salt and pepper
varies.
In some conditions there is no pepper, in other there is the same
amount of pepper and salt.
The quantity of salt (and pepper) varied between condition, let's say
3, 5, 7, 9, and 11 mg.
So to summarize here are the value of the independent variables:
Cond Salt Pepper
1 3 0
2 5 0
3 7 0
4 9 0
5 3 3
6 5 5
7 7 7
8 9 9
I have 6 estimations per conditions.
I have done an anova with two factors: 1] quantity of salt, 2]
presence of pepper.
Of course both factor are significant. The purpose of the experiment
is to test if the interaction is significant. We want to know if the
increase in the spice estimate with the introduction of pepper is
constant over the quantity of salt.
I have done the anova using Matlab (function anovan). I have to option
to set the quantity of the salt to a continuous variable. It seems
intuitive to me to use this option. But the problem is that I don't
know exactly of the algorithm used in that case.
I understand the algorithm of a typical ANOVA, but I can't find any
information on how to treat a continuous variable.
Thank you for your help.
Jem
Paige Miller
ANOVA with a continuous predictor is usually called Ordinary Least
Squares Regression, or just regression for short.
--
Paige Miller
paige\dot\miller \at\ kodak\dot\com
Paige Miller
Oh, if your goal is to estimate an interaction, the design you used
probably isn't much help. You might want to look at factorial
experiments.
Emmanuel Charpentier
You're barking up the wrong tree : what you're tring to do is not but
regression.
Indeed, both are special cases of general linear models. I suggest to
look that up in a good intermediate-level textbook.
I wouldn't use the general-purpose Matlab for this kind of problems, but
a stattistical package such as R.
Furthermore, there are some general (psychophysiological) reasons to
question the linearity of the relationships you're trying to discover. A
nonlinear regression might be more appropriate...
HTH
Emmanuel Charpentier
Bruce Weaver
I think you mean it is "nothing but regression", perhaps?
>
> Indeed, both are special cases of general linear models. I suggest to
> look that up in a good intermediate-level textbook.
>
> I wouldn't use the general-purpose Matlab for this kind of problems, but
> a stattistical package such as R.
>
> Furthermore, there are some general (psychophysiological) reasons to
> question the linearity of the relationships you're trying to discover. A
> nonlinear regression might be more appropriate...
>
> HTH
>
> Emmanuel Charpentier
Emmanuel, if you are referring to what has sometimes been called
"polynomial" regression (e.g., inclusion of both X and X^2 to model a
quadratic relationship between X and Y), that is still linear regression
in the terminology I am familiar with. I.e., it is linear in the
coefficients, and uses the same equations as when the functional
relationship is linear.
--
Bruce Weaver
bwe...@lakeheadu.ca
www.angelfire.com/wv/bwhomedir
"When all else fails, RTFM."
Emmanuel Charpentier
[ Snip... ]
>> You're barking up the wrong tree : what you're tring to do is not but
>> regression.
>
> I think you mean it is "nothing but regression", perhaps?
No : I meant "... not ANOVA but regression". Typo...
>>
>> Indeed, both are special cases of general linear models. I suggest to
>> look that up in a good intermediate-level textbook.
>>
>> I wouldn't use the general-purpose Matlab for this kind of problems, but
>> a stattistical package such as R.
>>
>> Furthermore, there are some general (psychophysiological) reasons to
>> question the linearity of the relationships you're trying to discover. A
>> nonlinear regression might be more appropriate...
>>
>> HTH
>>
>> Emmanuel Charpentier
>
>
> Emmanuel, if you are referring to what has sometimes been called
> "polynomial" regression (e.g., inclusion of both X and X^2 to model a
> quadratic relationship between X and Y), that is still linear regression
> in the terminology I am familiar with. I.e., it is linear in the
> coefficients, and uses the same equations as when the functional
> relationship is linear.
Nope. I was thinking about the fact that stimulus/response curve are
generally not linear. In the "useful" or "physiologic" range, they
appear to be logarithmic, but with thresholds effects, both for low
stimuli (sensitivy threshold) and high stimuli (receptor saturation),
which might be better modeled by sigmoïds, for example. And this is
*not* well modeled by polynoms (if you don't believe me, take the Taylor
expansion of f(x)=e^x/(1+e^x) around x=0, for example...).
But in real psychophysiology, things can be much more intricate... I'd
rather try to read the literature relevant to taste perception, build a
couple of "reasonable" models and try to assess them via non-linear
least squares and such...
Emmanuel Charpentier