Re: comparison of two distribution curves
From: Richard Ulrich (Rich.Ulrich_at_comcast.net)
Date: 01/29/05
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Date: Sat, 29 Jan 2005 11:40:34 -0500
On 27 Jan 2005 09:02:06 -0800, "john" <jkalexan@gmail.com> wrote:
[snip, intro]
If you are making good use of Ray's advice, then
that may be enough. However, I have curiosity about the
definition of the problem and experiment.
> anyway - here is my problem (the first of a couple)
>
> I need to compare the response of cultured cells to two conditions -
> one the control and one the experimental. I replicated the experiment
> 6 times (at least).
>
> The results from a single "analysis" yields a table of X,Y values:
> the X value is from 0 to 179 degrees (in integers)
With X in degrees of a half-circle, and with the results
mentioned below, the question pops into my mind,
"Should X be modeled as the sine of X?"
> the y values are between 90 and 110 (all datasets were normalized to
> average to 100) - they are to 3 decimal places of accuracy.
> I am comfortable with the scientific reasons for processing my data up
> to this point.
>
> Here is the problem with a more detailed description of what i have.
>
> controls:
> the y value varies between 99 and 101 - theoretically it should be
> exactly 100 at every X value.
> by the way, the repeatability at each X is very good, stdev is 0.8.
> Q1: how can i say that the distribution is random. I guess what i
> really want to say is that there is no correlation between the y value
> and the x value ?
Or say, "no association." For statisticians, and sometimes
for other people, "correlation" implies the linear association
which is measured by the Pearson product-moment r -- and
you don't have much of a linear r in either set of data, even
though the Experimental group has a fine, quadratic relation.
>
> experiments:
> the y values look like a bell curve.
> at 0 degrees it is at 95, then it curves up to about 105 at 90 degrees,
> then curves back down to 95 at 179 degrees.
> the repeatability is also very good - for any given X value, the Y from
> each repeat is +/- 1 with a stdev of 0.8
> Q2: what i want to say is that this curve is different that the
> control. I also want to say that the Y value depends on the X. and
> that there is a mximal Y value at X=90. (it is really 87)
How many of these X values are there? ALL the integers
from 0 to 179?
>
> a kink:
> I actually have two other experimental conditions
> they are just like the one i described, but with a slightly sharper
> curve. experiment 2 gives data that starts at a lower y value (94)
> curves to a higher y value (106) then back down.
> experiment 3 is the same trend, lower again at 93, up to 107, then back
> to 93.
> Q3: I would like to say that exp2, 3, and 4 are also different. but
> saying that distinction is not as important as Q2.
>
>
> any ideas on what i can do???
>
> my thoughts:
> first, the pearson coefficient of the X,Y control pairs is basically 0.
> I think that tells me that Y is unrelated to X.
- linearly - Isn't r=0 for the Experimentals, too?
> second, i don't know how to analyze a curvilinear set like the
> experimental data.
The *easy* approach, if it can be applied, is to transform
it to the rational problem where the prediction is linear.
That's the essence of my suggestion. Does it make sense
to use a trig function?
In the transformed model, these several comparisons are
each done as a comparison of slopes -- testing the interaction
term which says that the two slopes are not equal.
> The max value of my experimental occurs at 87 degrees. a t-test with
> the same Y of the control is significant. but so is the 86 and 85 etc
> etc degrees. not quite sure how/what i can say about these.
> thanks for anyones help!
If you consider sin(X) as a possible substitute for X,
then there would be the implication that the theoretical
max is at 90 degrees. Is the upswing (0-90) equivalent
to the downswing (90-179)? -- That is a testable hypothesis.
-- Rich Ulrich, wpilib@pitt.edu http://www.pitt.edu/~wpilib/index.html
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