Re: Simple Statistics Question

On Thu, 7 Apr 2005 10:28:11 -0500, "Ashok. R"
<ashokr@xxxxxxxxxxxxxxxxxx> wrote:

> Hello all,
>
> My message is a little verbose. But it is very simple. I urge you not to
> discard it purely because of its length. It is actually a very nice read :)
>
> An experiment to measure CUMULATIVE strains proceeds in four stages. Let us
> call them stage1, stage2, stage3, and stage 4. The INCREMENTAL strain
> (denoted by lambda) is measured experimentally at each stage. Different
> number of data points are used at each stage:
>
> lambda1 = incremental strain at stage 1 (N1 data points)
> lambda2 = incremental strain at stage 2 (N2 data points)
> lambda3 = incremental strain at stage 3 (N3 data points)
> lambda4 = incremental strain at stage 4 (N4 data points)
>
> Within each stage, we can calculate the mean and standard deviation for the
> lambdas. All this is simple and straightforward.
> mlambda1 = mean(lambda1) --->Computed from N1 data points
> mlambda2 = mean(lambda2) --->Computed from N2 data points
> mlambda3 = mean(lambda3) --->Computed from N3 data points
> mlambda4 = mean(lambda4) --->Computed from N4 data points
>
> std_lambda1 = ste(lambda1) --->Computed from N1 data points
> std_lambda2 = ste(lambda2) --->Computed from N2 data points
> std_lambda3 = ste(lambda3) --->Computed from N3 data points
> std_lambda4 = ste(lambda4) --->Computed from N4 data points
>
>
> Now comes the hard part: We need to compute the CUMULATIVE strain at each
> stage. This computed from the mean incremental strains at each stage:
>
> clambda1 = mlambda1
> clambda2 = mlambda2*mlambda1
> clambda3 = mlambda3*mlambda2*mlambda1
> clambda4 = mlambda4*mlambda3*mlambda2*mlambda1

I clearly don't understand what "strain" is, or how it is
measured. Does it exist (say) in a narrow range around 100%?
Is it centered (potentially) on zero?

Your formula seems to indicate a cumulative leveraging.
For numbers around zero, this multiplicative error
increases rapidly. Do you have data like that?

For numbers with *very* small SD relative
to the mean, the *variances* can be additive; see
my example below.


>
> Now I want to find out the standard error (not standard deviation) for each
> of these cumulative strains. Note: standard error = standard
> deviation/sqrt(N), where N is the number of data points. To do this, I need
> to find out the "net" standard deviations and the "net" number of data
> points used.

I don't comprehend a sampling framework that lets you
refer to any "standard error" across the experiment.
This *seems* to describe just one experiment.

If there are multiple experiments, the SE falls out naturally.

>
> Let us tackle the "net" standard deviation first:

[snip, confused stuff, which I have covered as much
as I can at this point.]
>
> The reason I am using standard errors is that if I am just adding the
> standard deviations from the individual stages, then the error bars will be
> really large in the cumulative strain plot and that does not look good in a
> published paper.
>

Sometimes a problem gives us huge error bars.
We have to live with it.

Variances are what we typically add; so the total SD
increases a *little* slower than from adding SDs.

But you can't add them unless you have a situation
where you are effectively adding the 'strains', too:
101% taken 4 times, multiplied, is approximately 104%,
just like 4 times 1% is 4%.

There are more complicated approximations for the
variances, if you are multiplying numbers around zero.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

Relevant Pages

  • Re: Effect size in meta-analysis
    ... If SEM is the Standard Error of a Mean, and each mean is based on ... would be if you were to use only the variances of the two groups whose ... differ substantially from the true variances of the four other groups. ...
    (sci.stat.edu)
  • Re: Effect size in meta-analysis
    ... If SEM is the Standard Error of a Mean, and each mean is based on ... would be if you were to use only the variances of the two groups whose ... differ substantially from the true variances of the four other groups. ...
    (sci.stat.edu)
  • Re: Effect size in meta-analysis
    ... If SEM is the Standard Error of a Mean, and each mean is based on ... would be if you were to use only the variances of the two groups whose ... differ substantially from the true variances of the four other groups. ...
    (sci.stat.edu)
  • Re: Bloody Johnny Foreigner
    ... standard error of the mean (which depends on the variance and the ... number of players) in order to be significant. ... your professional statistician, he will tell you exactly what I have ... several different population variances are involved", ...
    (uk.sport.cricket)