Simulating non-Normal data

[Margaret MacDougall]

Hello

  Apologies for cross-posting

  Hello

  I would like to do some testing on the robustness of a procedure for Normal data when applied to non-Normal data. I would therefore be most interested to receive advice on generating multiple samples of non-Normal continuous data which do not necessarily follow a standard distribution (such as the non-Normal distribution) and which therefore cannot necessarily be 'Normalized' easily under a transformation.

  Recommendations on suitable software would be very much appreciated.

  A further stage in the above investigation will involve consideration of multiple samples of ordinal data and any relevant suggestions here would also be gratefully received.


  Best wishes

  Margaret



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[Art Kendall]

Since you posted on the SPSS discussion list, you could do it in SPSS.
There is example syntax below the sig block.
There are many kinds of non-normal data you can generate with SPSS.
type rv. in the search box under <help> <topics>

Save all your current work, then open a new instance of SPSS. Make sure
that you put warnings, etc. into the output file. <edit> <options>
<viewer>. Cut-and-paste then run the syntax.
Does this do what you want?  If not please restate your question in more
detail.
Perhaps post a small data set with variables "have" and "want".

Hope this helps.

Art
[hidden email]
Social Research Consultants
(Inside the Washington, DC beltway.)




new file.
generate random integers from 1 to 25.
INPUT PROGRAM.
LOOP id=1 TO 30000.
COMPUTE vbx = rv.uniform(.5,25.5).
COMPUTE IVBX = rnd(vbx).
END CASE.
END LOOP.
END FILE.
END INPUT PROGRAM.
FORMATS id (F3.0) vbx (f7.4) IVBX(F2).
FREQUENCIES VARS= IVBX.


Margaret MacDougall wrote:

> Hello
>
>   Apologies for cross-posting
>
>   Hello
>
>   I would like to do some testing on the robustness of a procedure for Normal data when applied to non-Normal data. I would therefore be most interested to receive advice on generating multiple samples of non-Normal continuous data which do not necessarily follow a standard distribution (such as the non-Normal distribution) and which therefore cannot necessarily be 'Normalized' easily under a transformation.
>
>   Recommendations on suitable software would be very much appreciated.
>
>   A further stage in the above investigation will involve consideration of multiple samples of ordinal data and any relevant suggestions here would also be gratefully received.
>
>
>   Best wishes
>
>   Margaret
>
>
>
> ---------------------------------
>  New Yahoo! Mail is the ultimate force in competitive emailing. Find out more at the Yahoo! Mail Championships. Plus: play games and win prizes.
>
>
>

[statisticsdoc]

Would creating a bimodal distribution suit your purposes?  This can be
fairly easily done by generating two normal distributions with different
means and adding the results.

HTH,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Margaret MacDougall
Sent: Saturday, March 10, 2007 8:05 AM
To: [hidden email]
Subject: Simulating non-Normal data


Hello

  Apologies for cross-posting

  Hello

  I would like to do some testing on the robustness of a procedure for
Normal data when applied to non-Normal data. I would therefore be most
interested to receive advice on generating multiple samples of non-Normal
continuous data which do not necessarily follow a standard distribution
(such as the non-Normal distribution) and which therefore cannot necessarily
be 'Normalized' easily under a transformation.

  Recommendations on suitable software would be very much appreciated.

  A further stage in the above investigation will involve consideration of
multiple samples of ordinal data and any relevant suggestions here would
also be gratefully received.


  Best wishes

  Margaret



---------------------------------
 New Yahoo! Mail is the ultimate force in competitive emailing. Find out
more at the Yahoo! Mail Championships. Plus: play games and win prizes.

[Snider-Lotz, Tom]

More generally, you can create all sorts of non-normal distributions by adding together several normal distributions with different means and SDs.

 

 

___________________________________

Thomas G. Snider-Lotz, Ph.D.

Principal Scientist

 

PreVisor

1805 Old Alabama Road

Suite 150

Roswell, GA 30076

Ph:     678-832-0555

Ph:     800-281-9713 x555

Fax:    [phone]

 

http://www.previsor.com

[hidden email]

---

From: SPSSX(r) Discussion on behalf of Statisticsdoc
Sent: Sat 10-Mar-07 10:08 PM
To: [hidden email]
Subject: Re: Simulating non-Normal data

Would creating a bimodal distribution suit your purposes?  This can be
fairly easily done by generating two normal distributions with different
means and adding the results.

HTH,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [[hidden email]]On Behalf Of
Margaret MacDougall
Sent: Saturday, March 10, 2007 8:05 AM
To: [hidden email]
Subject: Simulating non-Normal data


Hello

  Apologies for cross-posting

  Hello

  I would like to do some testing on the robustness of a procedure for
Normal data when applied to non-Normal data. I would therefore be most
interested to receive advice on generating multiple samples of non-Normal
continuous data which do not necessarily follow a standard distribution
(such as the non-Normal distribution) and which therefore cannot necessarily
be 'Normalized' easily under a transformation.

  Recommendations on suitable software would be very much appreciated.

  A further stage in the above investigation will involve consideration of
multiple samples of ordinal data and any relevant suggestions here would
also be gratefully received.


  Best wishes

  Margaret



---------------------------------
 New Yahoo! Mail is the ultimate force in competitive emailing. Find out
more at the Yahoo! Mail Championships. Plus: play games and win prizes.

[Richard Ristow]

At 10:05 AM 3/10/2007, Margaret MacDougall wrote:

>   I would like to do some testing on the robustness of a procedure
> for Normal data when applied to non-Normal data. I would therefore be
> most interested to receive advice on generating multiple samples of
> non-Normal continuous data which do not necessarily follow a standard
> distribution (such as the non-Normal distribution) and which
> therefore cannot necessarily be 'Normalized' easily under a
> transformation.
>
>   Recommendations on suitable software would be very much
> appreciated.

You've heard that SPSS random-variable functions can do anything you're
likely to need.

To add: asking for "non-Normal continuous data" is like asking for
"places that aren't in Rhode Island." It leaves a pretty broad field.
You want to think what deviations from normality are most illuminating.

It's pretty well accepted, I think, that linear estimation methods -
regression, ANOVA, GLM - are robust against many deviations from
normality. (Remember, here, that it's the error terms, not the
variables, that need to be normally distributed.) An exception, a
deviation that isn't handled well, is long 'tails' - probability of
large residuals, well in excess of those for the normal distribution.
Unfortunately, it's also a fairly common deviation.

One source of a long-tailed distribution is to superimpose two normal
distributions one with a small standard deviation and drawn from with
high probability; the other with a much larger standard deviation (try
ten-fold), drawn from with low probability (single-digit percents, I
think).

The other interesting non-normality I think of offhand is skewed
distributions, where the mean is very different from the median. You
can use exponential for that; or a method showing this yet more
drastically, like the superposition of two exponentials with very
different means.

-Good luck and good wishes,
  Richard

[Margaret MacDougall]

Dear Stephen

  Thank you for your welcome message. My particular interest is in simulating data for continuous scores provided by sets of 2, 3, 4, ... raters.

  I understand that Monte Carlo simulation of experimental data may be the way ahead but I don't know where to start here. Any suggestions on this and the above would be most welcome. (I don't wish to use explicit functions to generate the data if possible but rather, to simulate more realistic experimental data.

  Many thanks

  Best wishes

  Margaret

Statisticsdoc <[hidden email]> wrote:
  Would creating a bimodal distribution suit your purposes? This can be
fairly easily done by generating two normal distributions with different
means and adding the results.

HTH,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Margaret MacDougall
Sent: Saturday, March 10, 2007 8:05 AM
To: [hidden email]
Subject: Simulating non-Normal data


Hello

Apologies for cross-posting

Hello

I would like to do some testing on the robustness of a procedure for
Normal data when applied to non-Normal data. I would therefore be most
interested to receive advice on generating multiple samples of non-Normal
continuous data which do not necessarily follow a standard distribution
(such as the non-Normal distribution) and which therefore cannot necessarily
be 'Normalized' easily under a transformation.

Recommendations on suitable software would be very much appreciated.

A further stage in the above investigation will involve consideration of
multiple samples of ordinal data and any relevant suggestions here would
also be gratefully received.


Best wishes

Margaret



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