Dummy-coded predictor in linear regression with unequal group sizes

[Tanja Gabriele Baudson]

Hi all,

I am conducting a multiple linear regression using a dummy-coded
predictor. However, the two groups (first language German vs. not
German) are very different in size (non-native speakers about 10%).
What consequences does this have on the interpretability of a
nonsignificant effect?

Thanks for your help.

Regards
Tanya
--
Tanja Gabriele Baudson
Universität Trier
FB I Psychologie
Hochbegabtenforschung und -förderung
54286 Trier
Fon 0651/201-4558
Fax [phone]
Email [hidden email]
Web http://www.uni-trier.de/index.php?id=9492

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[Swank, Paul R]

It will reduce the power of you significance test. For example, with a simple t test and a total sample size of 94, the power to detect a .5 sd effect size is .626 when the group sizes are 20 vs 74 but .776 when they are 47 vs 47.

Dr. Paul R. Swank,
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center-Houston


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Tanja Gabriele Baudson
Sent: Wednesday, May 04, 2011 11:37 AM
To: [hidden email]
Subject: Dummy-coded predictor in linear regression with unequal group sizes

Hi all,

I am conducting a multiple linear regression using a dummy-coded
predictor. However, the two groups (first language German vs. not
German) are very different in size (non-native speakers about 10%).
What consequences does this have on the interpretability of a
nonsignificant effect?

Thanks for your help.

Regards
Tanya
--
Tanja Gabriele Baudson
Universität Trier
FB I Psychologie
Hochbegabtenforschung und -förderung
54286 Trier
Fon 0651/201-4558
Fax [phone]
Email [hidden email]
Web http://www.uni-trier.de/index.php?id=9492

=====================
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[Rich Ulrich]

In particular, the "effective Ns" for a two group comparison
can be computed as the reciprocal-mean:  The reciprocal of
the average of the reciprocals.

For 10 vs 90 (deriving from the original Question), N=200,
this says that a comparison has the same power as comparing
two groups of 20 -

  Reciprocals are .1 and .011; average of them is .055;
  reciprocal of that is about 20.  Effectively, two groups of 20.
--
Rich Ulrich

----------------------------------------
> Date: Wed, 4 May 2011 12:48:04 -0500
> From: [hidden email]
> Subject: Re: Dummy-coded predictor in linear regression with unequal group sizes
> To: [hidden email]
>
> It will reduce the power of you significance test. For example, with a simple t test and a total sample size of 94, the power to detect a .5 sd effect size is .626 when the group sizes are 20 vs 74 but .776 when they are 47 vs 47.
>


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[Swank, Paul R]

It would be 2/(1/20 + 1/180) = 36 per group. I verified that by actually calculating the power and by simulation.

Dr. Paul R. Swank,
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center-Houston


-----Original Message-----
From: Rich Ulrich [mailto:[hidden email]]
Sent: Wednesday, May 04, 2011 1:59 PM
To: Swank, Paul R; [hidden email]
Subject: RE: Dummy-coded predictor in linear regression with unequal group sizes


In particular, the "effective Ns" for a two group comparison
can be computed as the reciprocal-mean:  The reciprocal of
the average of the reciprocals.

For 10 vs 90 (deriving from the original Question), N=200,
this says that a comparison has the same power as comparing
two groups of 20 -

  Reciprocals are .1 and .011; average of them is .055;
  reciprocal of that is about 20.  Effectively, two groups of 20.
--
Rich Ulrich

----------------------------------------
> Date: Wed, 4 May 2011 12:48:04 -0500
> From: [hidden email]
> Subject: Re: Dummy-coded predictor in linear regression with unequal group sizes
> To: [hidden email]
>
> It will reduce the power of you significance test. For example, with a simple t test and a total sample size of 94, the power to detect a .5 sd effect size is .626 when the group sizes are 20 vs 74 but .776 when they are 47 vs 47.
>


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