T-test with extreme difference in sample size

[Johnny Amora]

Is extreme difference in sample size (n1=140 and n2=40) a problem in the two independent sample t-test? Assume that normality and homoscedasticity assumptions are met.

  Thanks!

  J. Amora


Johnny T. Amora
  Statistician, Center for Learning and Performance Assessment
De La Salle-College of Saint Benilde
Manila, Philippines

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[Richard Ristow]

At 02:59 AM 5/30/2008, Johnny Amora wrote:

>Is extreme difference in sample size (n1=140 and n2=40) a problem in
>the two independent sample t-test? Assume that normality and
>homoscedasticity assumptions are met.

I invite the opinions of ANOVA experts here, but I very much doubt
there'd be a problem. T-test/ANOVA methods deal explicitly with
unbalanced designs; and though this imbalance is large, I wouldn't
call it extreme.

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[ViAnn Beadle]

I concur here. Researchers routinely use demographic variables with ratios
like 1 to 9 in T-tests.

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Richard Ristow
Sent: Monday, June 09, 2008 7:07 AM
To: [hidden email]
Subject: Re: T-test with extreme difference in sample size

At 02:59 AM 5/30/2008, Johnny Amora wrote:

>Is extreme difference in sample size (n1=140 and n2=40) a problem in
>the two independent sample t-test? Assume that normality and
>homoscedasticity assumptions are met.

I invite the opinions of ANOVA experts here, but I very much doubt
there'd be a problem. T-test/ANOVA methods deal explicitly with
unbalanced designs; and though this imbalance is large, I wouldn't
call it extreme.

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[Anthony Babinec]

I don't have the original post in front of me.

One issue is how small the smaller group is: Do
you have enough cases to get a good estimate of
the mean of that group?

Another issue is: Are the variances equal across groups?
If the variances are not equal across groups, then
the worse situation to be in is having the larger variance
associated with the smaller group. In this case,
the concern is that the test for equality of means is
"liberal," meaning that we false reject the null too often.

This and related issues is covered well in James Stevens'
Multivariate Statistics book.


Anthony Babinec

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[zstatman]

I agree that these tests are robust to sample size but do find the
differences a bit "lopsided." That said, the point that "Assume that
normality and homoscedasticity assumptions are met." makes it much more
palatable.

"1 to 9," good information

W


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
ViAnn Beadle
Sent: Monday, June 09, 2008 9:54 AM
To: [hidden email]
Subject: Re: T-test with extreme difference in sample size

I concur here. Researchers routinely use demographic variables with ratios
like 1 to 9 in T-tests.

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Richard Ristow
Sent: Monday, June 09, 2008 7:07 AM
To: [hidden email]
Subject: Re: T-test with extreme difference in sample size

At 02:59 AM 5/30/2008, Johnny Amora wrote:

>Is extreme difference in sample size (n1=140 and n2=40) a problem in
>the two independent sample t-test? Assume that normality and
>homoscedasticity assumptions are met.

I invite the opinions of ANOVA experts here, but I very much doubt
there'd be a problem. T-test/ANOVA methods deal explicitly with
unbalanced designs; and though this imbalance is large, I wouldn't
call it extreme.

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