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# st: Re: very small sample comarsion

 From ajjee To statalist@hsphsun2.harvard.edu Subject st: Re: very small sample comarsion Date Sat, 26 Feb 2011 05:51:08 -0800 (PST)

```Thanks Mr.Ronan for reply

I've panel data of near 50 firms for 15 years. I want to anlyse the
performance of CEO of each firm. Each CEO has 3 or 5 years in office. So I
have many indicators from the company's balance sheet and I want to check
improvement/distortion in these indicators before and after a new CEO comes.
Suppose I want to analsye capital to assets ratio (CAR), for this purpose I
computed 3/5 year average of CAR and then compare these averages before and
after the new CEO appointment. But it is very crude measure to evaluate the
performance.  About the independence of the samples, the firms are
independent, of course, but within firm, sample are not independent.

ajjee

---------- Forwarded message ----------
From: Ronan Conroy <rconroy@rcsi.ie>
Date: 26 February 2011 12:55
Subject: Re: st: very small sample comarsion
To: "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>

On 26 Feb 2011, at 09:33, ajjee wrote:

> Dear All
>
> I have many samples of very small samplesize (n=5 and some times n=3) and
> I
> want to compare the the sample means of two samples. But I don't think
> I'll
> be able to apply t-test for these sample of very small size. In this
> situation, which methods I should use?. Thanks in advance.

The problem here is that your statistical power is almost nil, and only
massive difference between the samples will be significant – and if this is
the case, commonsense would have told you that they were different without
the need to collect data.

Small samples generally contain an absence of evidence. The trouble is that
many people cannot tell the difference between an absence of evidence and
evidence of absence.

One note of optimism: if you have many small samples, can you tell us if
these samples are completely independent, or whether they have some
relationship. It may be possible to gain power by combining.

Ronán Conroy
rconroy@rcsi.ie
Associate Professor
Division of Population Health Sciences
Royal College of Surgeons in Ireland
Beaux Lane House
Dublin 2

ajjee wrote:
>
>
> Dear All
>
> I have many samples of very small samplesize (n=5 and some times n=3) and
> I want to compare the the sample means of two samples. But I don't think
> I'll be able to apply t-test for these sample of very small size. In this
> situation, which methods I should use?. Thanks in advance.
>
> Regards,
>
> ajjee
>

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