Please

Hope I will be able to help

Regards

Sugata Adhikari

Indian Statistical Institute

Kolkata

India

>From: Bill Gibson <[log in to unmask]>

>Reply-To: Concerned with the initial learning and teaching of statistics <[log in to unmask]>

>Subject: t for 2

>Date: Mon, 8 Oct 2001 19:09:10 +0100

>I am puzzled by something which seems to crop up consistently in biology

>textbooks for A-level students, and therefore in the teaching of my biology

>colleagues.

>When using fairly large samples (e.g. about 50 in each) they always seem to

>use a version of the two-sample t-test which I don't recognise.

>The formula which they use does not involve the pooled estimate of the

>assumed (or tested by an F-test) common variance. Instead, it uses the sum

>of the squares of the estimates of the separate standard errors. It seems to

>be assumed that Normal distributions are the appropriate models for the two

>populations. The degrees of freedom is what I expect: the sum of the two

>sample sizes minus two.

>I would expect them to use a z-test, based on the Central Limit Theorem ...

>or a Mann-Whitney test, or the Normal approximation to it.

>Having read a book last Easter which said that the t-test coped well with

>deviations from a Normal model, I am less anti the t-tests than I was

>previously! The same book mentioned the problems in testing for a common

>variance, and therefore dismissed the two sample t-test, with which I am

>familiar, as being almost useless.

>I think of a t-distribution as a N(0,1) divided by the root of (a

>chi-squared

>distribution divided by its degrees of freedom) ... so I don't see how the

>formula used by the biologists results in a t-distribution.

>Would someone please explain, in simple terms, what is going on here?

>Thanks in advance.

>Bill