[R] small sample techniques

Nair, Murlidharan T mnair at iusb.edu
Thu Aug 9 18:18:47 CEST 2007

```Thanks, that discussion was helpful. Well, I have another question
I am comparing two proportions for its deviation from the hypothesized
difference of zero. My manually calculated z ratio is 1.94.
But, when I calculate it using prop.test, it uses Pearson's chi-squared
test and the X-squared value that it gives it 0.74. Is there a function
in R where I can calculate the z ratio? Which is

('p1-'p2)-(p1-p2)
Z= ----------------
S
('p1-'p2)

Where S is the standard error estimate of the difference between two
independent proportions

Dummy example
This is how I use it
prop.test(c(30,23),c(300,300))

Cheers../Murli

-----Original Message-----
From: Moshe Olshansky [mailto:m_olshansky at yahoo.com]
Sent: Thursday, August 09, 2007 12:01 AM
To: Rolf Turner; r-help at stat.math.ethz.ch
Cc: Nair, Murlidharan T; Moshe Olshansky
Subject: Re: [R] small sample techniques

Well, this an explanation of what is done in the
paired t-test (and why the number of df is as it is).
I was too lazy to write all this.
It is nice that some list members are less lazy!

--- Rolf Turner <r.turner at auckland.ac.nz> wrote:

>
> On 9/08/2007, at 2:57 PM, Moshe Olshansky wrote:
>
> > As Thomas Lumley noted, there exist several
> versions
> > of t-test.
>
> 	<snip>
>
> > If you use t3 <- t.test(x,y,paired=TRUE) then
> equal
> > sample sizes are assumed and the number of degrees
> of
> > freedom is 4 (5-1).
>
> 	This is seriously misleading.  The assumption is
> not that the sample
> sizes
> 	are equal, but rather that there is ***just one
> sample***, namely
> the sample of differences.
>
> 	More explicitly the assumptions are that
>
> 		x_i - y_i
>
> 	are i.i.d. Gaussian with mean mu and variance
> sigma^2.
>
> 	One is trying to conduct inference about mu, of
> course.
>
> 	It should also be noted that it is a crucial
> assumption for the
> ``non-paired''
> 	t-test that the two samples be ***independent*** of
> each other, as
> well as
> 	being Gaussian.
>
> 	None of this is however germane to Nair's original
> question; it is
> clear
> 	that he is interested in a two-independent-sample
> t-test.
>
> 				cheers,
>
> 					Rolf Turner
>
>
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