[R] small sample techniques

[Greg Snow]

30 is not 30% of 300 (it is 10%), so your prop.test below is testing
something different from your hand calculations.  Try:

> prop.test(c(.30,.23)*300,c(300,300), correct=FALSE)

        2-sample test for equality of proportions without continuity
        correction

data:  c(0.3, 0.23) * 300 out of c(300, 300) 
X-squared = 3.7736, df = 1, p-value = 0.05207
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.000404278  0.140404278 
sample estimates:
prop 1 prop 2 
  0.30   0.23 

> sqrt(3.7736)
[1] 1.942576

Notice that the square root of the X-squared value matches your hand
calculations (with rounding error).  This is true if Yates continuty
correction is not used (the correct=FALSE in the call to prop.test).

Hope this helps,

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at intermountainmail.org
(801) 408-8111
 
 

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Nair, 
> Murlidharan T
> Sent: Thursday, August 09, 2007 1:02 PM
> To: Nordlund, Dan (DSHS/RDA); r-help at stat.math.ethz.ch
> Subject: Re: [R] small sample techniques
> 
> n=300
> 30% taking A relief from pain
> 23% taking B relief from pain
> Question; If there is no difference are we likely to get a 7% 
> difference?
> 
> Hypothesis
> H0: p1-p2=0
> H1: p1-p2!=0 (not equal to)
> 
> 1>Weighed average of two sample proportion
>     300(0.30)+300(0.23)
>     ------------------- = 0.265
>       300+300
> 2>Std Error estimate of the difference between two independent 
> 2>proportions
>       sqrt((0.265 *0.735)*((1/300)+(1/300))) = 0.03603
> 
> 3>Evaluation of the difference between sample proportion as a 
> deviation 
> 3>from the hypothesized difference of zero
>          ((0.30-0.23)-(0))/0.03603 = 1.94
> 
> 
> z did not approach 1.96 hence H0 is not rejected. 
> 
> This is what I was trying to do using prop.test. 
> 
> prop.test(c(30,23),c(300,300)) 
> 
> What function should I use? 
> 
> 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch on behalf of Nordlund, 
> Dan (DSHS/RDA)
> Sent: Thu 8/9/2007 1:26 PM
> To: r-help at stat.math.ethz.ch
> Subject: Re: [R] small sample techniques
>  
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch 
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Nair, 
> > Murlidharan T
> > Sent: Thursday, August 09, 2007 9:19 AM
> > To: Moshe Olshansky; Rolf Turner; r-help at stat.math.ethz.ch
> > Subject: Re: [R] small sample techniques
> > 
> > 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
> > 
> > 
> 
> Murli,
> 
> I think you need to recheck you computations.  You can run a 
> t-test on your data in a variety of ways.  Here is one: 
> 
> > x<-c(rep(1,30),rep(0,270))
> > y<-c(rep(1,23),rep(0,277))
> > t.test(x,y)
> 
>         Welch Two Sample t-test
> 
> data:  x and y
> t = 1.0062, df = 589.583, p-value = 0.3147 alternative 
> hypothesis: true difference in means is not equal to 0
> 95 percent confidence interval:
>  -0.02221086  0.06887752
> sample estimates:
>  mean of x  mean of y
> 0.10000000 0.07666667 
> 
> Hope this is helpful,
> 
> Dan
> 
> Daniel J. Nordlund
> Research and Data Analysis
> Washington State Department of Social and Health Services 
> Olympia, WA  98504-5204
> 
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> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
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> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>