small sample techniques

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small sample techniques

Nair, Murlidharan T
If my sample size is small is there a particular switch option that I need to use with t.test so that it calculates the t ratio correctly?

Here is a dummy example?

á =0.05

Mean pain reduction for A =27; B =31 and SD are SDA=9 SDB=12

drgA.p<-rnorm(5,27,9);

drgB.p<-rnorm(5,31,12)

t.test(drgA.p,drgB.p) # what do I need to give as additional parameter here?

 

I can do it manually but was looking for a switch option that I need to specify for  t.test.

 

Thanks ../Murli

 


        [[alternative HTML version deleted]]


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Re: small sample techniques

Moshe Olshansky-2
Hi Nair,

If the two populations are normal the t-test gives you
the exact result for whatever the sample size is (the
sample size will affect the number of degrees of
freedom).
When the populations are not normal and the sample
size is large it is still OK to use t-test (because of
the Central Limit Theorem) but this is not necessarily
true for the small sample size.
You could use simulation to find the relevant
probabilities.

--- "Nair, Murlidharan T" <[hidden email]> wrote:

> If my sample size is small is there a particular
> switch option that I need to use with t.test so that
> it calculates the t ratio correctly?
>
> Here is a dummy example?
>
> á =0.05
>
> Mean pain reduction for A =27; B =31 and SD are
> SDA=9 SDB=12
>
> drgA.p<-rnorm(5,27,9);
>
> drgB.p<-rnorm(5,31,12)
>
> t.test(drgA.p,drgB.p) # what do I need to give as
> additional parameter here?
>
>  
>
> I can do it manually but was looking for a switch
> option that I need to specify for  t.test.
>
>  
>
> Thanks ../Murli
>
>  
>
>
> [[alternative HTML version deleted]]
>
> > ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.
>

______________________________________________
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Re: small sample techniques

Nair, Murlidharan T
Indeed, I understand what you say. The df of freedom for the dummy example is n1+n2-2 = 8. But when I run the t.test I get it as 5.08, am I missing something?

-----Original Message-----
From: Moshe Olshansky [mailto:[hidden email]]
Sent: Tuesday, August 07, 2007 9:05 PM
To: Nair, Murlidharan T; [hidden email]
Subject: Re: [R] small sample techniques

Hi Nair,

If the two populations are normal the t-test gives you
the exact result for whatever the sample size is (the
sample size will affect the number of degrees of
freedom).
When the populations are not normal and the sample
size is large it is still OK to use t-test (because of
the Central Limit Theorem) but this is not necessarily
true for the small sample size.
You could use simulation to find the relevant
probabilities.

--- "Nair, Murlidharan T" <[hidden email]> wrote:

> If my sample size is small is there a particular
> switch option that I need to use with t.test so that
> it calculates the t ratio correctly?
>
> Here is a dummy example?
>
> á =0.05
>
> Mean pain reduction for A =27; B =31 and SD are
> SDA=9 SDB=12
>
> drgA.p<-rnorm(5,27,9);
>
> drgB.p<-rnorm(5,31,12)
>
> t.test(drgA.p,drgB.p) # what do I need to give as
> additional parameter here?
>
>  
>
> I can do it manually but was looking for a switch
> option that I need to specify for  t.test.
>
>  
>
> Thanks ../Murli
>
>  
>
>
> [[alternative HTML version deleted]]
>
> > ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.
>

______________________________________________
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Re: small sample techniques

Thomas Lumley
On Wed, 8 Aug 2007, Nair, Murlidharan T wrote:

> Indeed, I understand what you say. The df of freedom for the dummy example is n1+n2-2 = 8. But when I run the t.test I get it as 5.08, am I missing something?
>

Yes. You are probably looking for the version of the t.test that assumes equal variances (the original one), so you need var.equal=TRUE.

      -thomas


> -----Original Message-----
> From: Moshe Olshansky [mailto:[hidden email]]
> Sent: Tuesday, August 07, 2007 9:05 PM
> To: Nair, Murlidharan T; [hidden email]
> Subject: Re: [R] small sample techniques
>
> Hi Nair,
>
> If the two populations are normal the t-test gives you
> the exact result for whatever the sample size is (the
> sample size will affect the number of degrees of
> freedom).
> When the populations are not normal and the sample
> size is large it is still OK to use t-test (because of
> the Central Limit Theorem) but this is not necessarily
> true for the small sample size.
> You could use simulation to find the relevant
> probabilities.
>
> --- "Nair, Murlidharan T" <[hidden email]> wrote:
>
>> If my sample size is small is there a particular
>> switch option that I need to use with t.test so that
>> it calculates the t ratio correctly?
>>
>> Here is a dummy example?
>>
>> á =0.05
>>
>> Mean pain reduction for A =27; B =31 and SD are
>> SDA=9 SDB=12
>>
>> drgA.p<-rnorm(5,27,9);
>>
>> drgB.p<-rnorm(5,31,12)
>>
>> t.test(drgA.p,drgB.p) # what do I need to give as
>> additional parameter here?
>>
>>
>>
>> I can do it manually but was looking for a switch
>> option that I need to specify for  t.test.
>>
>>
>>
>> Thanks ../Murli
>>
>>
>>
>>
>> [[alternative HTML version deleted]]
>>
>>> ______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained,
>> reproducible code.
>>
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Thomas Lumley Assoc. Professor, Biostatistics
[hidden email] University of Washington, Seattle

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Re: small sample techniques

Tim Hesterberg
In reply to this post by Moshe Olshansky-2
About using t tests and confidence intervals for "large" samples -
"large" may need to be very large.
The old pre-computer-age rule of n >= 30 is inadequate.

For example, for an exponential distribution, the actual size
of a nominal 2.5% one-sided t-test is not accurate to within 10%
(i.e. between 2.25% & 2.75%) until n is around 5000.
The error (actual - nominal size) decreases very slowly, at the rate 1/sqrt(n).

In practice, real distributions may be even more skewed than
the exponential distribution, even though they appear less skewed,
if they have long tails.  In this case the sample size would need
to be even larger for t procedures to be reasonably accurate.

An alternative is to use bootstrapping.  Bootstrap procedures that
decrease at the rate 1/n include bootstrap t, BCa, and bootstrap
tilting.

Moshe Olshansky <[hidden email]> wrote:

>If the two populations are normal the t-test gives you
>the exact result for whatever the sample size is (the
>sample size will affect the number of degrees of
>freedom).
>When the populations are not normal and the sample
>size is large it is still OK to use t-test (because of
>the Central Limit Theorem) but this is not necessarily
>true for the small sample size.
>You could use simulation to find the relevant
>probabilities.
>...

========================================================
| Tim Hesterberg       Senior Research Scientist       |
| [hidden email]  Insightful Corp.                |
| (206)802-2319        1700 Westlake Ave. N, Suite 500 |
| (206)283-8691 (fax)  Seattle, WA 98109-3044, U.S.A.  |
|                      www.insightful.com/Hesterberg   |
========================================================
Short course - Bootstrap Methods and Permutation Tests
                Oct 10-11 San Francisco, 3-4 Oct UK.
http://www.insightful.com/services/training.asp

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Re: small sample techniques

Moshe Olshansky-2
In reply to this post by Nair, Murlidharan T
As Thomas Lumley noted, there exist several versions
of t-test.
If you use t1 <- t.test(x,y) then no assumption is
made of x and y having equal variance and of the two
sample sizes being equal and then an approximate
t-test is used with an approximate number of degrees
of freedom (and this is what you got).
If you use t2 <- t.test(x,y,var.equal=TRUE) then equal
variance is assumed and you get 8 degrees of freedom.
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).

--- "Nair, Murlidharan T" <[hidden email]> wrote:

> Indeed, I understand what you say. The df of freedom
> for the dummy example is n1+n2-2 = 8. But when I run
> the t.test I get it as 5.08, am I missing something?
>
>
> -----Original Message-----
> From: Moshe Olshansky [mailto:[hidden email]]
>
> Sent: Tuesday, August 07, 2007 9:05 PM
> To: Nair, Murlidharan T; [hidden email]
> Subject: Re: [R] small sample techniques
>
> Hi Nair,
>
> If the two populations are normal the t-test gives
> you
> the exact result for whatever the sample size is
> (the
> sample size will affect the number of degrees of
> freedom).
> When the populations are not normal and the sample
> size is large it is still OK to use t-test (because
> of
> the Central Limit Theorem) but this is not
> necessarily
> true for the small sample size.
> You could use simulation to find the relevant
> probabilities.
>
> --- "Nair, Murlidharan T" <[hidden email]> wrote:
>
> > If my sample size is small is there a particular
> > switch option that I need to use with t.test so
> that
> > it calculates the t ratio correctly?
> >
> > Here is a dummy example?
> >
> > á =0.05
> >
> > Mean pain reduction for A =27; B =31 and SD are
> > SDA=9 SDB=12
> >
> > drgA.p<-rnorm(5,27,9);
> >
> > drgB.p<-rnorm(5,31,12)
> >
> > t.test(drgA.p,drgB.p) # what do I need to give as
> > additional parameter here?
> >
> >  
> >
> > I can do it manually but was looking for a switch
> > option that I need to specify for  t.test.
> >
> >  
> >
> > Thanks ../Murli
> >
> >  
> >
> >
> > [[alternative HTML version deleted]]
> >
> > > ______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> > http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained,
> > reproducible code.
> >
>
>

______________________________________________
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Re: small sample techniques

Rolf Turner

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

######################################################################
Attention:\ This e-mail message is privileged and confidenti...{{dropped}}

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Re: small sample techniques

Moshe Olshansky-2
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 <[hidden email]> 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
>
>
######################################################################

> Attention:
> This e-mail message is privileged and confidential.
> If you are not the
> intended recipient please delete the message and
> notify the sender.
> Any views or opinions presented are solely those of
> the author.
>
> This e-mail has been scanned and cleared by
> MailMarshal
> www.marshalsoftware.com
>
######################################################################
>

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Re: small sample techniques

Nair, Murlidharan T
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:[hidden email]]
Sent: Thursday, August 09, 2007 12:01 AM
To: Rolf Turner; [hidden email]
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 <[hidden email]> 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
>
>
######################################################################

> Attention:
> This e-mail message is privileged and confidential.
> If you are not the
> intended recipient please delete the message and
> notify the sender.
> Any views or opinions presented are solely those of
> the author.
>
> This e-mail has been scanned and cleared by
> MailMarshal
> www.marshalsoftware.com
>
######################################################################
>

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Re: small sample techniques

Nordlund, Dan (DSHS/RDA)
> -----Original Message-----
> From: [hidden email]
> [mailto:[hidden email]] On Behalf Of Nair,
> Murlidharan T
> Sent: Thursday, August 09, 2007 9:19 AM
> To: Moshe Olshansky; Rolf Turner; [hidden email]
> 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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Re: small sample techniques

Nair, Murlidharan T
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 proportions
      sqrt((0.265 *0.735)*((1/300)+(1/300))) = 0.03603

3>Evaluation of the difference between sample proportion as a deviation 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: [hidden email] on behalf of Nordlund, Dan (DSHS/RDA)
Sent: Thu 8/9/2007 1:26 PM
To: [hidden email]
Subject: Re: [R] small sample techniques
 

> -----Original Message-----
> From: [hidden email]
> [mailto:[hidden email]] On Behalf Of Nair,
> Murlidharan T
> Sent: Thursday, August 09, 2007 9:19 AM
> To: Moshe Olshansky; Rolf Turner; [hidden email]
> 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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Re: small sample techniques

Nordlund, Dan (DSHS/RDA)
> -----Original Message-----
> From: [hidden email]
> [mailto:[hidden email]] On Behalf Of Nair,
> Murlidharan T
> Sent: Thursday, August 09, 2007 12:02 PM
> To: Nordlund, Dan (DSHS/RDA); [hidden email]
> 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 proportions
>       sqrt((0.265 *0.735)*((1/300)+(1/300))) = 0.03603
>
> 3>Evaluation of the difference between sample proportion as a
> deviation 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?
>
>

The proportion test above indicates that p1=0.1 and p2=0.07666667.  But in your t-test you specify p1=0.3 and p2=0.23.  Which is correct?  If p1=0.3 and p2=0.23, then use

prop.test(c(.30*300,.23*300),c(300,300))

Hope this is helpful,

Dan

Daniel J. Nordlund
Research and Data Analysis
Washington State Department of Social and Health Services
Olympia, WA  98504-5204

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
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Re: small sample techniques

Gregory Snow
In reply to this post by Nair, Murlidharan T
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
[hidden email]
(801) 408-8111
 
 

> -----Original Message-----
> From: [hidden email]
> [mailto:[hidden email]] On Behalf Of Nair,
> Murlidharan T
> Sent: Thursday, August 09, 2007 1:02 PM
> To: Nordlund, Dan (DSHS/RDA); [hidden email]
> 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: [hidden email] on behalf of Nordlund,
> Dan (DSHS/RDA)
> Sent: Thu 8/9/2007 1:26 PM
> To: [hidden email]
> Subject: Re: [R] small sample techniques
>  
> > -----Original Message-----
> > From: [hidden email]
> > [mailto:[hidden email]] On Behalf Of Nair,
> > Murlidharan T
> > Sent: Thursday, August 09, 2007 9:19 AM
> > To: Moshe Olshansky; Rolf Turner; [hidden email]
> > 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
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: small sample techniques

Moshe Olshansky-2
In reply to this post by Nair, Murlidharan T
Hi Murli,

First of all, regarding prop.test, you made a typo:
you should have used prop.test(c(69,90),c(300,300))
which gives you the squared value of 3.4228, and it's
square root is 1.85 which is not too far from 1.94.

I would use Fisher Exact Test (fisher.test).  Two
sided test has a p-value of 0.06411 so you do not
reject H0, One sided test (i.e. H1 is that the first
probability of success is smaller than the second) has
a p-value of 0.03206, so you reject H0 (with 95%
confidence level).
You get similar results with two-sided and one-sided
t-test.

Moshe.

P.S. if you use paired t-test you get nonsense since
it uses pairwise differences, and in your case only 21
of 300 differences are non-zero!

--- "Nair, Murlidharan T" <[hidden email]> wrote:

> 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 proportions
>       sqrt((0.265 *0.735)*((1/300)+(1/300))) =
> 0.03603
>
> 3>Evaluation of the difference between sample
> proportion as a deviation 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: [hidden email] on behalf of
> Nordlund, Dan (DSHS/RDA)
> Sent: Thu 8/9/2007 1:26 PM
> To: [hidden email]
> Subject: Re: [R] small sample techniques
>  
> > -----Original Message-----
> > From: [hidden email]
> > [mailto:[hidden email]] On
> Behalf Of Nair,
> > Murlidharan T
> > Sent: Thursday, August 09, 2007 9:19 AM
> > To: Moshe Olshansky; Rolf Turner;
> [hidden email]
> > 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
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.
>

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: small sample techniques

Daniel Nordlund
In reply to this post by Nair, Murlidharan T
> -----Original Message-----
> From: [hidden email]
> [mailto:[hidden email]] On Behalf Of Nair,
> Murlidharan T
> Sent: Thursday, August 09, 2007 12:02 PM
> To: Nordlund, Dan (DSHS/RDA); [hidden email]
> 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 proportions
>       sqrt((0.265 *0.735)*((1/300)+(1/300))) = 0.03603
>
> 3>Evaluation of the difference between sample proportion as a
> deviation 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?
>
>

I sent this from work but it seems to have disappeared into the luminiferous ether.

The proportion test above indicates that p1=0.1 and p2=0.07666667.  But in your t-test you specify p1=0.3 and p2=0.23.  Which is correct?  If p1=0.3 and p2=0.23, then use

prop.test(c(.30*300,.23*300),c(300,300))

Hope this is helpful,

Dan

Daniel J. Nordlund
Research and Data Analysis
Washington State Department of Social and Health Services
Olympia, WA  98504-5204

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.