Can stats analysis be done?

[Michelle Tan]

Hi

From a population of 1800, i draw a sample size of 220. The sample has a
binomial distribution of p=218 and q=2.
I want to extrapolate the sample results to the population and conclude
using 95% confidence interval that my population falls within a certain
range. CAn this be done with such a small q?
if not, what are the stats analysis that can be done?

thanks a lot!

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[Garry Gelade]

Dear Michele


Yes you can do it.  See here for various methdods of calculating a
confidence interval for binomial distributions.

http://www.measuringusability.com/wald.htm

Alternatively, it might be preferable to draw a large number of bootstrap
samples from your population and figure out the 95% confidence empirically.
It should be fairly straightforward to do this in SPSS.

Garry Gelade



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Michelle Tan
Sent: 16 May 2011 02:19
To: [hidden email]
Subject: Can stats analysis be done?

Hi

From a population of 1800, i draw a sample size of 220. The sample has a
binomial distribution of p=218 and q=2.
I want to extrapolate the sample results to the population and conclude
using 95% confidence interval that my population falls within a certain
range. CAn this be done with such a small q?
if not, what are the stats analysis that can be done?

thanks a lot!

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
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[Ryan]

For a binomial distribution, p reflects the probability of success,
while q reflects 1 - p. Anyway, here's some SPSS code that should help
you construct confidence limits for this particular sample:

data list list / x weight.
begin data
1 218
2 2
end data.

WEIGHT BY weight.

NPTESTS
  /ONESAMPLE TEST (x) BINOMIAL(TESTVALUE=0.5 CLOPPERPEARSON
SUCCESSCATEGORICAL=FIRST
    SUCCESSCONTINUOUS=CUTPOINT(MIDPOINT))
  /CRITERIA ALPHA=0.05 CILEVEL=95.

Ryan

On Sun, May 15, 2011 at 9:18 PM, Michelle Tan <[hidden email]> wrote:

> Hi
>
> From a population of 1800, i draw a sample size of 220. The sample has a
> binomial distribution of p=218 and q=2.
> I want to extrapolate the sample results to the population and conclude
> using 95% confidence interval that my population falls within a certain
> range. CAn this be done with such a small q?
> if not, what are the stats analysis that can be done?
>
> thanks a lot!
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>

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[Bruce Weaver]

But note that the adjusted (or modified) Wald method does not appear to be available through NPTESTS.  The Help lists only these 3 methods:

- Clopper-Pearson (exact). An exact interval based on the cumulative binomial distribution.
- Jeffreys. A Bayesian interval based on the posterior distribution of p using the Jeffreys prior.
- Likelihood ratio. An interval based on the likelihood function for p.

For discussion of why the adjusted Wald method is often (or maybe even usually) preferred to the Clopper-Pearson "exact" method, see the page Garry gave earlier, and also the note on the Graphpad QuickCalcs page.

   http://www.measuringusability.com/wald.htm#wilson
   http://www.graphpad.com/articles/CIofProportion.htm

<rant>
Note too that with NPTESTS, the desired CI output is buried in that infernal model viewer.  You have to first double-click to open the Model Viewer window, then you have to select "Confidence Interval Summary View" from a drop-down list.  Why all of this cannot be immediately visible in the output window is beyond me.  
</rant>

HTH.

R B wrote

For a binomial distribution, p reflects the probability of success,
while q reflects 1 - p. Anyway, here's some SPSS code that should help
you construct confidence limits for this particular sample:

data list list / x weight.
begin data
1 218
2 2
end data.

WEIGHT BY weight.

NPTESTS
  /ONESAMPLE TEST (x) BINOMIAL(TESTVALUE=0.5 CLOPPERPEARSON
SUCCESSCATEGORICAL=FIRST
    SUCCESSCONTINUOUS=CUTPOINT(MIDPOINT))
  /CRITERIA ALPHA=0.05 CILEVEL=95.

Ryan

On Sun, May 15, 2011 at 9:18 PM, Michelle Tan <[hidden email]> wrote:
> Hi
>
> From a population of 1800, i draw a sample size of 220. The sample has a
> binomial distribution of p=218 and q=2.
> I want to extrapolate the sample results to the population and conclude
> using 95% confidence interval that my population falls within a certain
> range. CAn this be done with such a small q?
> if not, what are the stats analysis that can be done?
>
> thanks a lot!
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>

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