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Q: Statistics: Calculating the Statistical Significance of a Population-Level Ratio ( No Answer,   2 Comments )
Question  
Subject: Statistics: Calculating the Statistical Significance of a Population-Level Ratio
Category: Science > Math
Asked by: sail16-ga
List Price: $25.00
Posted: 29 Nov 2005 13:55 PST
Expires: 29 Dec 2005 13:55 PST
Question ID: 599132
I need a measure of the statistical signficance of a ratio that is
calculated at a population level on a quarterly basis.  To illustrate,
I have quarterly data as follows:

             Q1 '04    Q2 '04
Pro             25%       28%       
Neutral         70%       57%
Con              5%        5%
==============================
Net (Pro-Con)   20%       23%
Sample size     1,000      256

What formula or process can I use to assess the level of confidence
that the net number for Q2 (23%) is different from Q1 (20%)?
Answer  
There is no answer at this time.

Comments  
Subject: Re: Statistics: Calculating the Statistical Significance of a Population-Level Ratio
From: jab_stats-ga on 12 Dec 2005 18:22 PST
 
Let r1 and r2 be the true population proportion of the difference
between pro and con for each population.

For large samples (>30) this test assumes normal approximation to the binomial.

Let p1 and p2 be the observed sample proportions for each population,
and n1 and n2 the sample size.
Thus p1 = .20, p2 = .23, n1 = 1000, n2 = 256

Define P = (p1*n1+p2*n2)/(n1+n2)

The test statistic Z = (p1-p2)/sqrt( P*(1-P)*(1/n1 + 1/n2) )

Under the null that r1 = r2, Z is approx distributed normally.

For your data, 
P = 0.2061

Z = -1.0588 

For a two tailed test, at the 95% confidence level, Crit Z = +or - 1.96
Thus, since |Z| < 1.96, we cannot reject the null hypothesis that r1 = r2.
Subject: Re: Statistics: Calculating the Statistical Significance of a Population-Level Ratio
From: sail16-ga on 25 Jan 2006 12:05 PST
 
Thanks for the information.  However, it seems like this approach
doesn't work if the ratio is a negative number (i.e., there are more
cons than pros).

Thoughts?

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