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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%)? |
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There is no answer at this time. |
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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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