# Negative Confidence Interval

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### Anonymous 310

Normal user

1 Nov 2010, 13:32

### Mark Myatt

Frequent user

1 Nov 2010, 15:55

(1) Meaning of a negative CI : A negative confidence lower confidence limit suggests the use of an approximate method for calculating the standard error usually in combination with a small sample size. Estimating SAM with reasonable precision using a cluster sampled survey might require a sample size of more than 4000. You will usually get a wide 95% CI from a survey designed to estimate GAM. If you get a negative confidence limit on a count, rate, or proportion then you should change your software or replace the reported negative number with a very small positive number.

(2) Tolerable width of 95% CI : This is difficult to answer. A survey should be as precise as you need it to be or (quite commonly) as you can afford it to be. As a rule of thumb ... I usually go for about 30% or better

**precision. Some examples: (a) If I think that prevalence might be 10% then I would go for a precision of 10% * 30% = 0.1 * 0.3 * 100 = 3%. That is, I would calculate the sample size for 10% with a 95% CI of +/- 3%; (b) If SAM is of interest then I might calculate the sample size for 1% with a 95% CI of +/- 0.3%; (c) In Bayesian SQUEAC coverage surveys I calculate sample size for 50% +/- 15%. On occasion you might want more or less precision than this.**

*relative*(3) CMR = 0.9 with 95% CI of 0.4 - 1.4 : This is a classic dilemma of estimation. You could have said that prevalence of GAM is 9% with a 95% CI of 6% to 12% with 6% being OK, 12% being worrying, and 9% being on the border between OK and worrying. When you have a

*problem it is usually best to use a classification technique. For proportions you can use a*

**classification***binomial test*or the

*z-test*and for rates you can use the

*poisson test*.

FANTA has some useful online tools for working with rates. You can try:

http://www.fantaproject.org/calculators/msss.shtml

With your data you would set the "Estimated population" to your sample size and specify the recall period. If your sample size was (e.g.) 1671 and the recall period was 90 days then enter 1671 as the "Estimated population" and 90 as the "Recall period" and 1 as the threshold rate and click the "Calculate" button. The "Threshold number" (22) is then used to make the classification (i.e. with this example you would declare an emergency if you had found more than 22 deaths. Also see:

http://www.fantaproject.org/calculators/msci.shtml

and:

http://www.fantaproject.org/calculators/mspt.shtml

for other tools that you may find useful in this context.

If you are working with proportions then you can use a calculator such as:

http://in-silico.net/statistics/z-test

If (e.g.) you have a survey with a sample size of 580 finding 79 cases you have an observed prevalence of 13.62 and you want to know if the true prevalence is likely to be above 10% then you would enter:

Sample 1 p = 0.1362

Sample 1 n = 580

Sample 2 p = 0.1

and click "Submit". This data gives "p = 0.00202879863627" ... p < 0.005 so we can conclude that prevalence is above 10%.

I hope this helps.

### Mark Myatt

Frequent user

8 Nov 2010, 09:06

**0.05**so we can conclude that prevalence is above 10%" ... sorry for any confusion.