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Name: Mary B.
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Question:
Is there a formula to calculate the 95% confidence interval with respect to the median?



Replies:
Hello,

You can formulate the problem but whether you can solve it analytically (without numerical computation) depends on the nature of the distribution.

I think you are trying to determine a range for the independent variable in your distribution such that 95% of the population fall within that range. Stated differently, lets assume x0 is the mean value. You want to determine c such that the population that falls in the x=x0-c to x=x0+c is 95% of the total. This is equivalent to wanting the area under the distribution curve between and x0-c to x0+c to be 95% of the total. Thus, an integration of the distribution between x-c to x+c is indicated; the objective is to find c such that:

Integral between x0-c to x0+c of [Distribution] =0.95,

where the distribution is normalized such that:

Integral between -L to +L of [Distribution] =0, where L is the limits of x (for symmetric distribution).

If the distribution is uniform, the limits are calculated from 2c=0.95*(2L)-> c=0.95L. For other distributions, one may have to do numerical integration in which c has to be selected such that value of the integral above is 0.95.

For normal distribution, the area under the curve is tabulated against c in many books on statistics. From those tables, one will select such value of c that the integral under the curve in 0.95.

AK



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