Name: Mary B.
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
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.
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