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Can somebody explain me with example what is confidence level and confidence interval in determining sample size ?
Stated simply, the confidence level, say 95%, is how confident you are that you would find a mean very similar to the mean in a current sample if the test were repeated in a similar fashion. Confidence interval, say 5%, is indicative of the true value (mean) or range of your mean from a sample study. Example, the mean is 37%. In this case with a 5% margin for error, the confidence interval is 32%-42%.
Thanks james for the reply,It was informative. I have a question on arriving at the sample size in case of attribute data. What is the method followed ? Kindly explain.
James has given the usual loose interpretation of Confidence Intervals. We can be more precise:
Given some population with Mean = m. If we take repeated samples from this population, and calculate 95% confidence intervals for the mean, 95% of the C.I.s will include the true value of m.
The confidence level is not a function of sample size. We can have any level of confidence we want regardless of sample size. Sample size does effect the width of the interval. As sample size increases the width decreases: we expect to see smaller deviations from the true mean. One other factor that obviously affects the size of the interval is the variability of the process being sampled. Other things being equal, the size of the interval is directly proportional to the variability (standard deviation) of the process.
As for examples, the web has plenty of examples if you search.
In response to your original question.Confidence interval for the mean:Xbar – confidence level*s.d./sqrt n < mu < Xbar + confidence level*s.d./sqrt nLet delta = confidence level*s.d./sqrt nSolve for n and you get ((confidence level*s.d.)/delta)squared.Now you see the relationship between confidence level, confidence interval and sample size.The same thing holds for proportion except you use the CI for a proportion. Following the same process you will get:n = (confidence level/delta)squared * p(1-p)
(Zsq * p(1-P)/margin of error))sq
Ex. (95% confidence level and a 5% margin of error yields a sample size of 368.
(1.96sq*.50(1-.50)/.05))sq=368
The .50 is used assuming you don’t have an idea what the desired response rate might be. If you do, say 25%, then P(1-P) is .25(1-.25) or .1875
Find the 1.96 in the Z table. Some tables may have .025 (.05/2 for two tail test); others may have .975.
Make sure you mention that computing sample size with the formulas only yields a beta of about .5 which isn’t too powerful for use in a hypothesis test.
I have one more related question. Confidence level and Confidence interval plays a very important role is determining the smaple size in case of variable data. In case of attribute data, can we use the military standards (Ex. milstd105e) for a decided AQL (lets say 1.5%) and arrive at the sample size ? Is this also a right methodology for attribute data in arriving at the sample size ?
MilStds were developed for use in incoming inspection. I don’t believe it would be appropriate for inferential statistics.
Darth,
If the military is inspecting “incoming”, they are too late :-)
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