Applied Calculus project

C

cmnalo

Junior Member
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Nov 5, 2006
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I'm doing a project on in my calculus class analyzing sampling for Avian Influenza.
I've dug up this equation for obtaining an appropriate sample size:

n = log (1-c) / log (1-p)

n = sample size, c = desired level of confidence, p = prevalence of positive samples in the population.

I was hoping someone could give me some help with ideas on how to apply this formula. I would like to make a graph of it as well and need assistance with that also. Any help would be appreciated.
 
Where did you get the formula? Was there no discussion surrounding it? Sample size for what? What is it that you are studying?

I'm thinking it looks a little odd. Suppose we are concerned with the proportion of the population infected.

Maybe:

c = 0.01
p = 0.20

\(\displaystyle \frac{log(1-c)}{log(1-p)} = 0.045\)

What does that even mean? Does it mean "Sample 4½% of the population?"
 
Here are some more details: The formula is from the USDA. Its used to find the appropritate sample size in wild bird species, when trying to detect Avian Influenza(AI). An adequate sample size should allow for >95% confidence that AI is detected at ≤ 1.5% prevalence (USDA estimate for indivdual bird species). There are definately some short cummings in this calculation and I plan on talking about that. The confindence level would remain the same in most cases however the prevalence in popullations is just an estimation and could vary widely. This in turn would cause the sample size to change drastically. I would like to analyze the formula at different degrees of "p".
Any suggestions or comment?
Thanks for the response.
 
Here is some more info:

An adequate sample size should allow for >95% confidence that Avian Influenza (AI) is detected at ≤ “p” prevalence.
The USDA uses an assumed prevalence of 1.5%. The following formula results in a sample size of 200 birds.

n = log (1-.95) / log (1-.015) = 200 (acutal 198.2138457)

This formula is terribly flawed in that the prevalence of H5N1 AI in Northern Pintails is truely unknown. Since the formula is sensitive to changes in prevalence this assumption could easily lead to over or under sampling. The following graph shows the amount of sampling depending on the prevalence of H5N1 AI in Northern Pintails in order to maintain a >95% confidence in your detection method.

Any ideas or suggestions on further analysis would be appreciated.
 
I see. I misunderstood the usage of the 'c' parameter.

Given a fixed confidence level, what's stopping you from graphing it? You have n as a function of p.
 
I got the graph but I can't seem to cut and paste it here. I just created a table for different values of p. I would still like to make further analysis of this formula, so if any one has ideas on a direction I might go in that would be great.
Thanks,
cmnalo
 


Okay, now what exactly is it that you are looking for?
 
I'm not sure what I'm looking for. I would like to apply more calculus operations since its for a calculus project. I'm looking for ideas on where I could possibly take this. What about finding the average rate of change through the derivative of the function? Would I apply the quotient rule?
 
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