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09-30-2015 11:28 AM

Consider the hypothetical setup:

X denotes counties in a city. We can have X1, X2,..., Xi.

Y denotes hospitals in the city. So let's say for county X1, we have Y11, Y12,..., Y1j, and so on for other counties.

Z denotes number of nurses in these hospitals. So for county X1, we have Z11 for hospital Y11, Z12 for hospital Y12,... Z1j for hospital Y1j, and so on.

We take a sample of hospitals, so not all of them are included in the sample. Let's say:

x denotes counties in the sample, x1, x2,..., x(i)

y denotes hospitals in the sample. For x1 we may have y1, y2,..., y(u), and so on.

z denotes number of nurses in the sample's hospitals. For x1 we have z1, z2,..., z(u).

I want to use the data from the sample to estimate the number of nurses in the target population (the city). Using mean value in a quick and dirty fashion for this purpose, I think of two potential approaches:

- In the first approach, simply assuming the overall mean of nurse in the sample represents the mean of population. That leads to the following estimation of Z:

Z = (mean of z)*Y

- In the second approach, I will calculate in a similar way but for each county and summing up those individual estimates. So for county X1,

Z1 = (z1 + z2 + ... + z(u))/(number of sampled hospitals of county x1)*number of hospitals of county X1

After that: Z = Z1 + Z2 + ... + Zi

It turns out that the two methods produce different results most of the time. I wonder which is the better estimates.

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09-30-2015 12:13 PM

Do you have hospital sizes at all?

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10-09-2015 01:12 AM

What do you mean with hospital sizes? Are they total staff working for those hospitals or some other measure?

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10-13-2015 01:40 AM

Bed counts or number of patients seen