Re: Is this sample representative of the population?
- From: Richard Ulrich <Rich.Ulrich@xxxxxxxxxxx>
- Date: Mon, 12 Dec 2005 18:18:32 -0500
On Mon, 12 Dec 2005 18:00:27 +0100, "Z" <zingerNOSPAM@xxxxxxx> wrote:
>
> Hello,
>
> I've received the following problem (no, it's not homework), and I'm trying
> to figure out what would be the best way to answer it.
>
> A client (in marketing, you can probably guess) sent us this table,
> containing counts:
>
> Profession Population Sample
>
> Executive 10041 1164
> Commercial 1734 162
> Employee/labourer 3591 309
> Farmer 414 29
> CEO or upper executive 5330 797
> Self-employed 3621 410
> Retired 5699 927
> Student 5051 294
> blank 21 21
> Other 8536 403
> Total 44038 4495
>
> "Population" implies the true population from which the sample ("Sample")
> was taken.
>
> The question asked by the client is : "Is this sample representative of the
> population?"
>
> I can't figure out how to answer this. I've tried as follows:
I think that you re-write this as a contingency table:
Look up chi squared contingency table.
The table wants to compare the two parts of a total,
rather than comparing one part to the total.
Thus, the numbers below should be written as
"In sample", "not in sample", "Total" and if you find
a calculator online, it will want the first two (not Total).
Executive 10041 1164
Commercial 1734 162
Employee/labourer 3591 309
Farmer 414 29
...
The contingency table tests whether all the rows share
the same proportions, that is, about 10% and about 90%.
I'm sure that you want to omit the "blank" numbers, 0+21 = 21.
I'd probably give the client the table in two ways, one of
them leaving out the large "other" category, which has a
low proportion sampled.
The standardized cell deviations can be used as a measure
for whether each cell is contributing to the total "test".
The raw proportions might also be interesting.
>
> I wondered if the idea was that the proportions should be compared, so I did
> a line-by-line parametric comparison of two percentages. I got the p-values
> (for each category/row respectively) as:
[snip, rest]
I spent a couple of minutes studying your examples,
and I could not come up with a reasonable guess
about what you were testing, in either one. So I won't
say more about them.
--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.
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