## Re: Help interpreting data

Subject: Re: Help interpreting data
From: "Jennifer Rondeau" <jrondeau -at- fabtrol -dot- com>
To: "TECHWR-L" <techwr-l -at- lists -dot- raycomm -dot- com>
Date: Fri, 25 Apr 2003 10:45:14 -0600

Ok, I'll bite, and attempt to dust off ancient algebra skills.

On 25 Apr 2003 at 10:33, Con & Yu wrote:

I have been asked to to show that the changes from agricultural to
industrial economies resulted in shifts of population almost
proportionately to the increase or decrease in agricultural employment.

The data I was given are as follows:
the cities,
Agricultural/Industrial population (%) in 1980,
Agricultural/Industrial population (%) in 1990,
their percentage changes in population from 1980 to 1990.

City A 95/5, 50/50, +95
City B 20/80, 50/50, -40
City C 80/20, 60/40, +20
City D 90/10, 10/90, +180

You could construct a formula that goes either way, but mine is

x = City A population ratio differential 1980 - 1990

which yields the following figures (all are percentages):

City A 90-0=+90 (compare to population growth of +95)
City B -60-0=-60 (compare to population growth of -40)
City C 60-20=+40 (compare to population growth of +20)
City D 80?80=+160 (compare to population growth of +180)

and just looking at the numbers gives you a rough sense of the
correlation. If you graphed the correlation between employment shifts and
population growth, I can't see that you'd get a very strong argument for
proportional correlation.

95/90 = .94
-60/-40 = 1.5
40/20 = 2.0
160/180 = .89

Cities A and D offer a good argument, maybe cities B and C, but not all
four together. Seems to me also as though the significance of these
percentages depends on the absolute numbers we're talking about. And that
4 cities do not offer a statistically significant sample, especially with
the variations in correlation we're looking at. But then, I tend toward
Mark Twain's view of statistics anyway.

Or have I gotten my equations all wrong?

Now back to work with me on a Friday. Thanks for the distraction.

Jennifer

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