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Re: st: Cell vs row proportions


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Cell vs row proportions
Date   Wed, 1 Mar 2006 15:22:15 -0500

It's not clear to me what you mean by "I'm not clear on the
implications" but look at this example:

. sysuse auto, clear
. tab rep78
     Repair |
Record 1978 |      Freq.     Percent        Cum.
------------+-----------------------------------
          1 |          2        2.90        2.90
          2 |          8       11.59       14.49
          3 |         30       43.48       57.97
          4 |         18       26.09       84.06
          5 |         11       15.94      100.00
------------+-----------------------------------
      Total |         69      100.00

Think of the percent column as being the probability of picking a car
with the given repair record when picking a car from your sample.
Now:
The row and column proportions are like conditional probabilities,
while the cell proportions are like joint probabilities.  From the
table below, we see that the probability of picking a car with repair
record 1 given that you are picking from domestic cars is 4.17% but
the probability of picking a domestic car given that you are picking
from cars with with repair record 1 is 100%. The cell proportion is
the chance you pick a domestic car with repair record 1 from the
sample (2.9%), i.e. P(domestic & rep.rec.1).
If you have survey data, you will use the -svy- analog, and you might
make inferences about whether (for example) a high-school dropout is
more likely to be poor than someone who finished HS (comparing the row
proportions in col 1 for a tab of hsgrad versus poor) or whether a
poor person is more likely to be a HS grad than a non-poor person
(comparing the col proportions in row 2 for a tab of hsgrad versus
poor).  The row and column proportions (to say nothing of cell
proportions) measure distinct and interesting concepts, but their use
is entirely up to you.

. tab rep78 for, row col cell nofr

+-------------------+
| Key               |
|-------------------|
|  row percentage   |
| column percentage |
|  cell percentage  |
+-------------------+

    Repair |
    Record |       Car type
      1978 |  Domestic    Foreign |     Total
-----------+----------------------+----------
         1 |    100.00       0.00 |    100.00
           |      4.17       0.00 |      2.90
           |      2.90       0.00 |      2.90
-----------+----------------------+----------
         2 |    100.00       0.00 |    100.00
           |     16.67       0.00 |     11.59
           |     11.59       0.00 |     11.59
-----------+----------------------+----------
         3 |     90.00      10.00 |    100.00
           |     56.25      14.29 |     43.48
           |     39.13       4.35 |     43.48
-----------+----------------------+----------
         4 |     50.00      50.00 |    100.00
           |     18.75      42.86 |     26.09
           |     13.04      13.04 |     26.09
-----------+----------------------+----------
         5 |     18.18      81.82 |    100.00
           |      4.17      42.86 |     15.94
           |      2.90      13.04 |     15.94
-----------+----------------------+----------
     Total |     69.57      30.43 |    100.00
           |    100.00     100.00 |    100.00
           |     69.57      30.43 |    100.00

HTH--Austin

On 3/1/06, Lauren Maxim <maximla@hotmail.com> wrote:
> Can someone explain conceptually the difference between calculating cell vs.
> row proportions, in a two-way tabulation?  I generated quite different
> values and confidence intervals, and I'm not clear on the implications or
> which best addresses my question of interest.

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