Wednesday, March 01, 2006

Re: st: Cell vs row proportions

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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