Percentages in table (Stata 18) and the across option

[John Hund]

I'm confused about how table handles the "across" option in percent across rows. The simplest example I can show is using the auto.dta data where the "across" percentages differ from the direct calculation from the frequencies. At first I thought this might be due to some case/listwise deletion, but with no missing data in the auto data, I'm perplexed as to why I get differing numbers from the two approaches.

. sysuse auto, clear
(1978 automobile data)

. table mpg foreign, stat(percent weight, across(foreign)) zerocounts

--------------------------------------------
| Car origin
| Domestic Foreign Total
--------------+-----------------------------
Mileage (mpg) |
12 | 100.00 100.00
14 | 85.55 14.45 100.00
15 | 100.00 100.00
16 | 100.00 100.00
17 | 54.16 45.84 100.00
18 | 83.02 16.98 100.00
19 | 100.00 100.00
20 | 100.00 100.00
21 | 69.27 30.73 100.00
22 | 100.00 100.00
23 | 100.00 100.00
24 | 78.18 21.82 100.00
25 | 19.98 80.02 100.00
26 | 72.19 27.81 100.00
28 | 74.19 25.81 100.00
29 | 100.00 100.00
30 | 51.71 48.29 100.00
31 | 100.00 100.00
34 | 100.00 100.00
35 | 100.00 100.00
41 | 100.00 100.00
Total | 77.20 22.80 100.00
--------------------------------------------

. table mpg foreign, stat(count weight) zerocounts

-------------------------------------------
| Car origin
| Domestic Foreign Total
--------------+----------------------------
Mileage (mpg) |
12 | 2 0 2
14 | 5 1 6
15 | 2 0 2
16 | 4 0 4
17 | 2 2 4
18 | 7 2 9
19 | 8 0 8
20 | 3 0 3
21 | 3 2 5
22 | 5 0 5
23 | 0 3 3
24 | 3 1 4
25 | 1 4 5
26 | 2 1 3
28 | 2 1 3
29 | 1 0 1
30 | 1 1 2
31 | 0 1 1
34 | 1 0 1
35 | 0 2 2
41 | 0 1 1
Total | 52 22 74
-------------------------------------------

For example, for mileage level 17, there are 2 foreign and 2 domestic, so I would expect the "across" table to generate 50% for each, but using percent I get 54.16 and 45.84. Is there an option that I'm missing? I feel like it must be something simple, but the difference between the percent option and doing the raw division is flummoxing me.

[Jeff Pitblado (StataCorp)]

From the documentation.

statistic(ratiostat [varlist] [, ratio_options]) specifies that ratio statistic ratiostat be
computed. If varlist is specified, ratios are computed based on the totals of the specified
variables. If varlist is not specified, ratios are computed based on frequencies.

For your hand calculations, you should be looking at totals instead of cell counts.

. quietly table mpg foreign, stat(total weight)

. collect style cell result[total], empty(0)

. collect preview

---------------------------------------------
              |           Car origin
              |  Domestic   Foreign     Total
--------------+------------------------------
Mileage (mpg) |
  12          |     9,560         0     9,560
  14          |    20,250     3,420    23,670
  15          |     7,800         0     7,800
  16          |    15,200         0    15,200
  17          |     7,090     6,000    13,090
  18          |    24,830     5,080    29,910
  19          |    26,640         0    26,640
  20          |     9,360         0     9,360
  21          |    11,000     4,880    15,880
  22          |    14,550         0    14,550
  23          |         0     6,600     6,600
  24          |     8,170     2,280    10,450
  25          |     2,200     8,810    11,010
  26          |     4,750     1,830     6,580
  28          |     5,060     1,760     6,820
  29          |     2,110         0     2,110
  30          |     2,120     1,980     4,100
  31          |         0     2,200     2,200
  34          |     1,800         0     1,800
  35          |         0     4,070     4,070
  41          |         0     2,040     2,040
  Total       |   172,490    50,950   223,440
---------------------------------------------

. di 100*7090/13090
54.163484

. di 100*6000/13090
45.836516

[John Hund]

Thanks a lot, that's super helpful!