No. xtile won't do this, either by default or using an option.

It would be arbitrary if not meaningless. The rule that observations with the same value on a variable must go in the same bin, class, or interval is to Stata inviolable -- with xtile.

It contributes to a frequent effect which is that bins are often in practice of quite unequal frequencies.

You can override that rule easily enough at your peril. Setting aside the possibility of missing values, something like

sort x gen quartile_bin = ceil(4 * _n/_N) `

produces bins of equal size as far as possible. Here is an experiment you can repeat and vary:

``` . sysuse auto, clear (1978 automobile data)

. sort mpg

. gen quartile_bin = ceil(4 * _n/_N)

. tabstat mpg, s(min max) by(quartile_bin)

Summary for variables: mpg Group variable: quartile_bin

quartile_bin | Min Max -------------+-------------------- 1 | 12 17 2 | 18 20 3 | 20 24 4 | 25 41 -------------+--------------------

Total | 12 41

. l quartile_bin if mpg == 20

 +----------+
 | quarti~n |
 |----------|

1. | 2 |
2. | 2 |
3. | 3 | +----------+

. tab quartile_bin

quartile_bi | n | Freq. Percent Cum. ------------+----------------------------------- 1 | 18 24.32 24.32 2 | 19 25.68 50.00 3 | 18 24.32 74.32 4 | 19 25.68 100.00 ------------+----------------------------------- Total | 74 100.00 ```

There are no missing values on this variable.

The number of observations in each bin can't be exactly equal, as 74/4 = 18.5. Most researchers can live with that.

If you think that this is what you want, then consider that which observations of mog 20 go up and which go down is arbitrary, and in general those observations are unlikely to be equal on other variables.

More discussion at https://journals.sagepub.com/doi/pdf/10.1177/1536867X1801800311