I'm sure you all know to use DBMS_STATS to gather statistics for your tables and indexes. The DBMS_STATS.GATHER_TABLE_STATS() method has as its first three parameters OWNNAME, TABNAME, and PARTNAME, specifying the schema owner name, table name, and table partition name, respectively.
I had been assuming that specifying a partition name via the PARTNAME parameter would mean that I'd be gathering stats for just that partition. Wrong! You also need to specify GRANULARITY => PARTITION if that is your goal. Otherwise the PARTNAME is simply ignored and global (table-wide) statistics will be gathered instead.
Thanks to Wolfgang Breitling for the cluestick.