Very interesting topic!
From your number, the 95% confidence intervals of the proportion who died from Smethwick do not overlap with those from Birmingham or Dudley, so the proportion who died in Smethwick is genuinely lower.
From what I know, I would suggest that mortality in the South African War was not evenly distributed. The risk was not the same for all units; and in any unit, of course officers fared worse than other ranks (they had a habit of standing up). Do you know the regiments the men of Smethwick joined? Then one can follow the course of these units, and compare to units from Dudley and Birmingham, bearing in mind that often men did not sign up for their local unit.
The two main questions I'd ask would be
(a) did the unit get caught up in the typhoid (enteric fever) epidemic - mainly in Bloemfontein, but also in other towns like Ladysmith? During the siege of Ladysmith, 5% died of typhoid. Of 556,653 men who served the Queen, 7,582 fell in battle, over 74,000 were treated for typhoid and 8,225 died of typhoid.
And as a sub-set of question (a), was the medical officer in charge of the troop ship to SA an enthusiastic typhoid vaccinator or a vaccine sceptic? The vaccine reduced typhoid mortality by about 50%, but was only offered to those on board, not forced on the soldiers. The typhoid dead included Prince Christian Victor, the Queen’s grandson, who had not been immunised, which is ironic because Prince Albert also died of typhoid in 1861 before the vaccine was invented by Almoth Wright.
(b) did the unit get caught up in a slaughter, like Spioenkop, Colenso, Magersfontein?
I look forward to see how other forummers approach your fascinating observation.
Rob