Citizen satisfaction: crude versus age-standardised rates
Two regions ran the same citizen satisfaction survey. Region A received 1,200 responses; Region B received 800. Overall satisfaction was 60% in A and 75% in B. A breakdown by age shows that in A, 900 respondents were aged under 50 and 300 were 50 or over; satisfaction was 50% among the younger group and 90% among the older group. In B, 200 respondents were under 50 and 600 were 50 or over; satisfaction was 45% among the younger group and 85% among the older group. The regional director of B states that B clearly outperforms A and should receive the larger share of next year's service-improvement budget. A analyst replies that the comparison is misleading because the age mix differs. Using the combined survey population as the standard mix, calculate crude and age-standardised satisfaction rates, and advise which region performed better on a like-for-like basis.
1. Verify the crude satisfaction rates for A and B and show the underlying counts.
Read the worked answer
Region A: younger satisfied = 900 × 0.50 = 450; older satisfied = 300 × 0.90 = 270; total = 720; crude rate = 720 ÷ 1,200 = 60%. Region B: younger satisfied = 200 × 0.45 = 90; older satisfied = 600 × 0.85 = 510; total = 600; crude rate = 600 ÷ 800 = 75%. The crude figures confirm the director's numbers. B leads by 15 percentage points. It is worth noting that a simple unweighted average of the two age-group rates gives A 70% and B 65%, which already signals that the age composition is driving the crude comparison.
2. Calculate the age-standardised satisfaction rates using the combined survey population as the standard mix, and interpret the result.
Read the worked answer
Combined population = 2,000: under 50 = 1,100 (55%); 50+ = 900 (45%). Standardised A = 0.55 × 50% + 0.45 × 90% = 27.5% + 40.5% = 68.0%. Standardised B = 0.55 × 45% + 0.45 × 85% = 24.75% + 38.25% = 63.0%.
On a like-for-like age mix, A is 5 percentage points higher, reversing the crude ranking. This is a composition effect: 75% of B's respondents are in the older, higher-satisfaction group, compared with only 25% of A's. Crude satisfaction mixes service performance with the age profile of respondents, so B's apparent lead does not establish that B performs better.
3. Advise the budget decision. Is the director's conclusion supported? What caveats should accompany the standardised comparison?
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The director's conclusion is not supported on performance grounds. If the budget is intended to reward service performance, the standardised comparison favours A, not B. If the budget is intended to target older citizens, B's larger older cohort may justify more spending, but that is a different policy criterion and should be stated explicitly.
Caveats: the standardised rates depend on the chosen standard mix; B's younger group has only 200 respondents, so its 45% rate has a wider margin of error; and non-response may differ by age and region, which could bias both crude and standardised figures. A defensible recommendation is to avoid awarding B the larger share on the crude figure alone, present both crude and standardised rates, and decide the budget criterion before allocating.