Financial Inclusion Survey and the 60% Target
A financial inclusion survey in Karnali sampled 400 households; 240 reported having a bank or cooperative account. The survey was designed as a simple random sample, but 15% of selected remote households did not respond, and non-response was concentrated among households with no mobile phone. The program target is 60% account ownership. A staff memo says '60% is within the sample estimate, so the target is met.' The donor wants a 95% confidence interval and a decision. Use z = 1.96. The survey cost NPR 2.5 million; a follow-up of non-respondents would cost NPR 600,000 and take three weeks. The manager now must decide whether to declare the target met, whether to do the follow-up, and how to report uncertainty.
1. Compute the 95% confidence interval for account ownership and interpret it against the 60% target.
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The sample proportion is p = 240/400 = 0.60. The standard error is sqrt[p(1-p)/n] = sqrt[(0.60)(0.40)/400] = sqrt(0.0006) = 0.0245. The 95% margin of error is 1.96 x 0.0245 = 0.0480, or 4.8 percentage points. The confidence interval is 0.60 +/- 0.048, which is 0.552 to 0.648, or 55.2% to 64.8%. The target of 60% lies inside the interval. The correct interpretation is not that the target is met; it is that the data are consistent with a true rate anywhere from about 55% to about 65%. The sample estimate happens to equal 60%, but the uncertainty is too wide to declare success. In addition, the 15% non-response concentrated among remote, no-phone households probably biases the estimate upward, because those households are likely to have lower account ownership.
2. Should the manager declare the target met or commission the follow-up? Explain the decision using both statistics and cost.
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The manager should not declare the target met. The confidence interval includes values below 60%, and the non-response bias likely pushes the estimate upward, so the true rate could be below the target. The follow-up costs NPR 600,000, which is about 24% of the original NPR 2.5 million survey cost, and takes three weeks. That is a relatively modest price for correcting a known bias in the hardest-to-reach group. If the follow-up can be done before the reporting deadline, it should be commissioned. If the deadline cannot move, the manager should report the estimate with the confidence interval, disclose the 15% non-response and its direction, and label the target status as 'not demonstrated' rather than 'met'. Declaring success on the current evidence would overstate precision and could mislead the donor.
3. How should the results be reported, and what additional analysis would strengthen the conclusion?
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The report should give the point estimate of 60%, the 95% confidence interval of 55.2% to 64.8%, the 15% non-response rate, and a clear statement that the target is not statistically demonstrated. It should explain that non-response was concentrated among remote households without mobile phones, so the estimate is likely optimistic. A stronger analysis would compare respondents and non-respondents on available characteristics, apply non-response weights if auxiliary data exist, and conduct a sensitivity analysis that assumes lower account ownership among non-respondents. For example, if all 60 non-respondents were unbanked, the overall rate would be 240/400? No: the 60 non-respondents are part of the 400, so the worst-case rate would be 240/400 = 60% only if the 240 are fixed; actually the 240 respondents are account holders, and if all 60 non-respondents were unbanked, the rate would still be 240/400 = 60%. A more informative bound uses the 340 respondents: 240/340 = 70.6%, and the 60 non-respondents could lower it. The report should avoid over-precision and recommend follow-up or weighted estimates.