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Notes
1. Odds, which are widely used in assessing probabilistic outcomes, are derived from probabilities (0 ≤ π
i
≤ 1) by the following formula: .
2. Suppose two individuals j and k who are closely matched on observables so that xj = xk , but for whom π j , the probability of j being selected into treatment, is not equal to π k ; that is, the probability of being selected into a programme is not the same for these individuals despite being equivalent on observables. The probability of being selected can be expressed as an odds ratio (the odds of probability of j / k (π j / π k ) being selected π j / (1 – π j ) or π k / (1 – π k )). Then imagine there is a number Γ (gamma) such that 1 / Γ ≤ {π j (1 – π k )} / {π k (1 – π j )} ≤ Γ; then if Γ = 1, π j = π k (that is, there is no difference in the odds of being selected). Γ = 2 means that individual j is twice as likely to be selected into a programme as individual k.
3. There are other commands developed for Stata to implement sensitivity analyses such as mhbounds (developed by Becker and Caliendo Citation2007) or sensatt (Nannicini Citation2007).