LGA | Budget B | Design | Relative bias | 5–95% spread of (Ť − T)/T | SE / SD | Coverage 95% |
|---|---|---|---|---|---|---|
Gabasawa | 30 | Conv (φ = 1) | 0.9% | 58.4% | 0.97 | 95% |
Best Improved (φ = 0.9) | -0.1% | 60.5% | 0.89 | 90% | ||
Improved (φ = 0.7) | 0.2% | 60.9% | 0.91 | 90% | ||
40 | Conv (φ = 1) | 1.6% | 45.6% | 1.02 | 94% | |
Best Improved (φ = 0.9) | 0.2% | 45.1% | 1.03 | 94% | ||
Improved (φ = 0.7) | 1.4% | 46.6% | 0.99 | 94% | ||
50 | Conv (φ = 1) | 1.0% | 43.9% | 0.95 | 94% | |
Best Improved (φ = 0.9) | 1.0% | 40.7% | 0.97 | 94% | ||
Improved (φ = 0.7) | 2.2% | 45.1% | 1.00 | 93% | ||
60 | Conv (φ = 1) | -0.2% | 35.0% | 1.03 | 95% | |
Best Improved (φ = 0.9) | 0.7% | 38.8% | 0.98 | 95% | ||
Improved (φ = 0.7) | 1.2% | 35.3% | 1.01 | 94% | ||
Gaya | 30 | Conv (φ = 1) | 0.0% | 50.0% | 1.09 | 94% |
Best Improved (φ = 0.9) | -0.1% | 52.4% | 1.01 | 93% | ||
Improved (φ = 0.7) | -0.1% | 53.4% | 1.01 | 92% | ||
40 | Conv (φ = 1) | 0.0% | 45.5% | 1.02 | 94% | |
Best Improved (φ = 0.9) | -0.4% | 38.6% | 1.05 | 95% | ||
Improved (φ = 0.7) | -0.7% | 42.3% | 1.13 | 93% | ||
50 | Conv (φ = 1) | -0.5% | 42.2% | 0.98 | 91% | |
Best Improved (φ = 0.8) | 0.6% | 49.5% | 0.92 | 91% | ||
Improved (φ = 0.7) | -0.6% | 38.2% | 1.15 | 97% | ||
60 | Conv (φ = 1) | -0.3% | 39.1% | 0.98 | 90% | |
Best Improved (φ = 0.9) | -0.1% | 35.8% | 1.07 | 93% | ||
Improved (φ = 0.7) | -0.1% | 39.4% | 0.98 | 92% | ||
Nassarawa | 30 | Conv (φ = 1) | 1.8% | 87.6% | 0.88 | 87% |
Best Improved (φ = 0.7) | -2.3% | 91.5% | 0.86 | 89% | ||
Improved (φ = 0.7) | -2.3% | 91.5% | 0.86 | 89% | ||
40 | Conv (φ = 1) | 4.4% | 78.3% | 0.92 | 90% | |
Best Improved (φ = 0.7) | 0.7% | 78.0% | 0.88 | 91% | ||
Improved (φ = 0.7) | 0.7% | 78.0% | 0.88 | 91% | ||
50 | Conv (φ = 1) | 4.0% | 68.0% | 0.95 | 91% | |
Best Improved (φ = 0.7) | 1.0% | 61.8% | 0.98 | 92% | ||
Improved (φ = 0.7) | 1.0% | 61.8% | 0.98 | 92% | ||
60 | Conv (φ = 1) | 3.2% | 56.9% | 0.97 | 93% | |
Best Improved (φ = 0.9) | 3.4% | 57.6% | 0.97 | 94% | ||
Improved (φ = 0.7) | 1.1% | 59.8% | 0.93 | 92% |
Appendix A — Technical Details
A.1 Adaptive Sampling
A.1.1 Reordering estimator
There are two components of the sample: (1) the preliminary component, drawn by a conventional gold-standard-style sampling design, and (2) the adaptive component, drawn by the adaptive selection rule. For the remainder of this annex, “preliminary” is reserved for this initial component of the Adaptive Sampling (AS) sample, and “conventional” is reserved for the matched-budget single-phase comparator design introduced in Section A.1.2.
Let the realized ordered sample be \(r_0 = (s_{0,C}, s_{0,A})\), where \(s_{0,C}\) is the preliminary component (subscript \(C\) retained for legacy notation) and \(s_{0,A}\) is the adaptive component. The unordered combined sample is \(s = s_{0,C} \cup s_{0,A}\), viewed as the set of selected Primary Sampling Units (PSUs) together with their observed values.
Rao–Blackwellization evaluates every admissible reordering of the same unordered sample. Let \(\mathcal{R}(s)\) denote the set of ordered partitions \(r = (s_{r,C}, s_{r,A})\) with \(s_{r,C} \cup s_{r,A} = s\), \(|s_{r,C}| = |s_{0,C}|\), and \(|s_{r,A}| = |s_{0,A}|\) that could have produced the observed unordered sample under the adaptive rule. For each \(r \in \mathcal{R}(s)\), let \(p_r = \Pr(R=r)\) be the marginal design probability of that ordered path. Orderings that could not have produced \(s\) have \(p_r = 0\) and are excluded from \(\mathcal{R}(s)\). The conditional probability of reordering \(r\) given the unordered combined sample is \[ q_r \;\equiv\; \Pr(R=r \mid S=s) \;=\; \frac{p_r}{\sum_{r' \in \mathcal{R}(s)} p_{r'}}. \tag{A.1}\]
For each admissible reordering \(r\), let \(\hat{\mu}_r\) be the Horvitz–Thompson estimate of the population quantity \(\mu\) computed from the preliminary component \(s_{r,C}\) using the first-order inclusion probabilities implied by that reordering. Let \(\widehat{\operatorname{Var}}(\hat{\mu}_r)\) be the corresponding design-variance estimator. The realized preliminary estimate is \(\hat{\mu}_{\text{prelim}} = \hat{\mu}_{r_0}\). The adaptive sampling estimate is the conditional expectation of the preliminary estimator over the admissible reorderings: \[ \hat{\mu}_{\text{RB}} \;\equiv\; \mathbb{E}\!\left[\hat{\mu}_{\text{prelim}} \mid S=s\right] \;=\; \sum_{r \in \mathcal{R}(s)} q_r \hat{\mu}_r \;=\; \frac{\sum_{r \in \mathcal{R}(s)} p_r \hat{\mu}_r}{\sum_{r \in \mathcal{R}(s)} p_r}. \tag{A.2}\]
The usual Rao–Blackwell variance estimator conditions the preliminary variance estimator on \(s\) and subtracts the conditional variance of the preliminary point estimates (Thompson 1990, 2006): \[ \widehat{\operatorname{Var}}\!\left(\hat{\mu}_{\text{RB}}\right) \;=\; \sum_{r \in \mathcal{R}(s)} q_r \widehat{\operatorname{Var}}(\hat{\mu}_r) \;-\; \sum_{r \in \mathcal{R}(s)} q_r \left(\hat{\mu}_r-\hat{\mu}_{\text{RB}}\right)^2. \tag{A.3}\] The weights in Equation A.3 are conditional probabilities and therefore sum to one. Equivalently, formulas written with the unnormalized \(p_r\) must divide each sum by \(\sum_{r' \in \mathcal{R}(s)} p_{r'}\). The subtraction term explains why the adaptive-sampling variance estimator can be negative in finite samples when the estimated within-reordering gain is larger than the average conditional variance estimate.
Exact enumeration of \(\mathcal{R}(s)\) is computationally expensive, so the implementation approximates the conditional distribution \(\{q_r\}\) by Markov Chain Monte Carlo (MCMC). Let \(M\) be the number of retained chain states. Suppose the current state is reordering \(r\). The chain proposes \(r^*\) by swapping one randomly selected PSU from \(r\)’s preliminary component with one randomly selected PSU from \(r\)’s adaptive component. This proposal is symmetric on the fixed-size reordering graph, so the Metropolis–Hastings acceptance probability is \[ \alpha(r, r^*) \;=\; \min\!\left\{ \frac{p_{r^*}}{p_r}, 1 \right\}, \tag{A.4}\] with \(p_{r^*}=0\) for inadmissible proposed reorderings. If the retained chain states are \(r_1,\ldots,r_M\), the Monte Carlo approximations are \[ \tilde{\mu} \;=\; \frac{1}{M}\sum_{m=1}^M \hat{\mu}_{r_m}, \qquad \widetilde{\operatorname{Var}}\!\left(\tilde{\mu}\right) \;=\; \frac{1}{M}\sum_{m=1}^M \widehat{\operatorname{Var}}(\hat{\mu}_{r_m}) \;-\; \frac{1}{M}\sum_{m=1}^M \left(\hat{\mu}_{r_m}-\tilde{\mu}\right)^2. \tag{A.5}\]
A.1.2 Break-even rule
A natural comparator for the adaptive design is a conventional Probability Proportional-to-Size (PPS)-without-replacement sample of the same total PSU budget — the question raised in Section 3.3.4.2. Let \(B\) and \(n_C\) be positive integers and write \(\phi = n_C/B \in (0,1]\). At fixed total budget \(B\), the adaptive design allocates \(n_C = \phi B\) PSUs to the preliminary component and \(n_A = B - n_C = (1-\phi)B\) PSUs to the adaptive component. The matched-budget conventional comparator allocates all \(B\) PSUs to a single-phase PPS-Without Replacement (WoR) draw on the same population size measure. This subsection proves a leading-order variance-scaling identity that determines when the adaptive sampling estimator beats matched-budget conventional. The claim is exact for the Rao–Blackwell step and exact for the composition once the stated \(1/n\) variance-scaling assumption is imposed; in this application the \(1/n\) step is an approximation because the sampling fractions are not negligible.
Throughout this subsection, let \(\hat{\mu}_{\text{prelim}}\) be the Horvitz–Thompson estimator computed on the \(n_C\)-PSU preliminary component of the adaptive design alone. Let \(\hat{\mu}_{\text{RB}}\) be the Rao–Blackwellized adaptive sampling estimator obtained by averaging \(\hat{\mu}_{\text{prelim}}\) over the reorderings of the realized combined sample \(s\). Let \(\hat{\mu}_{\text{Conv}}(n)\) be the Horvitz–Thompson estimator under a single-phase PPS-WoR sample of \(n\) PSUs on population size, applied to the same finite population. The two relevant estimators are \(\hat{\mu}_{\text{RB}}\) (the adaptive sampling estimator) and \(\hat{\mu}_{\text{Conv}}(B)\) (the matched-budget conventional).
Proposition. Assume that:
- the preliminary component of the adaptive design is drawn by the same PPS-WoR mechanism used by the single-phase conventional design at sample size \(n_C\);
- \(\hat{\mu}_{\text{prelim}}\) is design-unbiased and has positive finite variance;
- \(\hat{\mu}_{\text{RB}}=\mathbb{E}[\hat{\mu}_{\text{prelim}}\mid S]\), where \(S\) is the unordered combined sample generated by the adaptive design;
- the conventional PPS-WoR variance obeys the leading-order scaling \(\operatorname{Var}(\hat{\mu}_{\text{Conv}}(n)) \approx V_{\text{pop}}/n\) for the estimator or its Taylor-linearized form.
Then \[ \frac{\operatorname{SE}(\hat{\mu}_{\text{RB}})}{\operatorname{SE}(\hat{\mu}_{\text{Conv}}(B))} \;\approx\; \sqrt{\frac{1-R}{\phi}}, \] where \(R\) is the within-design Rao–Blackwell variance-reduction fraction defined in Equation A.8. Under the same approximation, the adaptive sampling estimator has lower standard error than matched-budget conventional if and only if \(R > 1 - \phi\).
Proof. First condition on the unordered combined sample \(S=s\). For this adaptive design, the conditional distribution over reorderings depends only on the observed PSU labels, observed values, and known design rule. The conditional expectation is therefore the weighted-reordering estimator in Equation A.2. Define the Rao–Blackwellized estimator \(\hat{\mu}_{\text{RB}} \equiv \mathbb{E}[\hat{\mu}_{\text{prelim}} \mid S]\).
By the law of total variance (Casella and Berger 2002, Thm. 4.4.7) applied with conditioning on \(S\), \[ \operatorname{Var}(\hat{\mu}_{\text{prelim}}) \;=\; \mathbb{E}\!\left[\operatorname{Var}(\hat{\mu}_{\text{prelim}} \mid S)\right] + \operatorname{Var}\!\left(\mathbb{E}[\hat{\mu}_{\text{prelim}} \mid S]\right). \tag{A.6}\] Substituting \(\hat{\mu}_{\text{RB}} = \mathbb{E}[\hat{\mu}_{\text{prelim}} \mid S]\) and rearranging, \[ \operatorname{Var}(\hat{\mu}_{\text{RB}}) \;=\; \operatorname{Var}(\hat{\mu}_{\text{prelim}}) - \mathbb{E}\!\left[\operatorname{Var}(\hat{\mu}_{\text{prelim}} \mid S)\right]. \tag{A.7}\] This is the variance-reduction form associated with Rao–Blackwellization (Rao 1945; Blackwell 1947): conditioning an estimator on the observed unordered sample produces an estimator with variance no greater than the original, with the gap equal to the expected within-equivalence-class variance.
Both terms on the right of Equation A.6 are non-negative (\(\operatorname{Var}(\cdot \mid S) \ge 0\) pointwise, so its expectation is non-negative; the second term is itself a variance), so the within-design Rao–Blackwell variance-reduction fraction \[ R \;\equiv\; \frac{\mathbb{E}\!\left[\operatorname{Var}(\hat{\mu}_{\text{prelim}} \mid S)\right]}{\operatorname{Var}(\hat{\mu}_{\text{prelim}})} \tag{A.8}\] satisfies \(R \in [0, 1]\). Equation A.7 then gives \(\operatorname{Var}(\hat{\mu}_{\text{RB}}) = (1 - R)\,\operatorname{Var}(\hat{\mu}_{\text{prelim}})\), and taking square roots, \[ \frac{\operatorname{SE}(\hat{\mu}_{\text{RB}})}{\operatorname{SE}(\hat{\mu}_{\text{prelim}})} \;=\; \sqrt{1 - R}. \tag{A.9}\]
Second, use the leading-order sample-size scaling for PPS-WoR. Let \(U = \{1, \ldots, N_{\text{frame}}\}\) index the frame PSUs, with size measures \(p_k > 0\) normalized so \(\sum_{k \in U} p_k = 1\), and PSU-level totals \(T_k\) of the variable of interest. For a fixed-population PPS-WoR design at sample size \(n\) with first-order inclusion probabilities \(\pi_k \approx n p_k\) and \(\pi_k \le 1\), the Horvitz-Thompson (HT) estimator of the population total \(T = \sum_{k \in U} T_k\) has variance, to first order in the sampling fraction \(f = n / N_{\text{frame}}\) (Särndal, Swensson, and Wretman 1992, ch. 2; Seber and Salehi 2013), \[ \operatorname{Var}(\hat{\mu}_{\text{Conv}}(n)) \;\approx\; \frac{1}{n}\,V_{\text{pop}}, \qquad V_{\text{pop}} \;=\; \sum_{k \in U} p_k \left( \frac{T_k}{p_k} - T \right)^2. \tag{A.10}\] \(V_{\text{pop}}\) is a population-level constant: it depends on the PSUs-level totals \(T_k\) and the size measures \(p_k\), but not on the sample size \(n\). The same \(1/n\) scaling carries through to HT-linear functionals of the total — including the ratio (prevalence) estimator used in this study, via Taylor linearization (Särndal, Swensson, and Wretman 1992, sec. 5.6) — with \(V_{\text{pop}}\) replaced by the corresponding linearized population constant.
Equation A.10 is the Hansen–Hurwitz with-replacement form, which approximates the PPS-WoR variance by dropping the finite-population correction \((1 - f)\). The approximation is exact in the limit \(f \to 0\). The full ratio retaining the Finite Population Correction (FPC) is \[ \frac{\operatorname{SE}(\hat{\mu}_{\text{Conv}}(B))}{\operatorname{SE}(\hat{\mu}_{\text{Conv}}(n_C))} \;\approx\; \sqrt{\frac{n_C}{B} \cdot \frac{1 - B/N_{\text{frame}}}{1 - n_C/N_{\text{frame}}}}; \tag{A.11}\] because \(B > n_C\) the FPC factor is less than 1, so the matched-budget conventional comparator gains a small additional precision boost that the no-FPC approximation below does not capture. In the universe-grid exercise the Local Government Area (LGA) frames hold roughly 500–750 PSUs and \(B\) ranges up to 60 (sampling fractions of about 5–13%), so the FPC is non-negligible and the leading-order identity below should be read as optimistic for the adaptive sampling estimator.
Dropping the FPC and taking square roots, \[ \frac{\operatorname{SE}(\hat{\mu}_{\text{Conv}}(B))}{\operatorname{SE}(\hat{\mu}_{\text{Conv}}(n_C))} \;\approx\; \sqrt{\frac{n_C}{B}} \;=\; \sqrt{\phi}. \tag{A.12}\]
Third, compose the two identities. The AS preliminary estimator is, by construction, the Horvitz–Thompson estimator on \(n_C\) PSUs drawn via PPS-WoR on population size. The preliminary component is drawn by the same mechanism as a single-phase conventional sample of size \(n_C\), so \(\hat{\mu}_{\text{prelim}}\) and \(\hat{\mu}_{\text{Conv}}(n_C)\) have the same distribution under the design measure and therefore the same standard error: \[ \hat{\mu}_{\text{prelim}} \;\stackrel{d}{=}\; \hat{\mu}_{\text{Conv}}(n_C), \qquad \operatorname{SE}(\hat{\mu}_{\text{prelim}}) \;=\; \operatorname{SE}(\hat{\mu}_{\text{Conv}}(n_C)). \tag{A.13}\] Combining Equation A.9 and Equation A.12 via Equation A.13, \[ \frac{\operatorname{SE}(\hat{\mu}_{\text{RB}})}{\operatorname{SE}(\hat{\mu}_{\text{Conv}}(B))} \;=\; \underbrace{\frac{\operatorname{SE}(\hat{\mu}_{\text{RB}})}{\operatorname{SE}(\hat{\mu}_{\text{prelim}})}}_{=\,\sqrt{1 - R}} \;\cdot\; \underbrace{\frac{\operatorname{SE}(\hat{\mu}_{\text{Conv}}(n_C))}{\operatorname{SE}(\hat{\mu}_{\text{Conv}}(B))}}_{\approx\,1/\sqrt{\phi}} \;\approx\; \sqrt{\frac{1 - R}{\phi}}. \tag{A.14}\]
This proves the displayed identity.
Break-even condition. Under the same no-FPC approximation, the ratio in Equation A.14 is less than \(1\) if and only if \((1 - R)/\phi < 1\), i.e., \[ R \;>\; 1 - \phi. \tag{A.15}\] That is: the within-design Rao–Blackwell variance reduction \(R\) must exceed the fraction of total budget diverted from the preliminary phase to the adaptive phase.
Retaining the common FPC term gives the stricter finite-frame approximation \[ \frac{\operatorname{SE}(\hat{\mu}_{\text{RB}})}{\operatorname{SE}(\hat{\mu}_{\text{Conv}}(B))} \;\approx\; \sqrt{ \frac{1-R}{ \phi \left\{(1-B/N_{\text{frame}})/(1-\phi B/N_{\text{frame}})\right\} } } \tag{A.16}\] so the corresponding break-even condition is \[ R \;>\; 1 - \phi \left\{\frac{1-B/N_{\text{frame}}}{1-\phi B/N_{\text{frame}}}\right\}. \tag{A.17}\] Because the factor in braces is less than one when \(B > n_C\), the FPC-adjusted condition requires a larger Rao–Blackwell gain than \(R > 1 - \phi\).
Under the no-FPC condition, at \(\phi = 0.5\) the design needs \(R > 0.5\) (a \(50\%\) within-design variance reduction) to break even; at \(\phi = 0.85\) it needs \(R > 0.15\); at \(\phi = 0.95\) it needs only \(R > 0.05\). The condition becomes easier to satisfy as \(\phi\) increases, but the of Rao–Blackwell variance reduction \(R\) available shrinks alongside \(\phi\). Heuristically: as \(n_A = (1-\phi) B\) shrinks, the equivalence class of orderings producing the same unordered combined sample \(s\) collapses (at the extreme \(n_A = 0\), there is a single ordering compatible with \(s\) and \(\operatorname{Var}(\hat{\mu}_{\text{prelim}} \mid s) = 0\)), so the conditional distribution of \(\hat{\mu}_{\text{prelim}}\) given \(s\) concentrates and the numerator of Equation A.8 shrinks — the chain has less reordering material to exploit. Using the model variance estimates from the current universe-grid exercise, the empirical diagnostic \(R_{\text{est}} = 1 - \bar{V}_{\text{Imp}}/\bar{V}_{\text{Prelim}}\) ranges, in the median across LGAs, from about \(0.13\) at \(\phi = 0.9\) to about \(0.38\) at \(\phi = 0.5\). The largest LGA-level value is about \(0.41\) in Nassarawa at \(\phi = 0.5\). Those values are consistent with Figure 3.8: adaptive-sampling/conventional ratios drop below \(1\) only in selected cells, mostly in Nassarawa and in a few near-tie cells elsewhere.
Positioning in the literature. The variance decomposition in Equation A.14 is elementary: it composes the Rao–Blackwell variance decomposition with the \(1/n\) scaling of finite-population HT variance. Both ingredients are textbook material (Casella and Berger 2002; Särndal, Swensson, and Wretman 1992; Seber and Salehi 2013), yet we have not located the composite identity stated explicitly in published adaptive-sampling work. A plausible explanation is that the adaptive-sampling literature has historically compared adaptive designs against simple random sampling, against fixed-network adaptive variants, or against the preliminary estimator within the same design — not against a matched-budget PPS-WoR single-phase comparator (Thompson 1990, 2006; Brown and Manly 1998; Salehi 1999; Felix-Medina and Thompson 2004; Dryver and Thompson 2005). The matched-budget comparator is the natural question for a survey practitioner deciding between two designs at a fixed total cost, but it is the wrong comparator for a methodologist defending the design against the “no information” simple-random baseline. The identity above makes the practitioner-level comparison transparent: at fixed budget, adaptive sampling pays off under the leading-order approximation when clustering in the outcome is strong enough, via the size measure, to drive the within-design \(R\) above \(1 - \phi\).
The same gap is not specific to adaptive sampling. The Rao–Blackwell theorem is a within-design variance ordering at fixed realized data (Rao 1945; Blackwell 1947); it does not say that the adaptive sampling estimator dominates the original at fixed budget once the cost of obtaining the conditioning structure is paid. Two adjacent literatures have flagged this explicitly. In simulation methodology, Glynn and Whitt (1992) frame estimator efficiency as \(1/(\text{variance} \times \text{cost})\) rather than as variance alone, and the Rao–Blackwellised-MCMC literature has noted that conditional estimators can have lower variance per draw yet be dominated on a cost-matched basis by the unconditional estimator run longer (Douc and Robert 2011; Robert and Roberts 2021). In survey sampling, the cost-constrained form of the same question is two-phase sampling: whether to spend budget on auxiliary or validation measurements that enable a better estimator, or on more phase-one units — the framing introduced by Neyman (1938) and developed in Cochran (1977, ch. 12). The matched-budget identity in Equation A.14 is the same kind of statement, with the “cost” of the conditioning paid as reallocation of PSUs from a single-phase to a two-phase design rather than as a separately priced measurement.
A.1.3 Diagnostics
Table A.1 checks whether the simulation results are stable enough to support the interpretation in Section 3.3.4.2. The bias column shows whether the estimates recover the sentinel-sample universe on average. The \(5\)–\(95\%\) spread shows how much estimates vary from one simulated survey to another. The Standard Error (SE)/Standard Deviation (SD) column compares the reported standard error with the empirical variability across replicates. Values close to \(1\) suggest that uncertainty is being reported at about the right scale.
A.2 Precision-Cost Tables
This section provides expanded table views for the precision-cost analysis in Section 4.3.3.1. It includes both marginal direct-field and total financial-cost perspectives for Gold Standard proportion assumptions (p=50%) across threshold values used in this chapter, with Design Effect (DEFF) sensitivity shown at 1.5, 2, and 3. Rapid Convenience Monitoring (RCM) is intentionally excluded because it is operationally anchored to a fixed sample size of 20. Lot Quality Assurance Sampling (LQAS) is intentionally excluded because application-specific lot planning and representativeness conditions govern whether pooled prevalence precision calculations are meaningful. Network Scale-Up Method (NSUM) is intentionally excluded because the empirical estimates in this study were highly biased and unstable, so cost-linked precision summaries would not support decision use.
DEFF | Cost Perspective | Target MOE (95% CI) | Required n | Fixed Financial Cost (USD) | Variable Financial Cost (USD) | Total Financial Cost (USD) | Incremental Total Financial Cost from Previous Threshold (USD) |
|---|---|---|---|---|---|---|---|
1.5 | Marginal direct field cost | 20.0% | 37 | $0 | $410 | $410 | |
2.0 | Marginal direct field cost | 20.0% | 49 | $0 | $543 | $543 | |
3.0 | Marginal direct field cost | 20.0% | 73 | $0 | $809 | $809 | |
1.5 | Marginal direct field cost | 15.0% | 65 | $0 | $720 | $720 | $310 |
2.0 | Marginal direct field cost | 15.0% | 86 | $0 | $952 | $952 | $410 |
3.0 | Marginal direct field cost | 15.0% | 129 | $0 | $1,429 | $1,429 | $620 |
1.5 | Marginal direct field cost | 10.0% | 145 | $0 | $1,606 | $1,606 | $886 |
2.0 | Marginal direct field cost | 10.0% | 193 | $0 | $2,138 | $2,138 | $1,185 |
3.0 | Marginal direct field cost | 10.0% | 289 | $0 | $3,201 | $3,201 | $1,772 |
1.5 | Marginal direct field cost | 7.5% | 257 | $0 | $2,846 | $2,846 | $1,240 |
2.0 | Marginal direct field cost | 7.5% | 342 | $0 | $3,788 | $3,788 | $1,650 |
3.0 | Marginal direct field cost | 7.5% | 513 | $0 | $5,682 | $5,682 | $2,481 |
1.5 | Marginal direct field cost | 5.0% | 577 | $0 | $6,391 | $6,391 | $3,544 |
2.0 | Marginal direct field cost | 5.0% | 769 | $0 | $8,517 | $8,517 | $4,729 |
3.0 | Marginal direct field cost | 5.0% | 1,153 | $0 | $12,770 | $12,770 | $7,088 |
1.5 | Marginal direct field cost | 3.0% | 1,601 | $0 | $17,732 | $17,732 | $11,341 |
2.0 | Marginal direct field cost | 3.0% | 2,135 | $0 | $23,646 | $23,646 | $15,129 |
3.0 | Marginal direct field cost | 3.0% | 3,202 | $0 | $35,464 | $35,464 | $22,694 |
1.5 | Total financial cost | 20.0% | 37 | $581,797 | $410 | $582,206 | |
2.0 | Total financial cost | 20.0% | 49 | $581,797 | $543 | $582,339 | |
3.0 | Total financial cost | 20.0% | 73 | $581,797 | $809 | $582,605 | |
1.5 | Total financial cost | 15.0% | 65 | $581,797 | $720 | $582,517 | $310 |
2.0 | Total financial cost | 15.0% | 86 | $581,797 | $952 | $582,749 | $410 |
3.0 | Total financial cost | 15.0% | 129 | $581,797 | $1,429 | $583,225 | $620 |
1.5 | Total financial cost | 10.0% | 145 | $581,797 | $1,606 | $583,403 | $886 |
2.0 | Total financial cost | 10.0% | 193 | $581,797 | $2,138 | $583,934 | $1,185 |
3.0 | Total financial cost | 10.0% | 289 | $581,797 | $3,201 | $584,997 | $1,772 |
1.5 | Total financial cost | 7.5% | 257 | $581,797 | $2,846 | $584,643 | $1,240 |
2.0 | Total financial cost | 7.5% | 342 | $581,797 | $3,788 | $585,584 | $1,650 |
3.0 | Total financial cost | 7.5% | 513 | $581,797 | $5,682 | $587,478 | $2,481 |
1.5 | Total financial cost | 5.0% | 577 | $581,797 | $6,391 | $588,187 | $3,544 |
2.0 | Total financial cost | 5.0% | 769 | $581,797 | $8,517 | $590,314 | $4,729 |
3.0 | Total financial cost | 5.0% | 1,153 | $581,797 | $12,770 | $594,567 | $7,088 |
1.5 | Total financial cost | 3.0% | 1,601 | $581,797 | $17,732 | $599,528 | $11,341 |
2.0 | Total financial cost | 3.0% | 2,135 | $581,797 | $23,646 | $605,443 | $15,129 |
3.0 | Total financial cost | 3.0% | 3,202 | $581,797 | $35,464 | $617,260 | $22,694 |