Survey sample size planning with svyplan

svyplan provides a simple and complete toolkit for survey sample size determination. It covers sample sizes for proportions and means, precision analysis, multistage cluster allocation, multi-indicator optimization, strata boundary optimization, and power analysis. All functions share a consistent interface built around S3 generics, enabling round-trip conversions between sample size and precision, and sensitivity analysis via predict().

Function ecosystem

The package exports 14 functions organized into five families. The diagram below shows how they relate to each other.

Family	Functions	Purpose
Sample size	n_prop, n_mean, n_cluster, n_multi	“How many units do I need?”
Precision	prec_prop, prec_mean, prec_cluster, prec_multi	“What precision does n achieve?”
Power	power_prop, power_mean	“Can I detect a change?”
Design	varcomp, design_effect, effective_n	Variance components and design effects
Strata	strata_bound	Optimal stratification boundaries

Every function returns an S3 object with print, summary, predict, and (where applicable) confint methods.

The n_*/prec_* duality

The most distinctive feature of svyplan is the bidirectional link between sample size and precision functions. Every n_* function has a prec_* counterpart, and they are exact inverses.

Because n_* and prec_* are S3 generics, you can pass a result object directly to its inverse. All design parameters travel with the object:

# Compute sample size for a proportion
s <- n_prop(p = 0.3, moe = 0.05, deff = 1.5)
s
#> Sample size for proportion (wald)
#> n = 485 (p = 0.30, moe = 0.050, deff = 1.50)

# What precision does this n achieve?
p <- prec_prop(s)
p
#> Sampling precision for proportion (wald)
#> n = 485
#> se = 0.0255, moe = 0.0500, cv = 0.0850

# Recover the original sample size
n_prop(p)
#> Sample size for proportion (wald)
#> n = 485 (p = 0.30, moe = 0.050, deff = 1.50)

You can also override a parameter on the way back:

n_prop(p, cv = 0.08)
#> Sample size for proportion (wald)
#> n = 547 (p = 0.30, cv = 0.080, deff = 1.50)

Sample sizes for proportions and means

Proportions

Estimate vaccination coverage (expected ~70%) with a 5 percentage point margin of error:

n_prop(p = 0.70, moe = 0.05)
#> Sample size for proportion (wald)
#> n = 323 (p = 0.70, moe = 0.050)

Three method options control how the margin of error is computed:

• "wald" (default): the textbook normal approximation
• "wilson": Wilson score interval, better coverage near 0 or 1
• "logodds": log-odds transformation, recommended for rare events

n_prop(p = 0.05, moe = 0.02, method = "wald")
#> Sample size for proportion (wald)
#> n = 457 (p = 0.05, moe = 0.020)
n_prop(p = 0.05, moe = 0.02, method = "wilson")
#> Sample size for proportion (wilson)
#> n = 469 (p = 0.05, moe = 0.020)
n_prop(p = 0.05, moe = 0.02, method = "logodds")
#> Sample size for proportion (logodds)
#> n = 475 (p = 0.05, moe = 0.020)

Target a coefficient of variation instead of a margin of error:

n_prop(p = 0.70, cv = 0.05)
#> Sample size for proportion (wald)
#> n = 172 (p = 0.70, cv = 0.050)

Means

Estimate average household expenditure (variance = 40,000, mean = 800) with a margin of error of 30:

n_mean(var = 40000, moe = 30)
#> Sample size for mean
#> n = 171 (var = 40000.00, moe = 30.000)

Common parameters

All n_* and prec_* functions accept:

Parameter	Meaning
deff	Design effect multiplier (default 1)
N	Finite population size (enables FPC correction)
alpha	Significance level (default 0.05)
resp_rate	Expected response rate (inflates n by 1/resp_rate)

n_prop(p = 0.70, moe = 0.05, deff = 1.5, N = 50000, resp_rate = 0.85)
#> Sample size for proportion (wald)
#> n = 566 (net: 481) (p = 0.70, moe = 0.050, deff = 1.50, resp_rate = 0.85)

The design effect can be less than 1 for efficient designs (e.g. well-stratified or PPS samples). svyplan accepts any deff > 0.

Evaluating precision

The prec_*() functions answer the reverse question: given a fixed sample size, what precision can you achieve?

prec_prop(p = 0.3, n = 400)
#> Sampling precision for proportion (wald)
#> n = 400
#> se = 0.0229, moe = 0.0449, cv = 0.0764

prec_mean(var = 40000, n = 300, mu = 800)
#> Sampling precision for mean
#> n = 300
#> se = 11.5470, moe = 22.6317, cv = 0.0144

Design parameters work identically:

prec_prop(p = 0.3, n = 400, deff = 1.5, resp_rate = 0.85)
#> Sampling precision for proportion (wald)
#> n = 400 (net: 340)
#> se = 0.0304, moe = 0.0597, cv = 0.1015

Confidence intervals

confint() extracts the expected confidence interval from any sample size or precision object:

s <- n_prop(p = 0.3, moe = 0.05)
confint(s)
#>  2.5 % 97.5 %
#>   0.25   0.35

pr <- prec_prop(p = 0.3, n = 400)
confint(pr)
#>      2.5 %    97.5 %
#>  0.2550916 0.3449084

confint(pr, level = 0.99)
#>      0.5 %    99.5 %
#>  0.2409803 0.3590197

For proportions, the interval is clamped to [0, 1].

Multi-indicator surveys

Household surveys like Demographic and Health Surveys (DHS) or Multiple Indicator Cluster Survey (MICS) track many indicators simultaneously. Each indicator has its own expected prevalence, precision target, and design effect. n_multi() finds the sample size that satisfies all targets at once.

targets <- data.frame(
  name = c("stunting", "vaccination", "anemia"),
  p    = c(0.25, 0.70, 0.12),
  moe  = c(0.05, 0.05, 0.03),
  deff = c(2.0, 1.5, 2.5)
)

n_multi(targets)
#> Multi-indicator sample size
#> n = 1127 (binding: anemia)
#> ---
#>  name        .n   .binding
#>  stunting     577         
#>  vaccination  485         
#>  anemia      1127 *

The binding indicator (marked with *) drives the overall sample size. The other indicators are estimated with better precision than requested.

Achieved precision

prec_multi() computes the achieved precision for each indicator at the chosen n:

plan <- n_multi(targets)
prec_multi(plan)
#> Multi-indicator sampling precision
#>  name        .se        .moe .cv       
#>  stunting    0.02551067 0.05 0.10204269
#>  vaccination 0.02551067 0.05 0.03644382
#>  anemia      0.01530640 0.03 0.12755336

Domain targets

Surveys often need adequate precision within subpopulations (urban/rural, regions). Add domain columns to the targets data frame and n_multi() optimizes each domain separately:

targets_dom <- data.frame(
  name       = rep(c("stunting", "vaccination", "anemia"), each = 2),
  residence  = rep(c("urban", "rural"), 3),
  p          = c(0.18, 0.32, 0.80, 0.60, 0.08, 0.16),
  moe        = c(0.05, 0.05, 0.05, 0.05, 0.03, 0.03),
  deff       = c(1.5, 2.5, 1.2, 1.8, 2.0, 3.0)
)

n_multi(targets_dom)
#> Treating column(s) 'residence' as domain variable(s)
#> Multi-indicator sample size (2 domains)
#> n = 1721 (binding: anemia)
#> ---
#>  residence .n   .binding
#>  rural     1721 anemia  
#>  urban      629 anemia

Any column not recognized as a standard parameter (name, p, moe, deff, etc.) is automatically treated as a domain variable.

Minimum sample size per domain

The min_n parameter sets a floor for the per-domain sample size:

n_multi(targets_dom, min_n = 300)
#> Treating column(s) 'residence' as domain variable(s)
#> Multi-indicator sample size (2 domains, min_n = 300)
#> n = 1721 (binding: anemia)
#> ---
#>  residence .n   .binding
#>  rural     1721 anemia  
#>  urban      629 anemia

Mixing proportions and means

Targets can mix proportion and mean indicators. Use var and mu columns for means (leave p as NA), and p for proportions (leave var/mu as NA):

targets_mixed <- data.frame(
  name = c("vaccination", "expenditure"),
  p    = c(0.70, NA),
  var  = c(NA, 40000),
  mu   = c(NA, 800),
  cv   = c(0.05, 0.10),
  deff = c(1.5, 2.0)
)

n_multi(targets_mixed)
#> Multi-indicator sample size
#> n = 258 (binding: vaccination)
#> ---
#>  name        .n  .binding
#>  vaccination 258 *       
#>  expenditure  13

Multistage cluster designs

For two-stage or three-stage designs, the question is not just “how many?” but “how many clusters and how many units per cluster?” The answer depends on the cost structure and the degree of clustering.

Variance components from frame data

If frame data with cluster identifiers is available, varcomp() estimates between-cluster and within-cluster variance components:

set.seed(1)
n_clust <- 80
n_hh <- 15
cluster_id <- rep(seq_len(n_clust), each = n_hh)
cluster_mean <- rnorm(n_clust, mean = 50, sd = 10)
expenditure <- cluster_mean[cluster_id] + rnorm(n_clust * n_hh, sd = 20)
frame <- data.frame(cluster = cluster_id, expenditure = expenditure)

vc <- varcomp(expenditure ~ cluster, data = frame)
vc
#> Variance components (2-stage)
#> varb = 0.0398, varw = 0.1700
#> delta = 0.1896
#> k = 1.0589
#> Unit relvariance = 0.1981

The delta value is the measure of homogeneity (intraclass correlation). It feeds directly into n_cluster() and design_effect().

Optimal two-stage allocation

Given per-stage costs and the variance structure, n_cluster() finds the allocation that either minimizes cost for a target CV, or minimizes CV for a given budget:

# Minimize cost to achieve CV = 0.05
n_cluster(cost = c(500, 50), delta = vc, cv = 0.05)
#> Optimal 2-stage allocation
#> n_psu = 27 | psu_size = 7 -> total n = 189 (unrounded: 171.9801)
#> cv = 0.0500, cost = 21751

# Maximize precision within a budget
n_cluster(cost = c(500, 50), delta = vc, budget = 100000)
#> Optimal 2-stage allocation
#> n_psu = 121 | psu_size = 7 -> total n = 847 (unrounded: 790.6791)
#> cv = 0.0233, cost = 100000

Passing delta = vc (the varcomp object) automatically extracts delta, rel_var, and k.

Three-stage designs

Add a third cost element and a second delta for three-stage designs:

n_cluster(
  cost  = c(1000, 200, 20),
  delta = c(0.01, 0.05),
  cv    = 0.05
)
#> Optimal 3-stage allocation
#> n_psu = 14 | psu_size = 6 | ssu_size = 14 -> total n = 1176 (unrounded: 931.3619)
#> cv = 0.0500, cost = 45654

Response rate in cluster designs

In budget mode, applying a response rate does not change the allocation (the budget constrains the design); instead, the achieved CV worsens. In CV mode, the first-stage sample is inflated by 1/resp_rate:

n_cluster(cost = c(500, 50), delta = vc, cv = 0.05, resp_rate = 0.90)
#> Optimal 2-stage allocation
#> n_psu = 30 | psu_size = 7 -> total n = 210 (unrounded: 191.089, net: 189)
#> cv = 0.0500, cost = 24168

Fixed overhead costs

The standard cost model is purely linear: C = c1*n_psu + c2*n_psu*psu_size. Real surveys also have a fixed overhead (training, infrastructure, setup). The fixed_cost parameter adds this term: C = C0 + c1*n_psu + c2*n_psu*psu_size. In budget mode, only budget - fixed_cost is available for the variable component, reducing n_psu while leaving the optimal psu_size/n_psu ratio unchanged. In CV mode, all sample sizes stay the same and fixed_cost is simply added to the total cost:

# Budget mode: fixed overhead reduces the allocatable budget
n_cluster(cost = c(500, 50), delta = vc, budget = 100000, fixed_cost = 5000)
#> Optimal 2-stage allocation
#> n_psu = 115 | psu_size = 7 -> total n = 805 (unrounded: 751.1452)
#> cv = 0.0239, cost = 100000 (fixed: 5000)

# CV mode: same allocation, cost increases by fixed_cost
n_cluster(cost = c(500, 50), delta = vc, cv = 0.05, fixed_cost = 5000)
#> Optimal 2-stage allocation
#> n_psu = 27 | psu_size = 7 -> total n = 189 (unrounded: 171.9801)
#> cv = 0.0500, cost = 26751 (fixed: 5000)

The same parameter is available in n_multi() for multistage multi-indicator designs.

Evaluating cluster allocations

prec_cluster() computes the achieved CV for any allocation:

alloc <- n_cluster(cost = c(500, 50), delta = vc, budget = 100000)
prec_cluster(alloc)
#> Sampling precision for 2-stage cluster
#> n_psu = 121 | psu_size = 7 -> total n = 847
#> cv = 0.0233

# Arbitrary allocation
prec_cluster(n = c(50, 12), delta = 0.05)
#> Sampling precision for 2-stage cluster
#> n_psu = 50 | psu_size = 12 -> total n = 600
#> cv = 0.0508

Design effects

The cluster design effect formula deff = 1 + (psu_size - 1) * delta links cluster size to precision loss:

design_effect(delta = 0.05, psu_size = 20, method = "cluster")
#> [1] 1.95

After data collection, compute the realized design effect from survey weights:

set.seed(123)
w <- runif(500, 0.5, 4)
design_effect(w, method = "kish")
#> [1] 1.198255
effective_n(w, method = "kish")
#> [1] 417.2735

Multi-indicator multistage

For surveys with multiple indicators in a cluster design, provide delta_psu columns and a cost/budget to n_multi():

targets_ms <- data.frame(
  name   = c("stunting", "vaccination"),
  p      = c(0.25, 0.70),
  cv     = c(0.10, 0.08),
  delta_psu = c(0.05, 0.02)
)

n_multi(targets_ms, cost = c(500, 50), budget = 80000)
#> Multi-indicator optimal allocation (2-stage)
#> n_psu = 68 | psu_size = 14 -> total n = 952 (unrounded: 927.2796)
#> cv = 0.0728, cost = 80000 (binding: stunting)
#> ---
#>  name        .cv_target .cv_achieved .binding
#>  stunting    0.10       0.0728       *       
#>  vaccination 0.08       0.0241

Optimal strata boundaries

When a continuous auxiliary variable is available on the frame, strata_bound() finds the cut points that minimize the sample size (or CV) for a given number of strata.

set.seed(12345)
x <- rlnorm(5000, meanlog = 6, sdlog = 1.2)

strata_bound(x, n_strata = 4, n = 300, method = "cumrootf")
#> Strata boundaries (Dalenius-Hodges, 4 strata)
#> Boundaries: 400.0, 1200.0, 3100.0
#> n = 300, cv = 0.0199
#> Allocation: neyman
#> ---
#>  stratum lower       upper    N_h  W_h   S_h    n_h
#>  1          3.826706   400.00 2473 0.495 105.3   48
#>  2        400.000000  1200.00 1647 0.329 222.7   68
#>  3       1200.000000  3100.00  672 0.134 519.5   65
#>  4       3100.000000 21957.85  208 0.042 3094.3 119

Four methods are available:

Method	Algorithm	Speed	Best for
"cumrootf"	Dalenius-Hodges cumulative root frequency	Fast	General use
"geo"	Geometric progression	Fast	Skewed data
"lh"	Lavall0e9e-Hidiroglou iterative	Moderate	Skewed data
"kozak"	Kozak random search	Slow	Global optimum

The Kozak method often finds better boundaries for highly skewed distributions:

strata_bound(x, n_strata = 4, cv = 0.05, method = "kozak")
#> Strata boundaries (Kozak, 4 strata)
#> Boundaries: 405.6, 1219.3, 3447.4
#> n = 59, cv = 0.0500
#> Allocation: neyman
#> ---
#>  stratum lower       upper      N_h  W_h   S_h    n_h
#>  1          3.826706   405.6271 2494 0.499 106.6  10 
#>  2        405.627119  1219.2788 1645 0.329 226.7  14 
#>  3       1219.278753  3447.3536  690 0.138 589.2  15 
#>  4       3447.353550 21957.8496  171 0.034 3206.8 20

Allocation methods

Allocation within strata is controlled by the alloc parameter:

• "proportional": $n_h \propto N_h$
• "neyman" (default): $n_h \propto N_h \cdot S_h$ (minimizes national CV)
• "optimal": $n_h \propto N_h \cdot S_h / \sqrt{c_h}$ (accounts for costs)
• "power": Bankier (1988) compromise, $n_h \propto S_h \cdot N_h^{power\_q}$, where $power\_q \in [0, 1]$ controls the trade-off between national precision ($power\_q = 1$, Neyman) and equal subnational CVs ($power\_q = 0$)

# Bankier power allocation (compromise, power_q = 0.5)
strata_bound(x, n_strata = 4, n = 300, alloc = "power", power_q = 0.5)
#> Strata boundaries (Lavallee-Hidiroglou, 4 strata)
#> Boundaries: 456.3, 1354.4, 4360.4
#> n = 300, cv = 0.0216
#> Allocation: power (power_q = 0.50)
#> Converged: yes
#> ---
#>  stratum lower       upper      N_h  W_h   S_h    n_h
#>  1          3.826706   456.3167 2710 0.542 120.7   34
#>  2        456.316687  1354.3749 1529 0.306 244.5   52
#>  3       1354.374865  4360.3970  650 0.130 743.3  103
#>  4       4360.396977 21957.8496  111 0.022 3441.5 111

Classifying new observations

predict() applies the learned boundaries to new data, returning a factor:

sb <- strata_bound(x, n_strata = 4, n = 200, method = "cumrootf")
new_x <- c(100, 500, 1500, 5000)
predict(sb, newdata = new_x, labels = paste0("S", 1:4))
#> [1] S1 S2 S3 S4
#> Levels: S1 S2 S3 S4

Visualizing allocation

plot() shows the sampling fraction per stratum. Under Neyman allocation, high-variance strata are sampled more intensively. The dashed line marks the overall fraction:

plot(sb)

Power analysis

Precision analysis answers “how precisely can we estimate a level?” Power analysis answers a different question: “can we detect a change or difference between two groups or time points?”

Sample size for a detectable change

A survey measured vaccination coverage at 70%. How many households are needed in a follow-up to detect a 5 percentage point increase with 80% power?

power_prop(p1 = 0.70, p2 = 0.75, power = 0.80)
#> Power analysis for proportions (solved for sample size)
#> n = 1248 (per group), power = 0.800, effect = 0.0500
#> (p1 = 0.700, p2 = 0.750, alpha = 0.05)

With a design effect:

power_prop(p1 = 0.70, p2 = 0.75, power = 0.80, deff = 2.0)
#> Power analysis for proportions (solved for sample size)
#> n = 2496 (per group), power = 0.800, effect = 0.0500
#> (p1 = 0.700, p2 = 0.750, alpha = 0.05, deff = 2.00)

Three solve modes

power_prop() and power_mean() each solve for whichever of n, power, or the effect size is left unspecified:

# Solve for n (default when p2 and power given)
power_prop(p1 = 0.70, p2 = 0.75, power = 0.80, deff = 2.0)
#> Power analysis for proportions (solved for sample size)
#> n = 2496 (per group), power = 0.800, effect = 0.0500
#> (p1 = 0.700, p2 = 0.750, alpha = 0.05, deff = 2.00)

# Solve for power (set power = NULL)
power_prop(p1 = 0.70, p2 = 0.75, n = 1500, power = NULL, deff = 2.0)
#> Power analysis for proportions (solved for power)
#> n = 1500 (per group), power = 0.584, effect = 0.0500
#> (p1 = 0.700, p2 = 0.750, alpha = 0.05, deff = 2.00)

# Solve for MDE (omit p2)
power_prop(p1 = 0.70, n = 1500, deff = 2.0)
#> Power analysis for proportions (solved for minimum detectable effect)
#> n = 1500 (per group), power = 0.800, effect = 0.0639
#> (p1 = 0.700, p2 = 0.764, alpha = 0.05, deff = 2.00)

Panel surveys

If the follow-up resamples a fraction of the original households and the between-round correlation is known, the required sample size drops:

power_prop(p1 = 0.70, p2 = 0.75, power = 0.80, deff = 2.0,
           overlap = 0.50, rho = 0.6)
#> Power analysis for proportions (solved for sample size)
#> n = 1749 (per group), power = 0.800, effect = 0.0500
#> (p1 = 0.700, p2 = 0.750, alpha = 0.05, deff = 2.00, overlap = 0.50, rho = 0.60)

Continuous outcomes

The same three solve modes work for means:

# Sample size to detect a difference of 5 (within-group var = 200)
power_mean(effect = 5, var = 200)
#> Power analysis for means (solved for sample size)
#> n = 126 (per group), power = 0.800, effect = 5.0000
#> (alpha = 0.05)

# MDE with n = 400 per group
power_mean(var = 200, n = 400)
#> Power analysis for means (solved for minimum detectable effect)
#> n = 400 (per group), power = 0.800, effect = 2.8016
#> (alpha = 0.05)

Power curve

plot() draws the power-vs-sample-size curve with reference lines at the solved point:

pw <- power_prop(p1 = 0.70, p2 = 0.75, power = 0.80, deff = 2.0)
plot(pw)

Sensitivity analysis

How sensitive is a sample size to assumptions about the design effect, response rate, or prevalence? The predict() method evaluates any svyplan result at new parameter combinations.

Varying design parameters

x <- n_prop(p = 0.3, moe = 0.05, deff = 1.5)
predict(x, expand.grid(
  deff = c(1.0, 1.5, 2.0, 2.5),
  resp_rate = c(0.8, 0.9, 1.0)
))
#>    deff resp_rate         n         se  moe         cv
#> 1   1.0       0.8  403.3532 0.02551067 0.05 0.08503558
#> 2   1.5       0.8  605.0298 0.02551067 0.05 0.08503558
#> 3   2.0       0.8  806.7064 0.02551067 0.05 0.08503558
#> 4   2.5       0.8 1008.3829 0.02551067 0.05 0.08503558
#> 5   1.0       0.9  358.5362 0.02551067 0.05 0.08503558
#> 6   1.5       0.9  537.8042 0.02551067 0.05 0.08503558
#> 7   2.0       0.9  717.0723 0.02551067 0.05 0.08503558
#> 8   2.5       0.9  896.3404 0.02551067 0.05 0.08503558
#> 9   1.0       1.0  322.6825 0.02551067 0.05 0.08503558
#> 10  1.5       1.0  484.0238 0.02551067 0.05 0.08503558
#> 11  2.0       1.0  645.3651 0.02551067 0.05 0.08503558
#> 12  2.5       1.0  806.7064 0.02551067 0.05 0.08503558

Cluster budget scenarios

cl <- n_cluster(cost = c(500, 50), delta = 0.05, budget = 100000)
predict(cl, data.frame(budget = c(50000, 100000, 150000, 200000)))
#>   budget     n_psu psu_size   total_n         cv   cost
#> 1  50000  42.04499 13.78405  579.5501 0.05318275  50000
#> 2 100000  84.08997 13.78405 1159.1003 0.03760588 100000
#> 3 150000 126.13496 13.78405 1738.6504 0.03070507 150000
#> 4 200000 168.17994 13.78405 2318.2006 0.02659137 200000

Power curves

pw <- power_prop(p1 = 0.30, p2 = 0.35, n = 500, power = NULL)
predict(pw, data.frame(n = seq(200, 1000, 200)))
#>      n     power effect
#> 1  200 0.1877131   0.05
#> 2  400 0.3272968   0.05
#> 3  600 0.4569385   0.05
#> 4  800 0.5707088   0.05
#> 5 1000 0.6665884   0.05

Precision by sample size

pr <- prec_prop(p = 0.3, n = 400)
predict(pr, data.frame(n = c(100, 200, 400, 800, 1600)))
#>      n         se        moe         cv
#> 1  100 0.04582576 0.08981683 0.15275252
#> 2  200 0.03240370 0.06351009 0.10801234
#> 3  400 0.02291288 0.04490842 0.07637626
#> 4  800 0.01620185 0.03175505 0.05400617
#> 5 1600 0.01145644 0.02245421 0.03818813

Putting it all together

A typical planning sequence for a national household survey ties several svyplan functions together:

1. Define indicators and precision targets per domain
2. Compute sample sizes with n_multi()
3. Evaluate achieved precision with prec_multi()
4. Run sensitivity analysis with predict()
5. If frame data is available, estimate variance components with varcomp()
6. Optimize the multistage allocation with n_cluster() or n_multi() with costs
7. Determine strata boundaries with strata_bound()
8. Check that the design has adequate power with power_prop() / power_mean()

# 1-2: multi-indicator sample size with domain targets
targets <- data.frame(
  name = c("stunting", "vaccination", "anemia"),
  p    = c(0.25, 0.70, 0.12),
  moe  = c(0.05, 0.05, 0.03),
  deff = c(2.0, 1.5, 2.5)
)
plan <- n_multi(targets)
plan
#> Multi-indicator sample size
#> n = 1127 (binding: anemia)
#> ---
#>  name        .n   .binding
#>  stunting     577         
#>  vaccination  485         
#>  anemia      1127 *

# 3: achieved precision for each indicator
prec_multi(plan)
#> Multi-indicator sampling precision
#>  name        .se        .moe .cv       
#>  stunting    0.02551067 0.05 0.10204269
#>  vaccination 0.02551067 0.05 0.03644382
#>  anemia      0.01530640 0.03 0.12755336

# 4: how sensitive is the binding indicator to the response rate?
predict(
  n_prop(p = 0.25, moe = 0.05, deff = 2.0),
  data.frame(resp_rate = c(0.7, 0.8, 0.9, 1.0))
)
#>   resp_rate        n         se  moe        cv
#> 1       0.7 823.1697 0.02551067 0.05 0.1020427
#> 2       0.8 720.2735 0.02551067 0.05 0.1020427
#> 3       0.9 640.2431 0.02551067 0.05 0.1020427
#> 4       1.0 576.2188 0.02551067 0.05 0.1020427

# 8: can we detect a 5pp decline in stunting with this sample?
power_prop(
  p1 = 0.25, p2 = 0.20,
  n = as.integer(plan), power = NULL,
  deff = 2.0
)
#> Power analysis for proportions (solved for power)
#> n = 1127 (per group), power = 0.521, effect = 0.0500
#> (p1 = 0.250, p2 = 0.200, alpha = 0.05, deff = 2.00)

All svyplan output objects support as.integer() (ceiling of n) and as.double() (exact n), making it straightforward to pass results between functions or into other packages.