# deffS: Spencer design effect for _pps_ sampling In PracTools: Tools for Designing and Weighting Survey Samples

 deffS R Documentation

## Spencer design effect for pps sampling

### Description

Compute the Spencer design effect for single-stage samples selected with probability proportional to a measure of size.

### Usage

```deffS(p, w, y)
```

### Arguments

 `p` vector of 1-draw selection probabilities, i.e., the probability that each unit would be selected in a sample of size 1. `w` vector of inverses of selection probabilities for a sample `y` vector of the sample values of an analysis variable

### Details

The Spencer design effect is the ratio of the variance of the pwr-estimator of the total of y, assuming that a single-stage sample is selected with replacement, to the variance of the total estimated in srswr. Varying selection probabilities can be used.

### Value

numeric design effect

### Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

### References

Park, I., and Lee, H. (2004). Design Effects for the Weighted Mean and Total Estimators under Complex Survey Sampling. Survey Methodology, 30, 183-193.

Spencer, B. D. (2000). An Approximate Design Effect for Unequal Weighting When Measurements May Correlate With Selection Probabilities. Survey Methodology, 26, 137-138.

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 14). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

`deff`, `deffCR`, `deffH`, `deffK`

### Examples

```set.seed(-500398777)
# generate population using HMT function
pop.dat <- as.data.frame(HMT())
mos <- pop.dat\$x
pop.dat\$prbs.1d <- mos / sum(mos)
# select pps sample
require(sampling)
n <- 80
pk <- n * pop.dat\$prbs.1d
sam <- UPrandomsystematic(pk)
sam <- sam==1
sam.dat <- pop.dat[sam, ]
dsgn.wts <- 1/pk[sam]
deffS(p=sam.dat\$prbs.1d, w=dsgn.wts, y=sam.dat\$y)
```

PracTools documentation built on Aug. 17, 2022, 5:06 p.m.