# power.rr.test: Power Analysis for Randomized Response In rr: Statistical Methods for the Randomized Response Technique

## Description

`power.rr.test` is used to conduct power analysis for randomized response survey designs.

## Usage

 ```1 2 3 4``` ```power.rr.test(p, p0, p1, q, design, n = NULL, r, presp, presp.null = NULL, sig.level, prespT, prespC, prespT.null = NULL, prespC.null, power = NULL, type = c("one.sample", "two.sample"), alternative = c("one.sided", "two.sided"), solve.tolerance = .Machine\$double.eps) ```

## Arguments

 `p` The probability of receiving the sensitive question (Mirrored Question Design, Unrelated Question Design); the probability of answering truthfully (Forced Response Design); the probability of selecting a red card from the 'yes' stack (Disguised Response Design). `p0` The probability of forced 'no' (Forced Response Design). `p1` The probability of forced 'yes' (Forced Response Design). `q` The probability of answering 'yes' to the unrelated question, which is assumed to be independent of covariates (Unrelated Question Design). `design` Call of design (including modified designs) used: "forced-known", "mirrored", "disguised", "unrelated-known", "forced-unknown", and "unrelated-unknown". `n` Number of observations. Exactly one of 'n' or 'power' must be NULL. `r` For the modified designs only (i.e. "forced-unknown" for Forced Response with Unknown Probability and "unrelated-unknown" for Unrelated Question with Unknown Probability), `r` is the proportion of respondents allocated to the first group, which is the group that is directed to answer the sensitive question truthfully with probability `p` as opposed to the second group which is directed to answer the sensitive question truthfully with probability `1-p`. `presp` For a one sample test, the probability of possessing the sensitive trait under the alternative hypothesis. `presp.null` For a one sample test, the probability of possessing the sensitive trait under the null hypothesis. The default is `NULL` meaning zero probability of possessing the sensitive trait. `sig.level` Significance level (Type I error probability). `prespT` For a two sample test, the probability of the treated group possessing the sensitive trait under the alternative hypothesis. `prespC` For a two sample test, the probability of the control group possessing the sensitive trait under the alternative hypothesis. `prespT.null` For a two sample test, the probability of the treated group possessing the sensitive trait under the null hypothesis. The default is `NULL` meaning there is no difference between the treated and control groups, specifically that `prespT.null` is the same as `prespC.null`, the probability of the control group possessing the sensitive trait under the null hypothesis. `prespC.null` For a two sample test, the probability of the control group possessing the sensitive trait under the null hypothesis. `power` Power of test (Type II error probability). Exactly one of 'n' or 'power' must be NULL. `type` One or two sample test. For a two sample test, the alternative and null hypotheses refer to the difference between the two samples of the probabilities of possessing the sensitive trait. `alternative` One or two sided test. `solve.tolerance` When standard errors are calculated, this option specifies the tolerance of the matrix inversion operation solve.

## Details

This function allows users to conduct power analysis for randomized response survey designs, both for the standard designs ("forced-known", "mirrored", "disguised", "unrelated-known") and modified designs ("forced-unknown", and "unrelated -unknown").

## Value

`power.rr.test` contains the following components (the inclusion of some components such as the design parameters are dependent upon the design used):

 `n` Point estimates for the effects of covariates on the randomized response item. `r` Standard errors for estimates of the effects of covariates on the randomized response item. `presp` For a one sample test, the probability of possessing the sensitive trait under the alternative hypothesis. For a two sample test, the difference between the probabilities of possessing the sensitive trait for the treated and control groups under the alternative hypothesis. `presp.null` For a one sample test, the probability of possessing the sensitive trait under the null hypothesis. For a two sample test, the difference between the probabilities of possessing the sensitive trait for the treated and control groups under the null hypothesis. `sig.level` Significance level (Type I error probability). `power` Power of test (Type II error probability). `type` One or two sample test. `alternative` One or two sided test.

## References

Blair, Graeme, Kosuke Imai and Yang-Yang Zhou. (2015) "Design and Analysis of the Randomized Response Technique." Journal of the American Statistical Association. Available at http://graemeblair.com/papers/randresp.pdf.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```## Calculate the power to detect a sensitive item proportion of .2 ## with the forced design with known probabilities of 2/3 in truth-telling group, ## 1/6 forced to say "yes" and 1/6 forced to say "no" and sample size of 200. power.rr.test(p = 2/3, p1 = 1/6, p0 = 1/6, n = 200, presp = .2, presp.null = 0, design = "forced-known", sig.level = .01, type = "one.sample", alternative = "one.sided") ## Not run: ## Find power varying the number of respondents from 250 to 2500 and ## the population proportion of respondents possessing the sensitive ## trait from 0 to .15 presp.seq <- seq(from = 0, to = .15, by = .0025) n.seq <- c(250, 500, 1000, 2000, 2500) power <- list() for(n in n.seq) { power[[n]] <- rep(NA, length(presp.seq)) for(i in 1:length(presp.seq)) power[[n]][i] <- power.rr.test(p = 2/3, p1 = 1/6, p0 = 1/6, n = n, presp = presp.seq[i], presp.null = 0, design = "forced-known", sig.level = .01, type = "one.sample", alternative = "one.sided")\$power } ## Replicates the results for Figure 2 in Blair, Imai, and Zhou (2014) ## End(Not run) ```

rr documentation built on May 29, 2017, 9:26 p.m.