# Power Analysis for Randomized Response

### Description

`power.rr.test`

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

### Usage

1 2 3 4 |

### 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), |

`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 |

`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 |

`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)
``` |