Function to conduct a statistical test with the null hypothesis that there is no "design effect" in a list experiment, a failure of the experiment.

ict.test(y, treat, J = NA, alpha = 0.05, n.draws = 250000, gms = TRUE, pi.table = TRUE)

y | A numerical vector containing the response data for a list experiment. |
---|---|

treat | A numerical vector containing the binary treatment status for a list experiment. |

J | Number of non-sensitive (control) survey items. |

alpha | Confidence level for the statistical test. |

n.draws | Number of Monte Carlo draws. |

gms | A logical value indicating whether the generalized moment selection procedure should be used. |

pi.table | A logical value indicating whether a table of estimated proportions of respondent types with standard errors is displayed. |

`ict.test`

returns a numerical scalar with the
Bonferroni-corrected minimum p-value of the statistical test.

This function allows the user to perform a statistical test on data from a list experiment or item count technique with the null hypothesis of no design effect. A design effect occurs when an individual's response to the non-sensitive items changes depending upon the respondent's treatment status.

Blair, Graeme and Kosuke Imai. (2012) ``Statistical Analysis of List Experiments." Political Analysis, Vol. 20, No 1 (Winter). available at http://imai.princeton.edu/research/listP.html

`ictreg`

for list experiment regression based on the
assumption of no design effect

data(affirm) data(race) # Conduct test with null hypothesis that there is no design effect # Replicates results on Blair and Imai (2010) pg. 30 test.value.affirm <- ict.test(affirm$y, affirm$treat, J = 3, gms = TRUE) print(test.value.affirm)#> #> Test for List Experiment Design Effects #> #> Estimated population proportions #> est. s.e. #> pi(Y_i(0) = 0, Z_i = 1) -0.0019 0.0070 #> pi(Y_i(0) = 1, Z_i = 1) 0.0882 0.0229 #> pi(Y_i(0) = 2, Z_i = 1) 0.1696 0.0287 #> pi(Y_i(0) = 3, Z_i = 1) 0.2388 0.0177 #> pi(Y_i(0) = 0, Z_i = 0) 0.0155 0.0051 #> pi(Y_i(0) = 1, Z_i = 0) 0.1359 0.0155 #> pi(Y_i(0) = 2, Z_i = 0) 0.2073 0.0271 #> pi(Y_i(0) = 3, Z_i = 0) 0.1466 0.0267 #> #> Y_i(0) is the (latent) count of 'yes' responses to the control items. Z_i is the (latent) binary response to the sensitive item. #> #> Bonferroni-corrected p-value #> If this value is below alpha, you reject the null hypothesis of no design effect. If it is above alpha, you fail to reject the null. #> #> Sensitive Item TRUE #> 0.7881128 #>test.value.race <- ict.test(race$y, race$treat, J = 3, gms = TRUE) print(test.value.race)#> #> Test for List Experiment Design Effects #> #> Estimated population proportions #> est. s.e. #> pi(Y_i(0) = 0, Z_i = 1) -0.0169 0.0084 #> pi(Y_i(0) = 1, Z_i = 1) 0.0101 0.0243 #> pi(Y_i(0) = 2, Z_i = 1) 0.0200 0.0281 #> pi(Y_i(0) = 3, Z_i = 1) 0.0545 0.0091 #> pi(Y_i(0) = 0, Z_i = 0) 0.0304 0.0069 #> pi(Y_i(0) = 1, Z_i = 0) 0.2140 0.0174 #> pi(Y_i(0) = 2, Z_i = 0) 0.3569 0.0263 #> pi(Y_i(0) = 3, Z_i = 0) 0.3309 0.0220 #> #> Y_i(0) is the (latent) count of 'yes' responses to the control items. Z_i is the (latent) binary response to the sensitive item. #> #> Bonferroni-corrected p-value #> If this value is below alpha, you reject the null hypothesis of no design effect. If it is above alpha, you fail to reject the null. #> #> Sensitive Item 1 #> 0.04431109 #>