Computes the callback shares and their confidence intervals. The analysis is restricted to the tests with at least one callback. It is the definition used in Riach and Rich (2006).
stat_tcs(x, method = "student", level = 0.95)A list with class "callback_stat" containing 4 components: specif,
counts, props and stats
specif: A list containing
convention: string "total callback shares".
cid: convention on 3 characters.
method: the estimation method, "cp" for Clopper-Pearson, "wilson" for Wilson and "student" for "Student" (the default).
level: the level of the confidence intervals (0.95 by default).
source: the R stats function used to compute the statistics (binom.test, prop.test or t.test).
name: the name of the statistic (Fisher, Pearson or Student).
counts: a data frame with the callback counts.
tests: number of tests.
callback: number of tests with at least one callback for either candidate.
disc: number of discrimination cases.
c00: number of test without a callback.
c10: number of tests with callbacks for candidate 1 only.
c01: number of tests with callbacks for candidate 2 only.
c11: number of tests with callbacks for both candidates.
props: A data frame containing the following proportions and their
confidence intervals (when relevant)
inf_p_cand1: 1st candidate total callback share, lower bound.
p_cand1: 1st candidate total callback share.
sup_p_cand1: 1st candidate total callback share, upper bound.
inf_p_cand2: 2nd candidate total callback share, lower bound.
p_cand2: 2nd candidate total callback share.
sup_p_cand2: 2nd candidate total callback share, upper bound.
inf_p_equal: equal treatment total callback share, lower bound.
p_equal: equal treatment total callback share.
sup_p_equal: equal treatment total callback share, upper bound.
inf_cand_dif: p_cand1-p_cand2, lower bound.
p_cand_dif: total callback share difference between the candidates.
sup_cand_dif: p_cand1-p_cand2, upper bound.
stats: a data frame containing the statistics for testing the equality
of proportions.
statistic: the value of the test statistic.
p_stat: the p-value of the test statistic.
c_stat: the significance code of the test statistic.
a callback object.
estimation method, "cp" for Clopper-Pearson, "wilson" for Wilson and "student" for Student (the default).
the level of the confidence intervals (0.95 by default).
Emmanuel Duguet
Clopper, C. J. & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26, 404–413. doi:10.2307/2331986.
Riach, P. A., & Rich, J. (2006). An experimental investigation of sexual discrimination in hiring in the English labor market. The BE Journal of Economic Analysis & Policy, 6(2),
Student. (1908). The Probable Error of a Mean. Biometrika, 6(1), 1–25. doi:10.2307/2331554.
Wilson, E.B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22, 209–212. doi:10.2307/2276774.
data(labour1)
x <- callback(data=labour1,cluster="offer",candid="hist",callback="callback")
str(stat_tcs(x))
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