Methods
Confidence interval
#
StatsAPI.confint
— Function
confint(test::BinomialTest; level = 0.95, tail = :both, method = :clopper_pearson)
Compute a confidence interval with coverage level
for a binomial proportion using one of the following methods. Possible values for method
are:
-
:clopper_pearson
(default): Clopper-Pearson interval is based on the binomial distribution. The empirical coverage is never less than the nominal coverage oflevel
; it is usually too conservative. -
:wald
: Wald (or normal approximation) interval relies on the standard approximation of the actual binomial distribution by a normal distribution. Coverage can be erratically poor for success probabilities close to zero or one. -
:waldcc
: Wald interval with a continuity correction that extends the interval by1/2n
on both ends. -
:wilson
: Wilson score interval relies on a normal approximation. In contrast to:wald
, the standard deviation is not approximated by an empirical estimate, resulting in good empirical coverages even for small numbers of draws and extreme success probabilities. -
:jeffrey
: Jeffreys interval is a Bayesian credible interval obtained by using a non-informative Jeffreys prior. The interval is very similar to the Wilson interval. -
:agresti_coull
: Agresti-Coull interval is a simplified version of the Wilson interval; both are centered around the same value. The Agresti Coull interval has higher or equal coverage. -
:arcsine
: Confidence interval computed using the arcsine transformation to make independent of the probability .
References
-
Brown, L.D., Cai, T.T., and DasGupta, A. Interval estimation for a binomial proportion. Statistical Science, 16(2):101—117, 2001.
-
Pires, Ana & Amado, Conceição. (2008). Interval Estimators for a Binomial Proportion: Comparison of Twenty Methods. REVSTAT. 6. 10.57805/revstat.v6i2.63.
External links
confint(x::FisherExactTest; level::Float64=0.95, tail=:both, method=:central)
Compute a confidence interval with coverage level
. One-sided intervals are based on Fisher’s non-central hypergeometric distribution. For tail = :both
, the only method
implemented yet is the central interval (:central
).
Since the p-value is not necessarily unimodal, the corresponding confidence region might not be an interval. |
References
-
Gibbons, J.D, Pratt, J.W. P-values: Interpretation and Methodology, American Statistican, 29(1):20-25, 1975.
-
Fay, M.P., Supplementary material to "Confidence intervals that match Fisher’s exact or Blaker’s exact tests". Biostatistics, Volume 11, Issue 2, 1 April 2010, Pages 373—374, link
confint(test::PowerDivergenceTest; level = 0.95, tail = :both, method = :auto)
Compute a confidence interval with coverage level
for multinomial proportions using one of the following methods. Possible values for method
are:
-
:auto
(default): If the minimum of the expected cell counts exceeds 100, Quesenberry-Hurst intervals are used, otherwise Sison-Glaz. -
:sison_glaz
: Sison-Glaz intervals -
:bootstrap
: Bootstrap intervals -
:quesenberry_hurst
: Quesenberry-Hurst intervals -
:gold
: Gold intervals (asymptotic simultaneous intervals)
References
-
Agresti, Alan. Categorical Data Analysis, 3rd Edition. Wiley, 2013.
-
Sison, C.P and Glaz, J. Simultaneous confidence intervals and sample size determination for multinomial proportions. Journal of the American Statistical Association, 90:366-369, 1995.
-
Quesensberry, C.P. and Hurst, D.C. Large Sample Simultaneous Confidence Intervals for Multinational Proportions. Technometrics, 6:191-195, 1964.
-
Gold, R. Z. Tests Auxiliary to Tests in a Markov Chain. Annals of Mathematical Statistics, 30:56-74, 1963.
p-value
#
StatsAPI.pvalue
— Function
pvalue(x::FisherExactTest; tail = :both, method = :central)
Compute the p-value for a given Fisher exact test.
The one-sided p-values are based on Fisher’s non-central hypergeometric distribution with odds ratio :
For tail = :both
, possible values for method
are:
-
:central
(default): Central interval, i.e. the p-value is two times the minimum of the one-sided p-values. -
:minlike
: Minimum likelihood interval, i.e. the p-value is computed by summing all tables with the same marginals that are equally or less probable:
References
-
Gibbons, J.D., Pratt, J.W., P-values: Interpretation and Methodology, American Statistican, 29(1):20-25, 1975.
-
Fay, M.P., Supplementary material to "Confidence intervals that match Fisher’s exact or Blaker’s exact tests". Biostatistics, Volume 11, Issue 2, 1 April 2010, Pages 373—374, link