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 lengthAll: Expected Length summary calculation using 6 base methods...
Expected Length summary calculation using 6 base methods (Wald, WaldT, Likelihood, Score, LogitWald, ArcSine)
Description
Expected Length summary calculation using 6 base methods (Wald, WaldT, Likelihood, Score, LogitWald, ArcSine)
Usage
1  lengthAll(n, alp, a, b)

Arguments
n 
 Number of trials 
alp 
 Alpha value (significance level required) 
a 
 Beta parameters for hypo "p" 
b 
 Beta parameters for hypo "p" 
Details
The sum of length for 6 base methods (Wald, WaldT, Likelihood, Score, LogitWald, ArcSine) for n
given alpha alp
and Beta parameters a
, b
Value
A dataframe with
sumLen 
The sum of the expected length 
explMean 
The mean of the expected length 
explSD 
The Standard Deviation of the expected length 
explMax 
The max of the expected length 
explLL 
The Lower limit of the expected length calculated using mean  SD 
explUL 
The Upper limit of the expected length calculated using mean + SD 
method 
The name of the method 
References
[1] 1993 Vollset SE. Confidence intervals for a binomial proportion. Statistics in Medicine: 12; 809  824.
[2] 1998 Agresti A and Coull BA. Approximate is better than "Exact" for interval estimation of binomial proportions. The American Statistician: 52; 119  126.
[3] 1998 Newcombe RG. Twosided confidence intervals for the single proportion: Comparison of seven methods. Statistics in Medicine: 17; 857  872.
[4] 2001 Brown LD, Cai TT and DasGupta A. Interval estimation for a binomial proportion. Statistical Science: 16; 101  133.
[5] 2002 Pan W. Approximate confidence intervals for one proportion and difference of two proportions Computational Statistics and Data Analysis 40, 128, 143157.
[6] 2008 Pires, A.M., Amado, C. Interval Estimators for a Binomial Proportion: Comparison of Twenty Methods. REVSTAT  Statistical Journal, 6, 165197.
[7] 2014 Martin Andres, A. and Alvarez Hernandez, M. Twotailed asymptotic inferences for a proportion. Journal of Applied Statistics, 41, 7, 15161529
See Also
Other Expected length of base methods: PlotexplAS
,
PlotexplAll
, PlotexplBA
,
PlotexplEX
, PlotexplLR
,
PlotexplLT
, PlotexplSC
,
PlotexplTW
, PlotexplWD
,
PlotlengthAS
, PlotlengthAll
,
PlotlengthBA
, PlotlengthEX
,
PlotlengthLR
, PlotlengthLT
,
PlotlengthSC
, PlotlengthTW
,
PlotlengthWD
, lengthAS
,
lengthBA
, lengthEX
,
lengthLR
, lengthLT
,
lengthSC
, lengthTW
,
lengthWD
Examples
1 2 3 4 5  ## Not run:
n=5; alp=0.05;a=1;b=1
lengthAll(n,alp,a,b)
## End(Not run)

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 Apackageforbinomialproportion: Proportion: Let x denote the number of successes in n...
 ciAAll: CI estimation of 6 adjusted methods (Wald, WaldT,...
 ciAAllx: CI estimation of 6 adjusted methods (Wald, WaldT,...
 ciAAS: Adjusted ArcSine method of CI estimation
 ciAASx: Adjusted ArcSine method of CI estimation
 ciAll: CI estimation of 6 base methods (Wald, WaldT, Likelihood,...
 ciAllx: Specific CI estimation of 6 base methods (Wald, WaldT,...
 ciALR: Adjusted Likelihood method of CI estimation
 ciALRx: AdjustedLikelyhood Ratio method of CI estimation
 ciALT: Adjusted LogitWald method of CI estimation
 ciALTx: Adjusted LogitWald method of CI estimation
 ciAS: ArcSine method of CI estimation
 ciASC: Adjusted Score method of CI estimation
 ciASCx: Adjusted Score method of CI estimation
 ciASx: Base ArcSine method of CI estimation
 ciATW: Adjusted WALDT method of CI estimation
 ciATWx: AdjustedWALDT method of CI estimation
 ciAWD: Adjusted Wald method of CI estimation
 ciAWDx: Adjusted Wald method of CI estimation
 ciBA: Bayesian method of CI estimation with different or same...
 ciBAx: Bayesian method of CI estimation with Beta prior distribution
 ciCAll: CI estimation of 5 continuity corrected methods (Wald,...
 ciCAllx: CI estimation of 5 continuity corrected methods (Wald,...
 ciCAS: Continuity corrected ArcSine method of CI estimation
 ciCASx: Continuity corrected ArcSine method of CI estimation
 ciCLT: Continuity corrected Logit Wald method of CI estimation
 ciCLTx: Continuity corrected LogitWald method of CI estimation
 ciCSC: Continuity corrected Score method of CI estimation
 ciCSCx: Continuity corrected Score method of CI estimation
 ciCTW: Continuity corrected WaldT method of CI estimation
 ciCTWx: Continuity corrected WaldT method of CI estimation
 ciCWD: Continuity corrected Wald method of CI estimation
 ciCWDx: Continuity corrected Wald method of CI estimation
 ciEX: Exact method of CI estimation
 ciEXx: Exact method of CI estimation
 ciLR: Likelihood Ratio method of CI estimation
 ciLRx: Likelihood Ratio method of CI estimation
 ciLT: Logit Wald method of CI estimation
 ciLTx: Logit Wald method of CI estimation
 ciSC: Score method of CI estimation
 ciSCx: Base Score method of CI estimation
 ciTW: WaldT method of CI estimation
 ciTWx: WaldT method of CI estimation
 ciWD: Wald method of CI estimation
 ciWDx: Wald method of CI estimation
 covpAAll: Coverage Probability for 6 adjusted methods (Wald, WaldT,...
 covpAAS: Coverage Probability of Adjusted ArcSine method for given n
 covpAll: Coverage Probability using 6 base methods (Wald, WaldT,...
 covpALR: Coverage Probability of Adjusted Likelihood method for given...
 covpALT: Coverage Probability of Adjusted Logit Wald method for given...
 covpAS: Coverage Probability of ArcSine method
 covpASC: Coverage Probability of Adjusted Score method for given n
 covpATW: Coverage Probability of Adjusted WaldT method for given n
 covpAWD: Coverage Probability of Adjusted Wald method for given n
 covpBA: Coverage Probability of Bayesian method
 covpCAll: Coverage Probability for 5 continuity corrected methods...
 covpCAS: Coverage Probability of Continuity corrected ArcSine method
 covpCLT: Coverage Probability of Continuity corrected Logit Wald...
 covpCSC: Coverage Probability of Continuity corrected Score method
 covpCTW: Coverage Probability of Continuity corrected WaldT method
 covpCWD: Coverage Probability of Continuity corrected Wald method
 covpEX: Coverage Probability of Exact method
 covpGEN: General Coverage Probability given hypothetical "p" Coverage...
 covpLR: Coverage Probability of likelihood method
 covpLT: Coverage Probability of Logit Wald method
 covpSC: Coverage Probability of Score method
 covpSIM: Coverage Probability using simulation Coverage probability...
 covpTW: Coverage Probability of WaldT method
 covpWD: Coverage Probability of Wald method
 empericalBA: The empirical Bayesian approach for BetaBinomial model
 empericalBAx: The empirical Bayesian approach for BetaBinomial model given...
 errAAll: Calculates error, long term power and pass/fail criteria...
 errAAS: Calculates error, long term power and pass/fail criteria for...
 errAll: Calculates error, long term power and pass/fail criteria...
 errALR: Calculates error, long term power and pass/fail criteria for...
 errALT: Calculates error, long term power and pass/fail criteria for...
 errAS: Calculates error, long term power and pass/fail criteria for...
 errASC: Calculates error, long term power and pass/fail criteria for...
 errATW: Calculates error, long term power and pass/fail criteria for...
 errAWD: Calculates error, long term power and pass/fail criteria for...
 errBA: Calculates error, long term power and pass/fail criteria for...
 errCAll: Calculates error, long term power and pass/fail criteria...
 errCAS: Calculates error, long term power and pass/fail criteria for...
 errCLT: Calculates error, long term power and pass/fail criteria for...
 errCSC: Calculates error, long term power and pass/fail criteria for...
 errCTW: Calculates error, long term power and pass/fail criteria for...
 errCWD: Calculates error, long term power and pass/fail criteria for...
 errEX: Calculates error, long term power and pass/fail criteria for...
 errGEN: Calculates error, long term power and pass/fail criteria for...
 errLR: Calculates error, long term power and pass/fail criteria for...
 errLT: Calculates error, long term power and pass/fail criteria for...
 errSC: Calculates error, long term power and pass/fail criteria for...
 errTW: Calculates error, long term power and pass/fail criteria for...
 errWD: Calculates error, long term power and pass/fail criteria for...
 hypotestBAF1: Bayesain Hypothesis testing : Hypothesis 1: Theta = Theta0 Vs...
 hypotestBAF1x: Bayesain Hypothesis testing given x: Hypothesis 1: Theta =...
 hypotestBAF2: Bayesain Hypothesis testing : Hypothesis 2: Theta = Theta0 Vs...
 hypotestBAF2x: Bayesain Hypothesis testing given x: Hypothesis 2: Theta =...
 hypotestBAF3: Bayesain Hypothesis testing : Hypothesis 3: Theta = Theta0 Vs...
 hypotestBAF3x: Bayesain Hypothesis testing given x: Hypothesis 3: Theta =...
 hypotestBAF4: Bayesain Hypothesis testing :Hypothesis 4: Theta <= Theta0 Vs...
 hypotestBAF4x: Bayesain Hypothesis testing given x: Hypothesis 4: Theta <=...
 hypotestBAF5: Bayesain Hypothesis testing : Hypothesis 5: Theta >= Theta0...
 hypotestBAF5x: Bayesain Hypothesis testing given x: Hypothesis 5: Theta >=...
 hypotestBAF6: Bayesain Hypothesis testing : Hypothesis 6: Theta < Theta1 Vs...
 hypotestBAF6x: Bayesain Hypothesis testing given x: Hypothesis 6: Theta <...
 lengthAAll: Expected Length summary calculation using 6 adjusted methods...
 lengthAAS: Expected length and sum of length of Adjusted ArcSine method
 lengthAll: Expected Length summary calculation using 6 base methods...
 lengthALR: Performs expected length and sum of length of Adjusted...
 lengthALT: Performs expected length and sum of length of Adjusted Logit...
 lengthAS: Expected length and sum of length of ArcSine method
 lengthASC: Performs expected length and sum of length of Adjusted Score...
 lengthATW: Performs expected length and sum of length of Adjusted WaldT...
 lengthAWD: Performs expected length and sum of length of Adjusted Wald...
 lengthBA: Expected length and sum of length of Bayesian method
 lengthCAll: Expected Length summary calculation using 5 continuity...
 lengthCAS: Expected Length summary of continuity corrected ArcSine...
 lengthCLT: Expected Length summary of continuity corrected Logit Wald...
 lengthCSC: Expected Length summary of continuity corrected Score method
 lengthCTW: Expected Length summary of continuity corrected WaldT method
 lengthCWD: Expected Length summary of continuity corrected Wald method
 lengthEX: Expected length and sum of length of Exact method
 lengthGEN: Calculates the sum of lengths for a specific LL and UL
 lengthLR: Expected length and sum of length of likelihood Ratio method
 lengthLT: Expected length and sum of length of Logit Wald method
 lengthSC: Expected length and sum of length of Score method
 lengthSIM: Sum of length calculated using simulation method
 lengthTW: Expected length and sum of length of WaldT method
 lengthWD: Expected length and sum of length of Wald method
 pCOpBIAAll: Performs pConfidence and pBias estimation of 6 adjusted...
 pCOpBIAAS: pConfidence and pBias estimation for adjusted ArcSine...
 pCOpBIAll: Calculates pconfidence and pbias for a given n and alpha...
 pCOpBIALR: pConfidence and pBias estimation for adjusted Likelihood...
 pCOpBIALT: pConfidence and pBias estimation for adjusted LogitWald...
 pCOpBIAS: pconfidence and pbias for ArcSine method given n and alpha...
 pCOpBIASC: pConfidence and pBias estimation for adjusted Score method
 pCOpBIATW: pConfidence and pBias estimation for adjusted WaldT method
 pCOpBIAWD: pConfidence and pBias estimation for adjusted Wald method
 pCOpBIBA: pconfidence and pbias for Bayesian method given n and alpha...
 pCOpBICAll: Performs pConfidence and pBias estimation for 5 continuity...
 pCOpBICAS: pConfidence and pBias estimation for continuity corrected...
 pCOpBICLT: pConfidence and pBias estimation for continuity corrected...
 pCOpBICSC: pConfidence and pBias estimation for continuity corrected...
 pCOpBICTW: pConfidence and pBias estimation for continuity corrected...
 pCOpBICWD: pConfidence and pBias estimation for continuity corrected...
 pCOpBIEX: pconfidence and pbias for Exact method given n and alpha...
 pCOpBIGEN: Performs pConfidence and pBias estimation only using n,...
 pCOpBILR: pconfidence and pbias for Likelihood method given n and...
 pCOpBILT: pconfidence and pbias for Logit Wald method given n and...
 pCOpBISC: pconfidence and pbias for Score method given n and alpha...
 pCOpBITW: pconfidence and pbias for TWald method given n and alpha...
 pCOpBIWD: pconfidence and pbias for Wald method given n and alpha...
 PlotciAAll: Plots the CI estimation of 6 adjusted methods (Wald, WaldT,...
 PlotciAAllg: Plots the CI estimation of 6 adjusted methods (Wald, WaldT,...
 PlotciAAllx: Plots the CI estimation of 6 adjusted methods (Wald, WaldT,...
 PlotciAAllxg: Plots the CI estimation of 6 adjusted methods (Wald, WaldT,...
 PlotciAAS: Plot of CI estimation of adjusted ArcSine
 PlotciAll: Plots the CI estimation of 6 base methods (Wald, WaldT,...
 PlotciAllg: Plots the CI estimation of 6 base methods (Wald, WaldT,...
 PlotciAllx: Plots the CI estimation of 6 base methods (Wald, WaldT,...
 PlotciAllxg: Plots the CI estimation of 6 base methods (Wald, WaldT,...
 PlotciALR: Plot of CI estimation of adjusted Likelihood Ratio
 PlotciALT: Plot of CI estimation of adjusted Logit Wald
 PlotciAS: Plots the CI estimation of ArcSine method
 PlotciASC: Plot of CI estimation of adjusted Score
 PlotciATW: Plot of CI estimation of adjusted WaldT
 PlotciAWD: Plot of CI estimation of adjusted Wald
 PlotciBA: Plots the CI estimation of Bayesian method
 PlotciCAll: Plots the CI estimation of 5 continuity corrected methods...
 PlotciCAllg: Plots the CI estimation of 5 continuity corrected methods...
 PlotciCAllx: Plots the CI estimation of 5 continuity corrected methods...
 PlotciCAllxg: Plots the CI estimation of 5 continuity corrected methods...
 PlotciCAS: Plots the CI estimation of continuity corrected ArcSine...
 PlotciCLT: Plots the CI estimation of continuity corrected Logit Wald...
 PlotciCSC: Plots the CI estimation of continuity corrected Score method...
 PlotciCTW: Plots the CI estimation of continuity corrected WaldT method...
 PlotciCWD: Plots the CI estimation of continuity corrected Wald method...
 PlotciEX: Plots the CI estimation of exact methods
 PlotciEXx: Plots the CI estimation of the exact method
 PlotciLR: Plots the CI estimation of Likelihood Ratio method
 PlotciLT: Plots the CI estimation of Logit Wald method
 PlotciSC: Plots the CI estimation of Score method
 PlotciTW: Plots the CI estimation of WaldT method
 PlotciWD: Plots the CI estimation of Wald method
 PlotcovpAAll: Plots the Coverage Probability using 6 adjusted methods...
 PlotcovpAAS: Plots the Coverage Probability using adjusted ArcSine method
 PlotcovpAll: Graphs of basic Coverage Probability 6 base methods (Wald,...
 PlotcovpALR: Plots the Coverage Probability using adjusted Likelihood...
 PlotcovpALT: Plots the Coverage Probability using adjusted Logistic Wald...
 PlotcovpAS: Plots Coverage Probability for base ArcSine method
 PlotcovpASC: Plots the Coverage Probability using adjusted Score method
 PlotcovpATW: Plots the Coverage Probability using adjusted WaldT method
 PlotcovpAWD: Plots the Coverage Probability using adjusted Wald method
 PlotcovpBA: Graphs of Coverage Probability of the Bayesian method
 PlotcovpCAll: Graphs of Coverage Probability for 5 continuity corrected...
 PlotcovpCAS: Graphs of Coverage Probability for continuity corrected...
 PlotcovpCLT: Graphs of Coverage Probability for continuity corrected...
 PlotcovpCSC: Graphs of Coverage Probability for continuity corrected Score...
 PlotcovpCTW: Graphs of Coverage Probability for continuity corrected...
 PlotcovpCWD: Graphs of Coverage Probability for continuity corrected Wald...
 PlotcovpEX: Graphs of Coverage Probability  exact method
 PlotcovpGEN: Plot of simulation based Coverage Probability with discrete...
 PlotcovpLR: Plots Coverage Probability for base Likelihood Ratio method
 PlotcovpLT: Plots Coverage Probability for base Logit Wald method
 PlotcovpSC: Plots Coverage Probability for base Score method
 PlotcovpSIM: Plots graph of simulation based Coverage Probability with...
 PlotcovpTW: Plots Coverage Probability for base WaldT method
 PlotcovpWD: Plots Coverage Probability for base Wald method
 PloterrAAll: Plot of error, long term power and pass/fail criteria using 6...
 PloterrAAS: Plots error, long term power and pass/fail criteria using...
 PloterrAll: Plots error, long term power and pass/fail criteria using 6...
 PloterrALR: Plots error, long term power and pass/fail criteria using...
 PloterrALT: Plots error, long term power and pass/fail criteria using...
 PloterrAS: Plots error, long term power and pass/fail criteria using...
 PloterrASC: Plots error, long term power and pass/fail criteria using...
 PloterrATW: Plots error, long term power and pass/fail criteria using...
 PloterrAWD: Plots error, long term power and pass/fail criteria using...
 PloterrBA: Plots error, long term power and pass/fail criteria using...
 PloterrCAll: Plots the calculated error, long term power and pass/fail...
 PloterrCAS: Plots the error, long term power and pass/fail criteria for...
 PloterrCLT: Plots the error, long term power and pass/fail criteria for...
 PloterrCSC: Plots the error, long term power and pass/fail criteria for...
 PloterrCTW: Plots the error, long term power and pass/fail criteria for...
 PloterrCWD: Plots the error, long term power and pass/fail criteria for...
 PloterrEX: Plots error, long term power and pass/fail criteria using...
 PloterrLR: Plots error, long term power and pass/fail criteria using...
 PloterrLT: Plots error, long term power and pass/fail criteria using...
 PloterrSC: Plots error, long term power and pass/fail criteria using...
 PloterrTW: Plots error, long term power and pass/fail criteria using...
 PloterrWD: Plots error, long term power and pass/fail criteria using...
 PlotexplAAll: Plots the Expected length using 6 adjusted methods (Wald,...
 PlotexplAAS: Plots the Expected length using adjusted ArcSine method
 PlotexplAll: Plots the Expected length using 6 base methods (Wald, WaldT,...
 PlotexplALR: Plots the Expected length using adjusted Likelihood Ratio...
 PlotexplALT: Plots the Expected length using adjusted Logit Wald method
 PlotexplAS: Plots ArcSine method of expected length
 PlotexplASC: Plots the Expected length using adjusted Score method
 PlotexplATW: Plots the Expected length using adjusted WaldT method
 PlotexplAWD: Plots the Expected length using adjusted Wald method
 PlotexplBA: Plot the Bayesian method of expected length calculation
 PlotexplCAll: Plots the Expected length using 5 continuity corrected...
 PlotexplCAS: Plots the Expected length using continuity corrected ArcSine...
 PlotexplCLT: Plots the Expected length using continuity corrected Logit...
 PlotexplCSC: Plots the Expected length using continuity corrected Score...
 PlotexplCTW: Plots the Expected length using continuity corrected WaldT...
 PlotexplCWD: Plots the Expected length using continuity corrected Wald...
 PlotexplEX: Plot for Exact method of expected length calculation
 PlotexplGEN: Plot the expected length given hypothetical "p"
 PlotexplLR: Plots likelihood Ratio method of expected length
 PlotexplLT: Plots Logit Wald method of expected length
 PlotexplSC: Plots the expected length for Score method
 PlotexplSIM: Plots the expected length using calculated using simulation
 PlotexplTW: Plots WaldT method of expected length
 PlotexplWD: Plots the expected length for Wald method
 PlotlengthAAll: Plots the length summary for 6 adjusted methods (Wald,...
 PlotlengthAAS: Plots the summary length using adjusted ArcSine method
 PlotlengthAll: Plots the length summary for 6 base methods (Wald, WaldT,...
 PlotlengthALR: Plots the summary length using adjusted Likelihood Ratio...
 PlotlengthALT: Plots the summary length using adjusted Logit Wald method
 PlotlengthAS: Plots ArcSine method of sum of length calculation
 PlotlengthASC: Plots the summary length using adjusted Score method
 PlotlengthATW: Plots the summary length using adjusted WaldT method
 PlotlengthAWD: Plots the summary length using adjusted Wald method
 PlotlengthBA: Plot the Bayesian method of length summary
 PlotlengthCAll: Plots the sum of length for 5 continuity corrected methods...
 PlotlengthCAS: Plots the sum of length using continuity corrected ArcSine...
 PlotlengthCLT: Plots the sum of length using continuity corrected Logit Wald...
 PlotlengthCSC: Plots the sum of length using continuity corrected Score...
 PlotlengthCTW: Plots the sum of length using continuity corrected WaldT...
 PlotlengthCWD: Plots the sum of length using continuity corrected Wald...
 PlotlengthEX: Plots the length summary for exact method
 PlotlengthGEN: Plots the sum of lengths for a specific LL and UL
 PlotlengthLR: Plots likelihood Ratio method of sum of length calculation
 PlotlengthLT: Plots Logit Wald method of sum of length calculation
 PlotlengthSC: Plots the length summary for Score method
 PlotlengthSIM: Plots the sum of length using calculated using simulation
 PlotlengthTW: Plots WaldT method of sum of length calculation
 PlotlengthWD: Plots the length summary for Wald method
 PlotpCOpBIAAll: Plots pconfidence and pbias for a given n and alpha level...
 PlotpCOpBIAAS: Plots pconfidence and pbias for adjusted ArcSine method
 PlotpCOpBIAll: Plots pconfidence and pbias for a given n and alpha level...
 PlotpCOpBIALR: Plots pconfidence and pbias for adjusted Likelihood Ratio...
 PlotpCOpBIALT: Plots pconfidence and pbias for adjusted Logit Wald method
 PlotpCOpBIAS: Plots pconfidence and pbias for base ArcSine method
 PlotpCOpBIASC: Plots pconfidence and pbias for adjusted Score method
 PlotpCOpBIATW: Plots pconfidence and pbias for adjusted WaldT method
 PlotpCOpBIAWD: Plots pconfidence and pbias for adjusted Wald method
 PlotpCOpBIBA: Plots pconfidence and pbias for Bayesian method given n and...
 PlotpCOpBICAll: Plots pconfidence and pbias for a given n and alpha level...
 PlotpCOpBICAS: Plots pconfidence and pbias for continuity corrected...
 PlotpCOpBICLT: Plots pconfidence and pbias for continuity corrected Logit...
 PlotpCOpBICSC: Plots pconfidence and pbias for continuity corrected Score...
 PlotpCOpBICTW: Plots pconfidence and pbias for continuity corrected WaldT...
 PlotpCOpBICWD: Plots pconfidence and pbias for continuity corrected Wald...
 PlotpCOpBIEX: Plots of pconfidence and pbias of Exact method given n and...
 PlotpCOpBIGEN: Plots pConfidence and pBias estimation for general method
 PlotpCOpBILR: Plots pconfidence and pbias for base Likelihood Ratio...
 PlotpCOpBILT: Plots pconfidence and pbias for base Logit Wald method
 PlotpCOpBISC: Plots pconfidence and pbias for base Score method
 PlotpCOpBITW: Plots pconfidence and pbias for base WaldT method
 PlotpCOpBIWD: Plots pconfidence and pbias for base Wald method
 probPOS: Bayesian posterior Probabilities
 probPOSx: Bayesian posterior Probabilities
 probPRE: The Predicted probability  Bayesian approach
 probPREx: The Predicted probability  Bayesian approach