# FcnsByCatPower: EnvStats Functions for Power and Sample Size Calculations In EnvStats: Package for Environmental Statistics, Including US EPA Guidance

## Description

The EnvStats functions listed below are useful for power and sample size calculations.

## Details

Confidence Intervals

 Function Name Description `ciTableProp` Confidence intervals for binomial proportion, or difference between two proportions, following Bacchetti (2010) `ciBinomHalfWidth` Compute the half-width of a confidence interval for a Binomial proportion or the difference between two proportions. `ciBinomN` Compute the sample size necessary to achieve a specified half-width of a confidence interval for a Binomial proportion or the difference between two proportions. `plotCiBinomDesign` Create plots for a sampling design based on a confidence interval for a Binomial proportion or the difference between two proportions. `ciTableMean` Confidence intervals for mean of normal distribution, or difference between two means, following Bacchetti (2010) `ciNormHalfWidth` Compute the half-width of a confidence interval for the mean of a Normal distribution or the difference between two means. `ciNormN` Compute the sample size necessary to achieve a specified half-width of a confidence interval for the mean of a Normal distribution or the difference between two means. `plotCiNormDesign` Create plots for a sampling design based on a confidence interval for the mean of a Normal distribution or the difference between two means. `ciNparConfLevel` Compute the confidence level associated with a nonparametric confidence interval for a percentile. `ciNparN` Compute the sample size necessary to achieve a specified confidence level for a nonparametric confidence interval for a percentile. `plotCiNparDesign` Create plots for a sampling design based on a nonparametric confidence interval for a percentile.

Hypothesis Tests

 Function Name Description `aovN` Compute the sample sizes necessary to achieve a specified power for a one-way fixed-effects analysis of variance test. `aovPower` Compute the power of a one-way fixed-effects analysis of variance test. `plotAovDesign` Create plots for a sampling design based on a one-way analysis of variance. `propTestN` Compute the sample size necessary to achieve a specified power for a one- or two-sample proportion test. `propTestPower` Compute the power of a one- or two-sample proportion test. `propTestMdd` Compute the minimal detectable difference associated with a one- or two-sample proportion test. `plotPropTestDesign` Create plots involving sample size, power, difference, and significance level for a one- or two-sample proportion test. `tTestAlpha` Compute the Type I Error associated with specified values for for power, sample size(s), and scaled MDD for a one- or two-sample t-test. `tTestN` Compute the sample size necessary to achieve a specified power for a one- or two-sample t-test. `tTestPower` Compute the power of a one- or two-sample t-test. `tTestScaledMdd` Compute the scaled minimal detectable difference associated with a one- or two-sample t-test. `plotTTestDesign` Create plots for a sampling design based on a one- or two-sample t-test. `tTestLnormAltN` Compute the sample size necessary to achieve a specified power for a one- or two-sample t-test, assuming lognormal data. `tTestLnormAltPower` Compute the power of a one- or two-sample t-test, assuming lognormal data. `tTestLnormAltRatioOfMeans` Compute the minimal or maximal detectable ratio of means associated with a one- or two-sample t-test, assuming lognormal data. `plotTTestLnormAltDesign` Create plots for a sampling design based on a one- or two-sample t-test, assuming lognormal data. `linearTrendTestN` Compute the sample size necessary to achieve a specified power for a t-test for linear trend. `linearTrendTestPower` Compute the power of a t-test for linear trend. `linearTrendTestScaledMds` Compute the scaled minimal detectable slope for a t-test for linear trend. `plotLinearTrendTestDesign` Create plots for a sampling design based on a t-test for linear trend.

Prediction Intervals

Normal Distribution Prediction Intervals

 Function Name Description `predIntNormHalfWidth` Compute the half-width of a prediction interval for a normal distribution. `predIntNormK` Compute the required value of K for a prediction interval for a Normal distribution. `predIntNormN` Compute the sample size necessary to achieve a specified half-width for a prediction interval for a Normal distribution. `plotPredIntNormDesign` Create plots for a sampling design based on the width of a prediction interval for a Normal distribution. `predIntNormTestPower` Compute the probability that at least one future observation (or mean) falls outside a prediction interval for a Normal distribution. `plotPredIntNormTestPowerCurve` Create plots for a sampling design based on a prediction interval for a Normal distribution. `predIntNormSimultaneousTestPower` Compute the probability that at least one set of future observations (or means) violates the given rule based on a simultaneous prediction interval for a Normal distribution. `plotPredIntNormSimultaneousTestPowerCurve` Create plots for a sampling design based on a simultaneous prediction interval for a Normal distribution.

Lognormal Distribution Prediction Intervals

 Function Name Description `predIntLnormAltTestPower` Compute the probability that at least one future observation (or geometric mean) falls outside a prediction interval for a lognormal distribution. `plotPredIntLnormAltTestPowerCurve` Create plots for a sampling design based on a prediction interval for a lognormal distribution. `predIntLnormAltSimultaneousTestPower` Compute the probability that at least one set of future observations (or geometric means) violates the given rule based on a simultaneous prediction interval for a lognormal distribution. `plotPredIntLnormAltSimultaneousTestPowerCurve` Create plots for a sampling design based on a simultaneous prediction interval for a lognormal distribution.

Nonparametric Prediction Intervals

 Function Name Description `predIntNparConfLevel` Compute the confidence level associated with a nonparametric prediction interval. `predIntNparN` Compute the required sample size to achieve a specified confidence level for a nonparametric prediction interval. `plotPredIntNparDesign` Create plots for a sampling design based on the confidence level and sample size of a nonparametric prediction interval. `predIntNparSimultaneousConfLevel` Compute the confidence level associated with a simultaneous nonparametric prediction interval. `predIntNparSimultaneousN` Compute the required sample size for a simultaneous nonparametric prediction interval. `plotPredIntNparSimultaneousDesign` Create plots for a sampling design based on a simultaneous nonparametric prediction interval. `predIntNparSimultaneousTestPower` Compute the probability that at least one set of future observations violates the given rule based on a nonparametric simultaneous prediction interval. `plotPredIntNparSimultaneousTestPowerCurve` Create plots for a sampling design based on a simultaneous nonparametric prediction interval.

Tolerance Intervals

 Function Name Description `tolIntNormHalfWidth` Compute the half-width of a tolerance interval for a normal distribution. `tolIntNormK` Compute the required value of K for a tolerance interval for a Normal distribution. `tolIntNormN` Compute the sample size necessary to achieve a specified half-width for a tolerance interval for a Normal distribution. `plotTolIntNormDesign` Create plots for a sampling design based on a tolerance interval for a Normal distribution. `tolIntNparConfLevel` Compute the confidence level associated with a nonparametric tolerance interval for a specified sample size and coverage. `tolIntNparCoverage` Compute the coverage associated with a nonparametric tolerance interval for a specified sample size and confidence level. `tolIntNparN` Compute the sample size required for a nonparametric tolerance interval with a specified coverage and confidence level. `plotTolIntNparDesign` Create plots for a sampling design based on a nonparametric tolerance interval.

EnvStats documentation built on July 15, 2018, 9:03 a.m.