EnvStats Functions for Power and Sample Size Calculations

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.