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