s+EnvironmentalStats Features

Feature Overview

• Use pull-down menus to easily perform statistical analyses.
• Compute quantities associated with probability distributions (probability density functions, cumulative distribution functions, quantiles), and generate random numbers from these distributions. (Several distributions have been added to the ones already available in S-PLUS.)
• Plot probability distributions so you can see how they change with the value of the distribution parameters.
• Compute several different kinds of summary statistics. (Several additional summary statistics have been added to the ones already available in S-PLUS.)
• Estimate distribution parameters and quantiles and compute confidence intervals for commonly used probability distributions.
• Perform and plot the results of a Goodness-of-Fit test:
  • Observed and Fitted Distributions
  • Quantile-Quantile Plots
  • Results of Shaprio-Wilk, Kolmogorov-Smirnov, etc.
• Compute optimal Box-Cox data transformations.
• Compute parameteric and non-parametric prediction and tolerance intervals.
• Easily perform several kinds of hypothesis tests, including ones not already built into S-PLUS such as:
  • Chen's modified one-sided t-Test for skewed distributions
  • Fisher's one-sample randomization (permutation) test for location
  • Quantile test to detect a shift in the tail of one population relative to another
  • Two-sample linear rank tests
  • Test for serial correlation based on von Neumann rank test
  • Nonparametric estimation and tests for seasonal trend
• Create power and sample size computations and plots.
• Perform calibration based on a machine signal to determine decision and detection limits and report estimated concentrations along with confidence intervals.
• Handle singly and multiply censored (less-than-detection-limit) data:
  • Empirical CDF and Quantile-Quantile Plots
  • Parameter/Quantile Estimation and Confidence Intervals
  • Prediction and Tolerance Intervals
  • Goodness-of-Fit Tests
  • Optimal Box-Cox Transformations
  • Two-Sample Rank Tests
• Perform probabilistic risk assessment.
• Look up statistical methods in the environmental literature in a hypertext help system that explains the equations, links the equations to the original reference, includes abstracts of selected references, and contains a glossary of statistical and environmental terms.
• Reproduce specific examples in EPA guidance documents by using built-in data sets from these documents.

Feature List

Pull-Down Menus and Dialogs: Perform Your Analyses via the New Pull-Down Menus

Probability Distributions: Compute Densities, Probabilities, Quantiles, and Random Numbers for the Following Distributions

• Continuous Distributions: Beta, Cauchy, Chi (square root of a chisquare), Chisquare, Empirical, Exponential, Extreme Value, Generalized Extreme Value, F (central and non-central), Gamma, Logistic, Lognormal, 3-Parameter Lognormal, Mixture of Two Lognormals, Truncated Lognormal, Normal, Mixture of Two Normals, Truncated Normal, Pareto, Stable, Student's t (central and non-central), Triangular, Uniform, Weibull
• Discrete Distributions: Binomial, Empirical, Geometric, Hypergeometric, Negative Binomial, Poisson, Wilcoxon
• Mixtures of Continuous and Distrete Distributions: Zero-Modified Lognormal (Also Called the Delta Distribution; Lognormal with positive mass at 0), Zero-Modified Normal (Normal with positive mass at 0)
  

Probability Density and Cumulative Distribution Plots

• Plot PDFs and CDFs so you can see how they change with the value of the distribution parameter(s)

Summary Statistics

• Several additional summary statistics have been added to the ones already available in S-PLUS
  

Q-Q Plots for All Probability Distributions

• Includes Standard Q-Q Plots and Tukey Mean-Difference Plots

Q-Q Plot Gestalt Function That Produces Numerous "Typical" Q-Q Plots for a Specified Distribution

• Allows You to Build Up a Visual Memory of "Typical" Q-Q Plots

Estimation of Distribution Parameters and Quantiles

• Several Estimation Methods Available: Maximum Likelihood, Minimum Variance Unbiased, Method of Moments, Method of L-Moments, etc.
• Results Printed in "Nice" Format: Data Set Name, Sample Size, Method of Estimation, Optional Confidence Interval

Confidence Intervals for Distribution Parameters

• Binomial: Exact, Normal Approximation
• Exponential: Exact
• Extreme Value: Normal Approximation
• Lognormal: Exact (Land, 1971), Parkin et al.'s (1990) Approximation, Cox's
• Approximation (Land, 1972), Normal Approximation
• Three-Parameter Lognormal: Normal Approximation, Likelihood Profile, Zero
• Skewness (Royston, 1992b)
• Normal: Exact
• Poisson: Exact, Pearson-Hartley Approximation, Normal Approximation
• Zero-Modified Lognormal (Delta): Normal Approximation
• Zero-Modified Normal: Normal Approximation

Confidence Intervals for Distribution Quantiles

• Lognormal
• Normal
• Poisson
• Nonparametric

Goodness-of-Fit Tests (New and Updated)

• Chi-Square, Kolmogorov-Smirnov, Probability Plot Correlation Coefficient, Shapiro-Francia, Shapiro-Wilk
• Allow User to Estimate the Distribution Parameters
• Results Printed in "Nice" Format: Data Set Name, Hypothesized Distribution, Estimated Parameters, Test Method
• Results Can Be Plotted. Optional Plots Include: Histogram with Overlaid Fitted Distribution, Q-Q Plot, CDF Plots of Observed and Fitted Distribution, Test Results

Optimal Box-Cox Transformations: Determine Optimal Power Transformation Based on Probability Plot Correlation Coefficient or Other Criteria

Prediction and Tolerance Intervals

• Lognormal
• Normal
• Poisson
• Nonparametric

Special Hypothesis Tests

• Chen's Modified One-Sided t-Test for Skewed Distributions
• Fisher's One-Sample Randomization (Permutation) Test for Location
• Quantile Test (Detects Shifts in Tail of Distribution)
• Two-Sample Linear Rank Tests
• Test for Serial Correlation Based on von Neumann Rank Test
• Seasonal Kendall Test for Trend

Power and Sample Size Calculations for Standard Hypothesis Tests

• Includes Sample Size, Power, Minimal Detectable Difference, and Significance Level
  Functions to Easily Plot These Quantities

Calibration

• Fit a Calibration Line or Curve
• Predict Concentrations Based on Fitted Calibration Curve and Compute Associated Confidence Intervals
• Determine Decision and Detection Limits

Methods for Type I Censored Data

• Empirical Cumulative Distribution Plots
• Quantile-Quantile (Probability) Plots
• Goodness-of-Fit Tests
• Parameter/Quantile Estimation and Confidence Intervals
• Prediction and Tolerance Intervals
• Hypothesis Testing

Tools for Probabilistic Risk Assessment

• Simple Random Sampling and Latin Hypercube Sampling
• Generate Random Numbers from a Multivariate Normal Distribution
• Generate a Multivariate Matrix from One or More Specified Distributions with a
• Specified Rank Correlation
• Create an Output Distribution of Exposure or Risk

Built-In Data Sets

• Data Sets Appearing in Selected EPA Guidance Documents
• Selected Data Sets from the Environmental Statistics Literature

Extensive Hypertext Help System

• Cross-Referenced Help Files that Clearly Explain Each Procedure and Provide Specific, Detailed Examples
• Detailed Abstracts of Selected Literature in Environmental Statistics
• A Fully Cross-Referenced, Hypertext Glossary of Statistical and Environmental Terms

System Requirements

• S+EnvironmentalStats version 2.0 module
• S+ Version 6 or higher
• 20 MB additional disk space
• Microsoft Windows 98, ME, 2000, NT or XP