Le P A C

			PAC
LesMoyennes	LesEffectifs	LesEchantillons	LesProportions	LeB‑A‑Bayésien	LesDistributions	LePrep

Download LePAC [Windows]

Authors

Bruno LECOUTRE Jacques POITEVINEAU

Download LePAC [Windows]

LePAC Copy and free diffusion of LePAC are authorized.

LePAC is a statistical software for the analysis of experimental data, especially suited for Bayesian inference, wihout excluding traditional frequentist procedures. It includes several programs.

PAC (Program for the Analysis of Comparisons)

is the main program
PAC is a general software for analyzing planned data. It is a unique tool that can be used for an initiation to experimental data analysis as well as for sophisticated applications.

			PAC
LesMoyennes	LesEffectifs	LesEchantillons	LesProportions	LeB‑A‑Bayésien	LesDistributions	LePrep

It is a unique tool that can be used for an initiation to experimental data analysis as well as for sophisticated applications.

Experimentation, clinical trials, systematic observations...
Beyond significance tests; confidence intervals, Bayesian methods
Didactical and convivial Bayesian module, for an easy interactive use of all the procedures

Traditional and Bayesian analysis of variance

Variance-covariance analysis
Polynomial regression and discriminant analysis
Experimental designs up to 26 factors
Univariate and multivariate analyses
Repeated measures designs with equal or unequal sample sizes

User-friendly WINDOWS program

Easy to use
Powerful design definition
Great number of options

From traditional to Bayesian inference

Frequentist inferences: null hypothesis significance tests, confidence intervals
Bayesian procedures: "noninformative" (standard) and conjugate priors

The graphical Bayesian module ('LesMoyennes'): beyond usual significance tests

Bayesian methods express by a probability distribution the incertitude about the true value of the parameter. They are well-suited to the aim of experimental data analysis and extend the usual null hypothesis test.

Synthetic showing of results for each inference
Interactive searching for confidence and credibility intervals
Displaying conclusions about the effect magnitude
Displaying the impact of external information (prior distributions)

Download LePAC [Windows]

Other programs

			PAC
LesMoyennes	LesEffectifs	LesEchantillons	LesProportions	LeB‑A‑Bayésien	LesDistributions	LePrep

LesMoyennes

Interactive Bayesian inferences for comparisons of means

LesMoyennes is used by PAC. It can be independently used for an interactive introduction to basic procedures (frequentist and Bayesian) for numerical experimental data analysis (traditional t and F tests, confidence intervals and Bayesian methods in order to assess effect sizes.

Easy interactive use
Raw and calibrated/standardized effects
Traditional t and F tests
Confidence interval
Bayesian procedures (and also frequentist procedures) for assessing effet sizes
Predictive inferences

LesCorrélations

Exact inference about a correlation coefficient

Tests (null hypothesis ρ=0 or ρ=ρ₀≠0) and confidence intervals
Fiducial Bayesian procedures

LesEffectifs

Computation of Bayesian predictive probabilities

Probability to achieve a given conclusion with a specified sample size
Sample size required to achieve a given conclusion with a specified predictive probability
Includes the traditional frequentist power as a particular case

LesEchantillons

Drawing of samples and simulations of sampling distributions for descriptive and inferential statistics

Mean, difference of two means from independent groups, standard deviation
t test statistic for one mean and of the difference of two means
Confidence or fiducial Bayesian credibility limits
Parent distributions: normal, gamma (or chi-square), exponential, or uniform

LesProportions

Bayesian inferences about proportions

The current version is a beta version.

One proportion (binomial or negative binomial model) for a beta prior distribution or for a mixture of beta distributions
Different parameters derived from the proportions of two independents groups (binomial or negative binomial model) for two independent beta prior distribution
The implication index in a 2×2 table with two binary variables (multinomial model), for a Dirichlet prior distribution

LeB-A-Bayésien

Didactical program

Allow to interactively investigate several prior distributions, and to understand the mechanisms of Bayesian inference.

Inférence about a proportion (binomial sampling)
Inference about a mean (normal sampling with known variance)

Use of prior mixture of the densities of the basic distributions, respectively beta for a proportion and normal for a mean. One can generate a very general family of distributions. The posterior distribution is also a mixture of the such densities.
The prior and posterior distributions are automatically updated.

LesDistributions

Probability and cumulative distribution functions - Probability statements (direct and reverse)

Many continuous and discrete distributions
Transformations for continuous distributions
Possibility of lower ('left') and upper ('right') truncatures.

The curent version is a beta version.
It is the responsability of the users to verify the 'correctness' of the outputs.
In case of doubt, it is recommended to generate the distribution by drawing a sample to get a verification of the outputs (computations are in most cases independent).

LePrep can be used after a Student t test or an ANOVA F test with with one degree of freedom.

Predictive probability prep (Killeen's probability of replication) of finding a same-sign effect in a replication,
Predictive probability psrep of finding a same-sign and significant at one-tailed level α effect in a replication,
Predictive probability ppreprep of finding a same-sign effect with prep larger than γ in a replication.

It is also available an an independent program, that can also be used as a Word macro

			PAC
LesMoyennes	LesEffectifs	LesEchantillons	LesProportions	LeB‑A‑Bayésien	LesDistributions	LePrep