Equipe Raisonnement Induction Statistique
The statistical researches of ERIS concern the methods for analysing experimental data. The privileged application fields are experimental psychology and clinical trials in medecine and pharmacology. The specificities of these fields are, one one hand that complex experimental desings are generally used, with precise objectives,and on the other hand that experimental results must be accepted by a large community.
"The test provides neither the necessary nor the sufficient scope or typeof knowledge that basic scientific social research requires."(D.E. Morrison & R.E. Henkel)
Although the use of Null Hypothesis Significance Testing (NHST) has been criticized by the most eminent and the most experienced scientists, both on theoretical and methodological grounds, it is always required in most scientific publications as an unavoidable norm. Our conclusion is that the use of NHST is a socially adapted but methodologically unsuited use of an inadequate tool promoted through misleading guidelines of standard textbooks.
Méthodologie de l'analyse des données expérimentales  Étude de la pratique des tests statistiques chez les chercheurs en psychologie, approches normative, prescriptive et descriptive
And... what about the researcher's point of view?
L'usage des tests statistiques par les chercheurs en psychologie: Aspects normatif, descriptif et prescriptif
Fisher: Responsible, not guilty
Consider an experiment involving two crossed factors Age and Treatment,
each with two modalities.
The means of the four experimental conditions (with 10 subjects in each) are respectively 5.77
(a1,t1), 5.25 (a2,t1), 4.83 (a1,t2) and 4.71 (a2,t2). 
It is strongly suggested to the reader that it has been demonstrated both a large main effect of treatment and a small interaction effect. 
Do you agree with these conclusions? 
There is nothing of the kind! 
The difference between the two observed treatment means is:

This clearly shows that it cannot be concluded both to a substantive difference between treatment means and to a small, or at least relatively negligible, interaction effect (and more again to a null interaction).. 
"Habit is habit and not to be flung out of the window by any man,but coaxed downstairs a step at a time." (Mark Twain)
Especially in psychology, changes could be the consequence of the Task Force on Statistical Inference
charged by the American Psychological Association of studying the role of NHST in psychological research.
[Wilkinson,
L. and Task Force on Statistical Inference,
APA Board of Scientific Affairs (1999)  Statistical Methods in Psychology Journals: Guidelines and Explanations.
American Psychologist,
54, 594604.
Azar B. (1999)  APA statistics task force prepares to release recommendations for public comment.
APA Monitor Online,
30, 5.]
Aller au delà des tests de signification traditionnels: Vers de nouvelles normes de publication
"The essence of science is replication: a scientist should always be concerned about what would happen if he or another scientist were to repeat his experiment." (Guttman).
In 2006, TheAssociation for Psychological Science introduced in the
"author guidelines"
of Psychological Science, a new norm of publication:
Statistics
Effect sizes should accompany major results. In addition, authors are
encouraged to use prep rather than p values (see the article by Killeen in the
May 2005 issue of Psychological Science, Vol. 16, pp. 345353).
Killeen's p_{rep} ("probability of replication")
now routinely appears in Psychological Science.
"It would not be scientifically sound to justify a procedure by frequentist arguments and to interpret it in Bayesian terms." (H. Rouanet)
Confidence intervals could quickly become a compulsory norm in experimental
publications. However, for many reasons due to their frequentist (Neyman and Pearson) conception,
confidence ntervals can hardly be viewed as the ultimate method.
Indeed the appealing feature of confidence intervals is the result of a fundamental
misunderstanding. As is the case with significance tests, the frequentist
interpretation of a 95% confidence interval involves a long run
repetition of the same experiment: in the long run 95% of computed
confidence intervals will contain the "true value" of the parameter; each
interval in isolation has either a 0 or 100% probability of containing it.
It is so strange to treat the data as random even after observation that the
orthodox frequentist interpretation of confidence intervals does not make sense for most users.
Et si vous étiez un bayésien "qui s'ignore"?
Isn't everyone a Bayesian?
And if you were a Bayesian without knowing it?
In an introductory statistical textbook, in a serie for the "grand public",
whose goal is to give the reader the possibility to "access the deep intuitions in the field",
one can find the following interpretation of a confidence interval for a proportion.

Do you agree with this interpretation? 
If you are not (again) a Bayasian and if your real intuition is that interpretation is, either right, or perhaps wrong but in any case desirable, you must seriously ask yourself if you are not a Bayesien "without knowing it". 
In the frequentist framework the possible values for the parameter cannot probabilised.
If, as in this example, the bounds computed for the observed sample are [0.58,0.64],
the event
"0.58<π<0.64"
is true or false
(because π is fixed), and we cannot give it a probability (other than 1 ou 0).

Ironically, it is the natural (Bayesian) interpretation of confidence
intervals in terms of "a fixed interval having a 95% chance of including
the true value of interest" which is their appealing feature.

"We [statisticians] will all be Bayesians in 2020, and then we can be a united profession." (D.V. Lindley)
We argue that Bayesian methods are ideally suited for creating a change of emphasis in the presentation
and interpretation of experimental results. We suggest using "noninformative" Bayesian methods as a therapy
for curing the misuses and abuses of NHST.
For many years we have worked with colleagues in France with this perspective in mind in order to develop
standard "noninformative" Bayesian methods for the most familiar situations encountered in experimental data analysis.
Beyond the significance test controversy: Prime time for Bayes?
Uses, abuses and misuses of significance tests in the scientific community: Won't the Bayesian choice be unavoidable?
"Maybe Fisher's biggest blunder [fiducial inference] will become a big hit in the 21st century." (B. Efron)
In order to promote these Bayesian methods, it seemed important to us to give them a more explicit
name than "standard", "noninformative" or "reference". We propose to call them fiducial Bayesian.
This deliberately provocative name pays tribute to Fisher's work on scientific inference for research workers.
It indicates their specificity and their aim to express "what the data have to say".
These fiducial Bayesian methods are concrete proposals in order to bypass the shortcomings of NHST and
improve current statistical methodology and practice
New ways in statistical methodology: From significance tests to Bayesian inference
Uses, abuses and misuses of significance tests in the scientific community: Won't the Bayesian choice be unavoidable?
Bayesian methods for experimental data analysis
"A common misconception is that Bayesian analysis is a subjective theory; this is neither true historically nor in practice." (J. Berger)
Our goal is to develop general alternative methods better suited to the needs of users.
The Bayesian inference is a privileged theorical framework, at least as objective as the traditional frequentist inference.
The fiducialBayesian methods have been applied many times to real data and well
accepted by experimental journals
Mémorisation de récits: Reconnaissance immédiate et différée d'énoncés par des
enfants de 7, 8 et 10 ans
Orientation of attention and sensory gatting: An evoked potential and RT study in cat
From production to selection of interpretations for novel conceptual combinations:
A developmental approach.
"Bayesian posterior probabilities are exactly what scientists want." (S.N. Goodman & J.A. Berlin)
I have find an article that report the results of a study designed to test the efficacy of a drug
by comparing two groups (treatment vs placebo) of 15 patients each.
The gives the observed difference d=+1.52 in favour of the treatment,
and a "Student t test": t=+0.683, 28 degrees of freedom, p=0.50, nonsignificant.

Is it possible?

Yes! 
For a 100(1α)%
interval, it is sufficient to know
t{(1α)/2}:
the (1α)/2 upper
point of the Student distribution with q degrees of freedom. [ d  (d/t)t{(1α)/2} , d + (d/t)t{(1α)/2} ] We find here for α = 0.05 and q=28 degrees of freedom t{0.975}= +2.0484, hence the 95% interval (of course it is assumed that d and t are computed with the needed accuracy):
[3.04,+6.08]

This interval can be interpreted as a 95% "frequentist" confidence interval or as a 95% "fiducialBayesian" interval. 
Teaching Bayesian methods for experimental data analysis
Beyond the significance test controversy: Prime time for Bayes?
A reason why not to ban Null Hypothesis Significance Tests
Asserting the smallness of effects in ANOVA
Aller au delà des tests de signification traditionnels: Vers de nouvelles normes de publication
Another look at confidence intervals for the noncentral t distribution
Tester les nouveaux medicaments: Les statisticiens et la réglementation
"An essential aspect of the process of evaluating design strategies is the ability to calculate predictive probabilities of potential results." (D.A. Berry)
The ease of making predictions is a particular attractive feature of Bayesian inference
Probabilités prédictives: Un outil pour la planification des expériences
Bayesian sample size determination in nonsequential clinical trials: Statistical aspects and some regulatory considerations
Bayesian predictive approach for inference about proportions
Bayesian predictive procedure for designing and monitoring experiments
"ANOVA may be the most commonly used statistical procedure. It is assuredly the most commonly misused statistical procedure!" (D.A. Berry)
The Bayesian Analysis of Comparisons gives a flexible methodological framework, in order to bypass the strict constraints imposed by the traditional "general linear model" and to privilege the users' questions. Two main principles are the notion of specific analysis and the use of Bayesian methods.
L'Analyse Bayésienne des Comparaisons
Traitement Statistique des données expérimentales: Des pratiques traditionnelles aux pratiques bayésiennes
Asserting the smallness of effects in ANOVA
Aller au delà des tests de signification traditionnels: Vers de nouvelles normes de publication
Geometric data: From euclidean clouds to Bayesian MANOVA
Lois bayésiennes a priori dans un plan binomial séquentiel
Bayesian priors in sequential binomial design
On Bayesian estimators in multistage binomial designs
An objective Bayesian approach to multistage hypothesis testing
Distribution of quadratic forms of multivariate Student variables
Two useful distributions for Bayesian predictive procedures under normal models
Computing Bayesian predictive distributions: The Ksquare and Kprime distributions
Bayesian predictive approach for inference about proportions
A note on new confidence intervals for the difference between two proportion based on an Edgeworth expansion
Bayesian procedures for prediction analysis of implication hypotheses in 2×2 contingency tables
New results for computing exact confidence intervals for one parameter discrete distributions.
Analyse bayésienne des données de survie  Application à des essais cliniques en pharmacologie
Assessment and monitoring in clinical trials when survival curves have distinct shapes in two groups: a Bayesian approach with Weibull modeling
Playthewinner rule in clinical trials: models for adaptative designs and Bayesian methods
Adaptative designs for multiarm clinical trials: The playthewinner rule revisited
Frequentist performance of Bayesian inference with responseadaptive designs.
Comparing performances of several responseadaptive designs in dose finding studies.
Inférence statistique causale sur les effets individuels: Quelques éléments de réflexion
Expérimentation, inférence statistique et analyse causale
"In fact, I find it easier teaching Bayesian statistics than frequentist statistics. There is a single, pivotal notion  Bayes' rule  that describes the process of learning. Bayes' rule is especially easy to teach, and it is easy for students to use." (D.A. Berry)
Psychologists  Pharmaceutical companies.
Teaching Bayesian methods for experimental data analysis
A Challenge for Statistical Instructors: Teaching Bayesian inference without discarding the official significance tests
Training students and researchers in Bayesian methods for experimental data analysis