Equipe Raisonnement Induction Statistique  Some questions
 The abusesofinterpretation There is intervalandinterval! I have the testCan I getan interval? Evenstatisticians... What isthe probabilityof finding again... A problemwithsocks There is randomandrandom

### The abuses of interpretation of significance tests

 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). The following typical comments, based on ANOVA \$F\$ tests, are found in an experimental review: "the only significant effect is a main effect of treatment (F[1,36]=6.39, p=0.016), reflecting a substantial improvement''; and again "clearly, there is no evidence (F[1,36]=0.47, p=0.50) of an interaction". 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? The abusesofinterpretation There is intervalandinterval! I have the testCan I getan interval? Evenstatisticians... What isthe probabilityof finding again... A problemwithsocks There is randomandrandom

### There is interval and interval!

 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. "If in an opinion poll of size 1000, the observed proportion P is equal to 0.613, the proportion π to estimate has a probability 0.95 of lying in the range: [0.58,0.64]" Do you agree with this interpretation? The abusesofinterpretation There is intervalandinterval! I have the testCan I getan interval? Evenstatisticians... What isthe probabilityof finding again... A problemwithsocks There is randomandrandom

### I have the test statistic, can I get an interval?

 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. I would be interested in an interval estimate (frequentist confidence interval, or fiducial-Bayesian credible interval) in order to assess if the inefficacy of the treatment has really been proved. Is it possible? The abusesofinterpretation There is intervalandinterval! I have the testCan I getan interval? Evenstatisticians... What isthe probabilityof finding again... A problemwithsocks There is randomandrandom

### Even statisticians...

 Consider 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 drug is to be considered clinically interesting by experts in the field if the unstandardized difference between the treatment mean and the placebo mean is more than +3. The observed difference is d=+1.52. The difference is non significant (t=+0.683, p=0.50). What conclusion would you draw for the efficacy of the drug? Answer spontaneously (without computation) The abusesofinterpretation There is intervalandinterval! I have the testCan I getan interval? Evenstatisticians... What isthe probabilityof finding again... A problemwithsocks There is randomandrandom

### What is the probability of finding again...

 In a study that compares an experimental condition to a control condition, a difference +1.82 between the two moyennes has been observed. The difference is significant at two tailed level 0.05: t=+2.09, 19 degrees of freedom, p=0.05. (1) What, for you, is the probability that, in a replication of the experiment, the observed difference will be positive? (2) What, for you, is the probability that the observed difference will be positive, and the result of Student's test will be at least significant? Answer spontaneously (without computation) The abusesofinterpretation There is intervalandinterval! I have the testCan I getan interval? Evenstatisticians... What isthe probabilityof finding again... A problemwithsocks There is randomandrandom

### A problem with socks

 A pair of socks is (blindly) draw from a drawer in which there are a pair of red socks and a pair of green socks. Consider the following results:   Result 1: A pair of socks that match (two red or two green) is obtained   Result 2: A pair of socks that do not match (one red and one green) is obtained Do you think there is: 1) more chance of obtaining result 1 2) more chance of obtaining result 2 3) an equal chance of obtaining the two results Answer spontaneously (without computation) The abusesofinterpretation There is intervalandinterval! I have the testCan I getan interval? Evenstatisticians... What isthe probabilityof finding again... A problemwithsocks There is randomandrandom

### There is random and random

 Consider the two following events: "The fact that a pair of socks that match is obtained from a blindly draw of two socks from a drawer in which there are two pairs of different socks" "The fact that a planted seed germinates or not" Do you think that randomness is involved or not in each of these two events? Answer spontaneously The abusesofinterpretation There is intervalandinterval! I have the testCan I getan interval? Evenstatisticians... What isthe probabilityof finding again... A problemwithsocks There is randomandrandom   