Dr. Guido Consonni

Department of Economics and Quantitative Methods

University of Pavia (Italy)

* Title: *" Tests based on intrinsic priors for the equality of two correlated proportions "

* Abstract:*

Correlated proportions arise in longitudinal (panel) studies. A typical example

is the "opinion swing'' problem: "Has the proportion of people favoring a

politician changed after his recent speech to the nation on TV?''.

Since the same group of individuals is interviewed before and after the speech,

the two proportions are correlated. A natural null hypothesis to be tested is

whether the corresponding population proportions are equal.

A standard Bayesian approach to this problem has already been considered in the

literature, based on a Dirichlet prior for the cell-probabilities of the

underlying two-by-two table under the alternative hypothesis, together with an

induced prior under the null.

In lack of specific prior information, a diffuse (e.g. uniform) distribution may

be used. We claim that this approach is not satisfactory, since in a testing

problem one should make sure that the prior under the alternative be adequately

centered around the region specified by the null, in order to obtain a fairer

comparison between the two hypotheses, especially when the data are in reasonable

agreement with the null.

Following an intrinsic prior methodology, we develop two strategies for the

construction of a collection of objective priors increasingly peaked around the null.

We provide a simple interpretation of their structure in terms of weighted imaginary

sample scenarios. We illustrate our method by means of three examples, carrying out

sensitivity analysis and providing comparison with existing results.

(This is joint work with Luca La Rocca, University of Modena and Reggio Emilia, Italy)