Testing for preference change in marketing or opinion research
| STATISTICA & APPLICAZIONI - 2012 - 2
Let us suppose we have two important products or parties or opinions indicated respectively by A
and B and a pool of small other choices indicated by C and we are interested in understanding if
the percentage of preferences for A and the percentage of preferences for B are unchanged, increased
or decreased after some event (f.i. advertising). If the sample size is big, we propose to use
a two stage hypotheses test proposed by Duncan (Miller, 1981) and improved by Pollastri (2008).
The test considered is based on the exact distribution of the absolute maximum (Zenga, 1979) and
on the exact distribution of the absolute minimum (Pollastri and Tornaghi, 2004) of the components
of a Bivariate Correlated Normal. Tables of the critical values are reported. The test proposed allows
to accept one of the nine hypotheses about the invariance or increasing or decreasing of the
percentage of A combined with the three movements of the percentage of B.
Keywords: Trinomial Distribution, Bivariate Correlated Normal, Two Stage Hypotheses Test, Absolute
Maximum and Minimum.