Statistics

Tiago Oliveira toliveira@isegi.unl.pt

www.isegi.unl.pt

3. Comparison of Two Populations

Independent samples and paired samples
 Independent samples
 Independent samples are those samples selected from the

same population, or different populations, which have no effect on one another. That is, no correlation exists between the samples.


Example

 Paired samples
 In paired samples, each data point in one sample is matched to

a unique data point in the second sample.


An example of a paired sample is a pre-test/post-test study design in which a factor is measured before and after an intervention.

18-03-2014

Instituto Superior de Estatística e Gestão de Informação - Universidade Nova de Lisboa

2

Sign test (157-164)
 The sign test
 Conditions of Use: Use the sign test when you have one sample

of subjects with some measure repeated on each subject (e.g. before and after scores) and you can not use a repeated measures t-test
(because one of the assumptions of the t-test has been violated, but the assumptions of the sign test for the same data are not violated).
 The data consist of observation on a bivariate random sample

(X1, Y1), (X2, Y2), …. (Xn, Yn), Where there are n pairs of observations. Within each par (Xi, Yi) a comparison is made, and the pair is classified:

– “+” if Xi < Yi ; – “-” if if Xi > Yi ; – “0” IF if Xi = Yi ;
18-03-2014

At least ordinal scale

Instituto Superior de Estatística e Gestão de Informação - Universidade Nova de Lisboa

3

Sign test (157-164)
1. Assumptions
 Two paired samples

 The bivariate random variables (Xi > Yi ), i=1,2,…,n, are mutually

independent.  The measurement scale is at least ordinal within each pair. That is, each pair (X1, Y1) may be determined to be a “plus,” “minus,” or “tie.”  The pairs (Xi, Yi) are internally consistent, in that if P(+) > P(-) for one pair (Xi, Yi), then P(+) > P(-) for all pairs. The same is true for P(+) > P(-), and...