"The public will believe anything, so long as it is not founded on truth."

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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...

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...

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