Hi

1. You can develop the non-parametric correlation coefficient (Spearman).

2. The sample sizes of the random variables must be equal.

Regards,

Zuhair

For more details, please refer to,

Snedecor, W.G. and Cochran,W.G. (1989). Statistical Methods, Blackwell.

Regards,

Zuhair

thank you for your response,

Can you be (if you know) a bit more specific with the procedure..?

The sample sizes need to be similar for the Spearman Correlation, or in general for the samples to be compared?

I also want to find a pattern of subsidence, that the different age groups follow. I understand that the sample size is very important, but how can different sample sizes be compared?

I am using R programming language.

Thanks

Hi Alexandros

1. This assumption has to be satisfied for all measures of correlation coefficients.

2. The Correlation is used to test relationships between quantitative variables or categorical variables. In other words, it’s a measure of how things are related. The study of how variables are correlated is called correlation analysis.

3. A correlation coefficient gives a numerical summary of the degree of association between two variables .

4. For testing the significance between different samples non-parametric tests could be developed. If you have two groups you can develop Wilcoxon test for related samples, and Mann-Whitney for unrelated samples.

5. For three samples, Friedman test for related samples, and Kruskal-Wallis for unrelated samples.

6. In SPSS, the attached book is very useful.

Regards,

Hello Alexandros,

Some texts (Quinn and Keough), publications (Tacha et al 1982), and statistical packages treat the evaluation of assumptions of homogeneity and normality as preliminary to statistical analysis of data. This points to evaluation of the response variable. While this can be a useful guide to initial choice of error distribution (normal, something else) it is short of sufficient. The assumptions for the general linear model (including regression, ANOVA, and ANCOVA) are that the errors (residuals) are normal and homogeneous (Eisenhart 1947, Seber 1966, Neter et al 1983 pp 31& 49, Quinn and Keogh 2002 pp 110 & 280). Evaluation of assumptions in advanced texts, where it occurs, often entails a residual versus fit plot (for homogeneity) and a normal score plot or Quantile-Quantile plot (for normality of the residuals).

The statistical literature warns against statistical tests to evaluate assumptions and advocates graphical tools (Montgomery & Peck 1992; Draper & Smith 1998, Quinn & Keough 2002).

Before "bailing out" via rank based tests, have a look at assumptions by plotting the residuals vs fits, to see if (1) the straight line assumption in your regression is valid; and (2) the homogeneity assumption is valid (no change in spread across the graph). Then look at a histogram of the residuals, or a quantile plot, so see if the normality assumption is valid.

What you lose by doing rank based stats, if they are not necessary, is substantial-- you lose and estimate of what you want-- the slope of your regression line - subsidence rate/year. Correlation is inappropriate in this case, as you have a clear physical basis for regression.

If you want to compare groups, the appropriate model is called ANCOVA, which compares slopes among groups. As with simple regression, check the assumptions (as above) by looking at the residuals.

Good luck with your research,

David S

Thanks for your reply. I will try the approach you suggested.

But I was wondering if there is a standard procedure that can be followed?

Hello Alexandros,

I am not sure what you mean by 'standard procedure.'

ANCOVA is a procedure found in any of the many statistical packages. Most statistical packages will allow you to look at the residual vs fit plot, and the normal score plot of the residuals.

Here is a step by step approach to ANCOVA.

http://www.mun.ca/biology/schneider/b4605/LNotes/Pt4/Ch14_1.pdf

In general it is best to learn how to write the model and execute it. Better than searching for the 'right test.'

Hope that helps,

David S

thank you very much!