Because of the involvement of a discrete variable a nonparametric correlation measure like Spearman's rank or Kendall's tau may be used.

Q-Q plot, BOX plots: qualitative comparisons.

None-parametric correlation: quantitative comparison

last time I had this situation I used Kendall's Tau C. I am not sure I understand what "frequency of the stream flow in a station" means - it might help to provide a little more context. Is "stream flow" a discrete event?

Thanks everyone for your answers.It is really helpful. Tony, I am counting the days, which stream flow in a station is greater than a defined threshold level. In fact, it is a frequency of extreme stream flow based on my defined threshold.

You can simply use Kendall's tau since Kendall's tau measure is more powerful than Spearman's rho. This will be same as correlation between drought severity and duration, where drought severity is a continous variable whereas duration is discrete since duration can vary from 1-months or more. In general, if you count drought duration, you will find there are more counts of one month drought as compared to longer time, so it is in general considered as a discrete quantity.

Thanks Poumoni for your detailed explanation. I wanted to be sure that I am on the right tract. Thanks for bringing that example on drought duration and severity. It totally makes sense to me now.

Hi Maryam

1. This assumptions of the sample size, both variables should be normally distributed (normally distributed variables have a bell-shaped curve). Other assumptions include linearity and homoscedasticity. Linearity assumes a straight line relationship between each of the two variables and homoscedasticity assumes that data is equally distributed about the regression line have to be satisfied for all measures of correlation coefficients and hypotheses testing.

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. Types:

Pearson r correlation: Pearson r correlation is the most widely used correlation statistic to measure the degree of the relationship between linearly related variables. For example, in the stock market, if we want to measure how two stocks are related to each other, Pearson r correlation is used to measure the degree of relationship between the two. The point-biserial correlation is conducted with the Pearson correlation formula except that one of the variables is dichotomous.

Kendall rank correlation: Kendall rank correlation is a non-parametric test that measures the strength of dependence between two variables. If we consider two samples, a and b, where each sample size is n, we know that the total number of pairings with a b is n(n-1)/2.

Spearman rank correlation: Spearman rank correlation is a non-parametric test that is used to measure the degree of association between two variables. The Spearman rank correlation test does not carry any assumptions about the distribution of the data and is the appropriate correlation analysis when the variables are measured on a scale that is at least ordinal.

5. If the assumptions of normality is not assured, or the sample size is not satisfied Kendall rank correlation or Spearman rank correlation could be developed.

6. 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.

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

8. In SPSS, please refer to:

i.Landau, S. and Everitt, B. S.(2004). A Handbook of Statistical analyses using SPSS.

ii.Howitt, D. and Cramer, D.(2008). Introduction to SPSS.

Regards,

Zuhair

I have one more question, related to the my original question. I am using the Kendall function in R to conduct the correlation. Though I get the result for p and tau, I get the following warning "WARNING: Error exit, tauk2. IFAULT = 12 ". What does this mean?

Thanks Dear Zuhair for your explanation.

Kearl Pearson's product moment correlation and regression can be applied in studying

(1) the regression of volume of the stream flow in a reservoir on the frequency of the stream flow in a station ,

(2) the regression of volume of the frequency of the stream flow in a station on the volume of stream flow in a reservoir

& (3) the correlation between the two said variables.

The art of application is as follows:

(1) Construct a frequency table of the frequency of the stream flow in a station corresponding to the volume of the stream flow in a reservoir.

(2) If the observations on the volume are in class intervals, take the mid values of the class intervals.

(3) Now apply the formulas of regression coefficients and correlation coefficient due to Kearl Pearson to the mid values and the corresponding frequencies.

Dear Maryam. You can not use pearson, I think and even if you use it, p-values would be very tricky. I think point biserial correlation of simply a logistic regression can solve your problem.

In the problem, as mentioned by Maryam Pournasiri Poshtiri , the variable Vi (volume of stream flow in a reservoir) is continuous. But, the data on this variable are discrete.

The pairs of data on the two variables, namely volume of stream flow in a reservoir and the frequency of the stream flow in a station, are

(V1, N1) , (V2, N2) , (V3, N3) , ....... , (Vi, Ni) , .................

Thus the data are of discrete type.

Accordingly,

Kearl Pearson's product moment correlation and regression can be applied in studying

(1) the regression of volume of the stream flow in a reservoir on the frequency of the stream flow in a station ,

(2) the regression of volume of the frequency of the stream flow in a station on the volume of stream flow in a reservoir

& (3) the correlation between the two said variables.

The formulas for correlation and regression due to Kearl Pearson's are applicable to the data if the data are discrete irrespective of whether the variables under study are discrete or continuous.

Because of the discreteness of one of the variables a nonparametric technique like Spearman's rank method must be used. Good luck.