hi, what do you mean by correlation? correlation of different points of interface you mean?

Pearson's is a fine test, especially if your data is normally distributed--though a normal distribution is not a requirement. However--and importantly!--this is a strictly linear correlation! If your trend is not linear--for example due to strong outliers--it's not ideal. Of course, you could transform the data, depending on what the relationship is, but this is not always feasible. Thus, you may want to use a non-parametric test, like Spearman's rank correlation or Kendall's tau.

Edit: If the concepts of linearity and normality aren't clear, I recommend taking a look at the four graphs on this wikipedia page:

http://en.wikipedia.org/wiki/Anscombe%27s_quartet

All 4 have the same Pearson's coefficient indicating a reasonably strong correlation, but clearly it's not an ideal test for all 4 cases.

I agree  with Peter. If the relationship is based on linearity you can use Pearson's otherwise I would choose Spearman's method

Our data is not normally distributed but linear. Both Spearman and Pearson's method gave very similar correlation coefficients (-0.97). But still is it reliable I am not sure.

Masoud I will check the paper as soon as possible, thank you.

First of all, for the correct understanding, are your variables just the contact angle of the surface of a polymer and cell spread area? I mean: when you say "different surface modifications" it doesn't act as a variable.

Second, if you can ensure your data are not normally distributed, then there is no need of calculating Pearson's correlation coefficient (I guess you have used any test, like Shapiro-Wilks or Kolmogorov-Smirnov for evaluating the normality of your data).

Now: how about the p-value of the Spearman test? It is maybe an unnecessary question given the strong negative correlation found, but due to the fact that you are asking about the reliability of your result, then the p-value is the answer you are looking for.

In any case, my sugestion is to use the Kendall's Tau too, I believe it could be more powerfull in this case (actually the correlation you have found is elevated so it maybe do not make any difference). By the way, how about the sample size?

Knowing that the contact angle/cell spreading data generally does not produce many outliers, I think that a Spearman test with a good p-value should be reliable enough as Dr. Pupo suggested. I think that it is a question of the range of contact angles, if the data is linear, it means that you have not reach the maxima point of hydrophilic/hydrophobic interactions (where cell attachment and spreading start to decrease again) and with such a range a linear correlation should work. Give Kendall's Tau a try too, it is more robust..

Thank you Engin.