Hi,

First you can start with correlation analysis. You should choose the pearson or spearman correlation coefficient according to the type of data and the normality of the distribution. Before applying linear regression, always check the assumptions.

Best, İbrahim.

If you seriousely want to investigate the bacterial growth (measured as OD) depending on pH, then you should come up with a sensible model (I'd expect it to be some optimum curve) and fit the model coefficients using the observed data (in my example, interesting coefficients would be those for the location and the width of the optimum). This eventually is a regression analysis, but not neccesarily a linear regression.

some notes

1- The idea of the correlation coefficient is false and the linear regression idea is more than false.

2- Basically, these issues are categorized in non-linear models such as dose-response, Enzyme Kinetics , ... .

3- In these issues, software such as Prism and Minitab has made great progress. Use them.

@Abolfazl where is your answer I'm asking about tests not about softwares ?

following

Firstly you should identify your sample (representative or not) , How many variables? Dependant or inde pendent, but I think that using Pearson coefficient (r) is the best way with the P to study the correlation, you can also use another multivariable analysis such us ACH ( or ACP ) if the stress is presented in quantitative data .

Furthermore, correlation is unit independent; if you scale one of the objects ten times, you will get different euclidean distances and same correlation distances. Therefore, correlation metrics is excellent when you want to measure distance between such objects as genes defined by their expression profile.

Often, absolute or squared correlation is used as a distance metrics, because we are more interested in the strength of the relationship than in its sign. However, correlation is only suitable for highly dimensional data; there is hardly a point of calculating it for two- or three dimensional data points.