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I have 9 sampling sites. I did the sampling in May, July, and September in the sediments and the water. So, I have 27 samples. I want to know if there is a linear correlation between total nitrogen concentration in the water and the sediments. What is the best correlation test if :

a) the data is normally distributed? b) the data is not normally distribute?

Please explain it as simply as possible because I don't have a lot of knowledge in this field. If possible can you give some references too?

Thanks,

Simon Leclair
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  • Perhaps you don't need a test and you don't need to compute or estimate what is usually known as "correlation." Why not draw a suitable plot, such as a scatterplot of the (sediment, N) data, perhaps distinguishing the symbols by site and date? That will reveal far more useful information than any suite of statistical tests you might devise. – whuber Nov 16 '21 at 17:18

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With only 27 samples, I think that you can not use any relevant spatio-temporal method. Controlling for time and space will require the estimation of several parameters and you don't have enough observations to do so.

You could use a descriptive approach by calculating a locally weighted correlation (the weight will be a function of the distance between observations) in time, space and both, but you will not be able to do inference.

jérémy Gelb
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  • Okay thanks, but can you explain to me how to do this descriptive approach. Also, how much observation do I need to use the Spatio-temporal methods? If I have enough observation, what are the method that you suggest to me? – Simon Leclair Nov 16 '21 at 17:23
  • A locally weighted correlation is calculated as follow : for each observation i of the dataset, you calculate the correlation and apply a weight to each observation equal to the inverse (or some other function) to the to the selected observation i. You will end up with several correlation values, varying in space. The method could be extended in time. Considering the number of observations, this is a more difficult question, it will depend on the method. To control for both space and time, I would work with Mixed effect model (GLMM or LMM) including space and temporal dependcy structure. – jérémy Gelb Nov 16 '21 at 17:35
  • Can you give me an example because I still don't understand? How to determine a correlation with one observation, usually you need a least 3 observations to determine a correlation. Thanks, – Simon Leclair Nov 17 '21 at 11:18
  • I will try to give more details : for one observation i, located in space, you will calculate the correlation beween the two considered variables, using ALL the observations (not only i), but the weight (i.e. the contribution) of each observation to this value is based on their distance to i (inverse of the distance or an other function). Thus, close observations to i contribute more to the correlation calculated at i. You end up with correlation values calculated at each location, varying in space and you can map them. Is it clearer ? – jérémy Gelb Nov 17 '21 at 15:29