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I have a gamma distribution. I am looking to determine if higher concentrations of a toxin are correlated to larger organism size. I think a non-parametric test would be best, but I'm not sure which one. I also would like help with the code for the appropriate test.

Concentration Weight Organism 
1.991727448   3.4123 1 
1.966596882   3.4123 1 
1.897810551   3.4123 1 
1.771298539   2.7919 2 
1.878570524   2.7919 2 
1.951663352   2.7919 2 
2.154681989   2.9017 3 
2.379345401   2.9017 3 
2.255437583   2.9017 3
2.728399933   1.7309 4
2.795955935   1.7309 4
3.623074493   1.7309    4
2.411676322   2.1697    5
2.519907253   2.1697    5
2.665514334   2.1697    5
2.006952992   3.1073    6
2.160155328   3.1073    6
2.053309183   3.1073    6
2.171144811   2.4293    7
2.226966008   2.4293    7
2.17666109    2.4293    7
2.297641387   1.9812    8
2.509240112   1.9812    8
2.60277021    1.9812    8
2.071601009   3.4279    9
1.996824488   3.4279    9
2.081764306   3.4279    9
3.808645757   3.925    10
3.645882141   3.925 10
3.41459793    3.925 10
2.942431806   5.079 11
3.075279922   5.079 11
2.993338069   5.079 11
1.678786617  3.6897 12
2.016055177  3.6897 12
2.005601238  3.6897 12
2.390359396  2.1345 13
2.193587554  2.1345 13
2.355520221  2.1345 13
2.707149057  2.8203 14
2.860405275  2.8203 14
2.75714013   2.8203 14
2.103323063  2.5271 15
2.011219111  2.5271 15
2.161352975  2.5271 15
2.10         1.9946 16
2.15         1.9946 16
1.83         1.9946 16
3.500305111  2.2549 17
3.500305111  2.2549 17
3.35833618   2.2549 17
2.40408813   2.8263 18
2.351461025  2.8263 18
2.65780759   2.8263 18
6.052936417  2.0314 19
6.588537672  2.0314 19
6.783591055  2.0314 19
2.654459452  2.6177 20
2.750625025  2.6177 20
2.715865923  2.6177 20
2.404360854  3.3416 21
2.879751607  3.3416 21
3.134152046  3.3416 21
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  • $\begingroup$ I have 21 organisms, was showing an example of how my data is set up. I can upload all of the data if that would help-just didn't know if it was necessary $\endgroup$ – Ellen Jan 30 '15 at 6:00
  • $\begingroup$ Also I have been taking the mean of these organisms and plotting standard error bars on them $\endgroup$ – Ellen Jan 30 '15 at 6:09
  • $\begingroup$ Is there a meaning to the ordering of values w/i each organism? Eg, are these measures taken over time (& would you have the times)? $\endgroup$ – gung - Reinstate Monica Jan 31 '15 at 21:02
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If that is your complete dataset, there isn't much you can do. You seem to have only three organisms, each with the values for Toxicity. Those values are dependent, so you would have to deal with that somehow. A simple approach would be to average them, but then you'd still have only three data. It is possible to get an $r$ score with three data, but essentially pointless to try to test the correlation, even if you were sure all the assumptions of the test were met, you would have only 1 degree of freedom. The best you can do here, really, is plot the data:

enter image description here

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