A basic assumption in correlation is that there are no many outliers. In my opinion you can follow two routes: a) Detect outliers using "casewise diagnostics" and delete them (but you have to justified this), or b) Use a non-parametric alternative (Spearman's rank-order correlation or Kendall's Tau Correlation). Both of them are less sensitive to outliers.

Dear Michael

I personally do not see a big problem to remove outliers from data set. For example in biology usually there are some outliers. This is a reason (among others) why we use replicates. What is important is to remove outliers correctly. Dixon's test could be use for this if Your data are normal distributed. There is also Grubb's test, but it detects only one outlier in the data set per 1 applying. It means that it is risky to use it for large data sets.

Thank you for the speedy answers. Well, my question concerns a small data set (n=14). When using Data Graph for a pearsons correlation test between Variable A and Variable B (physiological data), one has the option to include/remove outliers. This option entails "distance: 1.5σ"for selecting outliers. After selecting this option, the sample size is reduced to n=13 or 12, depending on the variables selected. WIth only one or two subjects being selected as outliers, and with the new result being statistically significant, can one then report the results as significant? My knowledge of using Data Graph and SOFA statistics is quite good, so I am a bit shy of using a whole new program. Also, since the data is numerical, I use a pearsons test, as a spearmanns is used for nominal or ordinal data.

Hi all, I'd like to add that spearman isn't used only for nominal or ordinal data but it can be used when the assumptions for parametric statistics is violated. Moreover spearman is much less affected by outliers.

Thanks Stefano! Spearmanns does have the advantage that it is less sensitive to outliers, however, does a statistically significant result from a spearmanns test have the same strength of a pearsons test? Sorry to get off topic, but primarily I want to be able to find advice on dealing with outliers whilst performing a pearsons test.

Thanks for the info!!

Go for the non parametric solution anyway. Your sample is rather small!

Ok, Ill try the spearmanns and compare the results with the pearsons test!

@Albert: "in biology usually there are some outliers" means that you are usually doing the wrong analysis/using the wrong model.

Outliers are rare. When they are "usual", then you should think about the *analysis* (and maybe the measurement technique and experimental design) but not the data.

The assessment of "statistical significance" is a statistical assessment (sounds funny, but think about it!). Given the correct analysis and model (what is anyway an assumption that should not be grossly violated!) "outliers" will not neither hamper the power nor the level of significance. So again, one should think about the model and not about the data.

Given some values are so strange that the are not physiologically meaningful, the HAVE to be removed anyway.

Given you know reasons why a particular value shouldn't be trusted, you should down-weight or exclude it anyway.

Whatever remains is data, valuable data. There might be some values far away from other values, but this is ok. Now you can have a lot of data (large sample size), then outliers won't have much effect anyway. Or you have a small sample, than you must face the possibility that removing the "outlier" might be introduce a severe bias.

So, coming to your case, Michael: using some "automatic procedure" to label or exclude outliers is a bad strategy. One can do this when one knows that the rule will only very rarely detect "outliers" given the model is ok. Now when relatively frequently outlieres are detected, it indicates that the model might not be appropriate. If you suspect (for some reason) that a value might not be ok ("outlier"), you should agrue why, and then best present the analysis results with and without this suspected value included.

Spearman's test is not restricted to ordinal data. It is used to show a "monotone relationship" between variables. It is just that anything else (like a linear or quadratic etc. relationship) is not defined on ordinal variables, so there showing a monotone relationship is the most one can do.

Very helpful info Jochen. Im new to the universe of statistics, and one can quickly become overwhelmed with the plethora of test to use. Thankfully, this platform allows for newbies like me to ask quetions and recieve very thoughtful feedback. I plan on performing the spearmanns test later today, as well as taking a magnifying glass to this "outlier" problem. Will update with the findings!

Dear Jochen Wilhelm

What I mean is that usually in each single experiment could be 1/2 outliers. For instance, injection to GC-MS went wrongly and whole sample came out on a very low level. Internal standard did not fix it due to undetectable level. I am not sure that whole analysis is wrong in this case. Using Dixon's test I hypothesise that there is no outlier, and alternative hypothesis that this extremely low value is outlier, reject the null-hypothesis, and exclude outlier from the analysis.

Dear Michael

I am not familiar with these softwares that You are using, but tests on outliers can be done in R. You can find it here: http://cran.r-project.org/web/packages/outliers/outliers.pdf

Hi Michael,

The first analysis is about the quality of data. Those obtained in conditions not considered in the study should be isolated from the models. This done, data are data.

Nature says “this is the way how I behave” and the researcher says “This is an outlier”. This is a typical and unacceptable form of bias: the researcher accepts only what he likes. It often happens that outliers result from a bad model and not by its nature.

If you appreciate a model and you find some outliers, describe the complete finding: without the outliers to show your model and with them to show its stability conditions. It is possible that outliers are a great finding. Don’t reject them.

Jorge Ortiz Pinilla

Dear Albert, the example you give reads like a typical case of a "failed" experiment. The injection obviousely did not work and standard dis not fix it. If you consider this data, what would it tell you, how much would you trust in conclusions based on such data?

And then you suggest outlier tests. what are they for? How do you specify the power of these tests? And again, what would be the minimum relevant effect size and why? If you take this seriousely, you end up again with the same questions as before: when is it really worth to remove an outlier, and when might it be rather harmful? The p-value of an outlier test is the lest helpful thing in answering these questions (and, btw, it is logically flawed because these questions must be essentially answered before the test, making everything quite absurd).

Outlier tests are good to identify data that do not fit to an otherwise correct model. It is about these outlying data, to do something about these values (not to "remove" them from analysis, but to *use* these values for something) and not to forget about their findings and concentrated on the rest of the data that failed to give small-enough p-values in the outlier test.

Using tests to remove outliers in order to "clean up" data for a test seems like a perverted logic to me. It makes no sense.