Hola Irlan como va la vida .... mira segun entiendo lo que estas es comparando 2 variables que no siguen una distribucion normal .... para eso son las pruebas no parametricas , osea puedes primero hacerle una prueba de remuestreo o de Monte Carlos o la de kholmov-smirnov para ver que distribucion real siguen tus datos y luego los comparas , pero en dependencia de para que lo necesites (o sea si es para ver su relacion , o la evolucion en el tiempo , etc)... para eso es mejor que vieras un libro de stadisticas ...... osea para datos que no siguen una distribucion normal hay muchas pero muchas pruebas (todas las no-parametricas), si buscas la relacion entre ellas (tendrias que ver tambien el tipo de variable y la escala en que la tienes acotada) ....... hoy no lo traje pero manana te voy a mandar por aqui mismo un libro de stadistica en que aparecen todas las pruebas que se pueden realizar y graficamente te ubicas en dependencia de tus variables .......

suerte

To my opinion, "best practice" is to think about and to preciely formulate the aim of your analysis, and then to find a practicable way to get an adequate answer, based on a thorough understanding of the kind of data you have.

The normal distribution comes in the story when we have a model about the expected value but have no idea about any structure behind the residuals (the deviations of the observed values from the model predictions). Under the assumptions that these residuals will scatter independently (of anything) and symmetric, one can derive a probability model for such residuals, and this is the normal probability model. Since frequency distributions can serve as empirical approximations of such probability models, an observerd non-normal distribution simply tells us that either the (functional) model is wrong (like missing predictors), or that there is an unconsidered relation between residuals and/or the expected value (like independence of observations, or the information that the observations are concentrations, counts, or proportions, for which the assumption about symmetry is inappropriate). The former "problem" would lead to a revised model, the latter to a different probability model.

You were mentioning the Spearman test, so I assume you have two at least ordinally scaled variables for whch you want to have a measure of their (linear?) correlation. The answer to this question is given only by Pearson's test (NB: I would not call this a "test", I would rather say that I like to estimate the correlation coefficient!). The estimate and the inferred uncertainty (standard error or confidence interval) will be reasonably "correct" when both variables are reasonably well "normal-distributed". If this is not the case, then there is nothing like a sensible coefficient of a linear correlation. However, sometimes there is a sensible linear correlation between the logarithms (at least when biological data is concerend).

Spearman gives you a coefficient for the rank correlation. This is applicable (and valid) for any kind of monotone relationship of the variables, independent of their distribution. The problem is the meaning. It is already hard to say what Pearson's coefficient really means, but one (at least I) gets seriousely lost when it comes to a sensible interpretation of Sprearman's coefficient. It is well worth to compare the relative "strength" of monotone relationships between differen variables, but a single coefficient is something uninterpretable.

If your aim is just to have a look at some kind of relationship, then do exactly this: plot the data and have a look (and don't calculate some funny coefficients)!

If your aim is some kind of predictive model, then you should really first have a sensible model (that's the hard part), and the rest will come "automatically" (and correlation coefficients won't be very helpful anyway).

In general, tests that compare distributions are not great, so most important: plot a graph. Any obvious outliers? Does the relationship look linear (not curved)?

If not, can you make the relationship linear by transforming one or both of the variables?

If the relationship isn't linear and can't be made linear, use Spearman's as a measure of correlation. If it can be made linear, use Pearson's.

Hola irlan revisa el libro este (no te lleves porque sea de biostadistica), mira los diagramas iniciales y la forma en que analizan datos .... el otro es un articulo que alomejor te sirva por la estadistica ...... mira tengo un libro con todas las pruebas estadisticas pero pesa 25 megas y sabes como es la internet aqui para upload eso ... bueno igual trata de buscar un libro que se llama estadisticas no parametricas de sieguel y castellanos del 1995 que ahi si esplican detalladamente todas las pruebas no parametricas y sus casos especificos .... suerte y espero te sirva de algo

What will a test tell him?

Consider plots of the the data along with a consideration of the underlying structural model.  You can also use flexible distributions, i.e., partially adaptive estimation which can accommodate a wide range of skewness and kurtosis. 

Try the Q-Q (Quantile-Quantile) plot where you plot the quantiles of two distributions against each other. One is your (empirical) distribution of your data and the other is a test distribution.  When the two distributions are linearly related, the points of the QQ plot should approximately lie on a line. The QQ plot is nice because you can visualize outliers and also judge the "impulsiveness" of your data. That is, if the distribution-tail of your data falls slower than the test distribution tail. This is observaed when the QQ plot points form an "S" shaped curve. Wikipedia has a good page on the QQ plot and it is also implemented in R, MATLAB, etc... usually as a function qqplot().

 Dear Grangel.

There´s no problem with normal distribution to make the correlation. Spearman test is very helpfull in this case, not Pearson. You can transform your variables if you want at any case the normality. But there´s a limit in transforming such variable. Non-parametrical is what researchers use when they face such case. I think you speak spanish, i give a paper about precaution in transforming variable.

Regards

Josefina de Calzadilla, Walkiria Guerra, Verena Torres (2002). El uso y abuso de transformaciones matemáticas. Aplicaciones en modelos de análisis de varianza.  Revista Cubana de Ciencia Agrícola, vol. 36, no. 2, pp. 103-106.

Robert B. O’Hara1* and D. Johan Kotze (2010), Do not log-transform count data.

Methods in Ecology and Evolution  1, pp. 118–122.

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