# Parametric or non-parametric test?

#### tfm09

##### New Member
I need to perform a correlation test between a parametric data set and a non-parametric data set: should I use a parametric test (Pearson) or a non-parametric test (Spearman's rho)?
I'll be performing the analysis on SPSS.

#### Miner

##### TS Contributor
What do you mean by a nonparametric data set? Non-normal, ordinal...? What does the scatter plot show? Linear relationship, monotonic increasing/decreasing...?

#### tfm09

##### New Member
So by non-parametric I mean not normal (ie one of the conditions for normality: homogeneity, normality, interval data and independence is breached)

#### Miner

##### TS Contributor
While many sites will tell you that normality is a requirement for Pearsons, in my experience, it is not. What does a scatter plot of the data show?

#### tfm09

##### New Member
The scatter chart shows a linear relationship

#### Miner

##### TS Contributor
Pearson's will work. I attached a marginal plot of two variables. The x variable is from a uniform distribution. The y variable was created by adding a uniformly distributed error term to the x variable. Both the x and y terms are clearly non-normal. There is also a strong linear relationship and a strong Pearson's correlation.

As Ellis Ott always said: "Plot the Data!"

#### tfm09

##### New Member
Dear miner, thanks very much for all your help :tup:. I have another question for you if you can help it would be greatly appreciated:
I'm going to model the non-parametric data sets to try and model the relationship between them: I was going to use a generalised mixed linear model, but thats for normal data isnt it- what would be the best model to use for non-normal data?

#### Miner

##### TS Contributor
I am guessing that you intended "general linear model" rather than "generalized linear model".

Regression analysis does not require normality in the variables themselves, but normality of the residuals. Run your analysis then test the normality of the residuals (as well as the remaining residuals diagnostics such as no unusual patterns vs. fitted values or time).

#### GretaGarbo

##### Human
...the non-parametric data...
Hmm, there are no "non-parametric data". But there are some non-parametric methods.

There are many parametric methods for skewed non-normal data. Examples are the the binomial distribution, the Poisson distribution and the exponential distribution.

The above mentioned distributions can be estimated in models like "generalized linear models" (that will also include the normal distribution as a special case). It does not seem clear at the moment if you need the "mixed" part in the model.

#### noetsi

##### Fortran must die
There are distributions that are non-parametric Normality of the residuals is actually not required for point estimates of regression. But it is neccessary for the CI and assessment of the model (the p values) and most won't be interested in running regression if they can not test the null hypothesis.

While Pearson might work with some non-normal data that is questionable if you have binary data (data with two levels). Polychoric correlations are commonly recommended for that.