Sorry colleagues, but I disagree with most of you. Strictly speaking, there is no non-parametric three-way anova analysis and try to apply a parametric anova with ranking data is not that simple, because there must be some criteria in the ranking order as in the cases of Kruskal-Wallis and Friedman tests.

What would be the way to rank the data of three factors or independent variables? If this problem were be solved it must be already incorporated into statistical texts and statistical programs such as SPSS.

The answer to the problem is the application of more complex statistical processes (that do have SPSS) and are the Generalized Linear Mixed Models.

Good luck

The simplest approach is just to rank the data then run it. There is some dispute about this approach, but it is the simplest. I believe the non-linear regression procedure in SPSS allows you to define your own loss function. This won't be "non-parametric" but will lessen the effect of outliers which is often what people want, but is more complex. Any reason why you are limited to SPSS? 

I agree with Daniel. Many non-parametric techniques are simply ranked versions of the original. Even if your data were actually Normally distributed, you would lose at most about 15% of power.

 One way to handle three way classified non-parametric ANOVA is rank the observations of dependent variable and perform the analysis as usual ANOVA. For details one may refer to Conover and Imam (1976, Communications in Statistics: Theory and Methods).

Hi,

Your question:  I need to run a non-parametric three-way ANOVA using SPSS. Is this possible? If yes, how?

There is no way to do three way ANOVA by using SPSS.

Rodrigo, I'm curious:  Why do you need to use a nonparametric (presumably rank-based) method?  What is the outcome variable for your analysis?  Thank you for clarifying.

Try to use Minitab I think it can do it

Sorry colleagues, but I disagree with most of you. Strictly speaking, there is no non-parametric three-way anova analysis and try to apply a parametric anova with ranking data is not that simple, because there must be some criteria in the ranking order as in the cases of Kruskal-Wallis and Friedman tests.

What would be the way to rank the data of three factors or independent variables? If this problem were be solved it must be already incorporated into statistical texts and statistical programs such as SPSS.

The answer to the problem is the application of more complex statistical processes (that do have SPSS) and are the Generalized Linear Mixed Models.

Good luck

I think that the question is clear: Is there a non-parametric three-way anova or it is possible?  And the answer is no, you can try a Generalized Linear Mixed Models techniques.  This methodology it can be applied for normal and no-normal sets of data and when you have one, two or more independent variables.  There's no way to rank the data for a three-way design and if the response is a quantitative variable (not frequencies) you can't apply Chi-squared or Fisher tests.

This paper may give some help;

http://leg.ufpr.br/lib/exe/fetch.php/wiki:internas:biblioteca:fr-70-319.pdf

You must think that GLMM or other non-classical techniques can be useful in some cases, it depends of your research question, variables, etc.  A researcher uses the statistical techniques on this basis and for what of them will give the better results minimizing the data manipulations (better if the data are used without any manipulation), for that reason it's inadmissible to catalog a researcher like Gaussian, Bayesian or something like that like we were in the middle of XX century viewing the fight between Fisher's and Neyman-Pearson's followers.

Best regards to everybody.

Federico, I think one reason why the question will seem unclear to some is the phrase "non-parametric" means different things depending on discipline. Some will think a chi-square is parametric as parameters can be estimated by the model being used, whereas in some disciplines non-parametric means not assuming interval data (perhaps even not meeting the distributions assumptions of some test). This is why on places like stackexchange the questions tend to be longer, include a minimal working example to illustrate the problem, and the norm is to edit the question based on a feedback so that the question improves.

Thank you all... The problem is that we performed an experimental decision making task and the dependent variable is non normally distributed (sample size is around 700 cases). We would like to test the between effects of group (2 levels), the gain value condition (2 levels) and gain loss condition  (2 levels) => 3 independent variables. If possible we need to include IQ as covariate (normally distributed). 

Yes. I tried to check residuals normality, but they also failed. I should try generalized linear model.

In the case of positive skew (more than 2) you should try to use Gamma-log regression. The only issue is that this method does not permit patients with 0 in the outcome.

Try for GLM it should work first investigate the nature of dependent variable wether it is left or right skewed or variance is more.The select suitable link function and distribution and perform GLM.Another option is to use BOX COX transformation

Hi Rodrigo. In fact there is several ways to deal with your situation as I will explain:

1 ) Did you check for outliers in your VD for the 3 groups? If not, please check and redone your analysis.

2) You can assume that ANOVA is suficient robust against the normality assumption. This means that ANOVA tolerates violations to its normality assumption rather well. As regards the normality of group data, ANOVA can tolerate data that is non-normal (skewed or kurtotic distributions) with only a small effect on the Type I error rate.

3) If You don't assume ANOVA's robustness, analyse graphically your data and apply adequate transformations to normalize the distribution. If your data got a normal distribution after transformation, apply a parametric 3-way Anova.

4) If the data transformation was unuseless, please consider to use the ARtool for a align rank transformation. This kind of ranking overcomes the limitations of classical rank tranformation which leads to biased interactions effects. After apply the aligned ranks on a parametric 3-way ANOVA

Some interesting papers related to align rank transformation:

Higgins, J.J., Blair, R.C. and Tashtoush, S. (1990). The aligned rank transform procedure. Proc. Conf. on Applied Statistics in Agriculture. Kansas State, 185-195.

Higgins, J.J. and Tashtoush, S. (1994). An aligned rank transform test for interaction. Nonlinear World 1 (2), 201-211.

Salter, K.C. and Fawcett, R.F. (1993). The art test of interaction: A robust and powerful rank test of interaction in factorial models. Communications in Statistics: Simulation and Computation 22 (1), 137-153.

I leave here a nice document.

Here there is the link for the AR tool

I hope it helps you.

Convert the dependent variables to normal scores (one of the ranking options.)  Do the analyses twice: on raw variables and on normal transforms.  The differences (which will likely not be very great, given what you wrote above) are the effects of non-normality.  If in fact the differences between the normal scores and raw score analyses are not very great, then your original distribution was sufficiently close to normal.

Assumptions  never exactly match the reality, so results are always approximate at best.  So the question is always whether the assumptions are "close enough" to the reality that the conclusions are also "close enough".  With normal score transforms, the calculated results, like p-values for contrasts, are very close.  You'll still want to examine the variances and potential outliers and influential cases.

Rodrigo, I forgot to mention the 5th option, which was already stressed out by you, that is, the generalized linear models in SPSS. In this case,  you should perform a gzlm by choosing an appropriate link function to link random and systematic component.

I leave here some links to pdfs and videos.

https://www.youtube.com/watch?v=FhcP717lQrk

http://calcnet.mth.cmich.edu/org/spss/StaProcGenedLM.htm

Cheers

http://academic.macewan.ca/burok/Stat371/notes/glm.pdf

Once the data is ranked - does it have to be normaly distributed before we can run mixed model in SPSS?

Once the data is ranked - does it have to be normaly distributed before we can run mixed model in SPSS?