I'm working on 10 dependant variables, half of them have normal distribution but the other are not normally distributed so I transformed them by Log10 but only one variable still always non normal even with ln, sqrt.... My question is: Can I analyse this variable by Kruskal-Wallis test whereas the other variables will tested by one way ANOVA?
NB: one way ANOVA because there is one independant variable.
Are you talking about the *data* or about the model *residuals*? Only the latter (i.e. the conditional distribution) needs to be assumed normal distributed (if the IV does affect the DV in some way, the assumption of a normal distribution of the DV is nonsense anyway).
What kind is the data? Is count data, or proportions, or concentrations, is the domain bounded (and if so: where and why)? Or how is the data obtained? Maybe one can formulate a meaningful probability model for some stage of the data generating process and so derive what the probability distribution for the data should be.
If you are simply interested in appying ANOVA, then the question is more: how many values do you have? If you have a lot of data, the conditional distribution does not really matter to estimate mean differences.
Dear Billal Nia,
Try to apply the Johnson transformation (the Johnson translation system) to normalize the values of the dependant variable (to transform non-normal data into normal data). I have not yet seen the actual data that could not be normalized using this transformation.
I want at first thank you for your responses. In fact, I'm working on oil for frying (3 levels) and it's effect on some parameters (10) of lab mice. For each level, we used 5 mices (each mouse is a repetition). I'll send you data file in message box.
Best regards
Dear Billal
You can perform nonparametric test ( Kruskal-Walis ) with non-normal distributed data
Good Luck
Dear Khalid,
Is there a post hoc test when we use Kruskal-Walis test? And is it correct to use Anova and Kruskal-Wallis test in the same analysis?
Is there a post hoc test when we use Kruskal-Walis test?
yes - perform simple Man-Whitney with Bonferoni correction
And is it correct to use Anova and Kruskal-Wallis test in the same analysis?
why not - you have different outcomes, hence different questions and differnet answers
Thank you very much Mr Jean Maccarion for your concise and precise responses.
Dear Billal
You can use multiple Mann-Whitney tests between each pair groups ( treatments ) as a post hoc test after Kruskal-Wallis test, as well as, there are many other tests in the attached files.
About your question, doing ANOVA and Kruskal-Wallis test in the same time, you can do the both analysis in the case of normally distributed data but in the case of non-normal distributed data, you can not perform ANOVA because one of its assumptions that the experimental error has a normal distribution.
Good Luck
Dear Khaled,
Thank you very much for your precious explication.
Sincerly yours
If you rank your variable and then proceed with an ANOVA+ post-hoc. It seems to be working well (see Conover & Iman 1981).
There is a post-hoc test for K-W, called the Dunn test, that is probably the preferred post-hoc test. See the references here:
https://rdrr.io/cran/FSA/man/dunnTest.html
There is an example in R here:
http://rcompanion.org/handbook/F_08.html
Be careful with the hypotheses in the K-W test. It is not a test of medians. There's an example here, about 25% percent of the way down of 3 groups having the same mean and median, but resulting in a significant K-W test.
http://www.biostathandbook.com/kruskalwallis.html
P.S. Please be sure you understand Jochen Wilhelm's initial comment. If you have one-way data with differences in groups, the dependent variable _shouldn't_ be normally distributed. It _should_ look mult-modal. For example, see the plots linked below.
In any case it is the residuals that should be investigated to check model assumptions.
Example, dependent variable:
http://rcompanion.org/handbook/images/image095.png
Same as residuals:
http://rcompanion.org/handbook/images/image096.png
There are good answers from the colleagues, but usually there are many steps to be taken for non-normal data:
check extreme / outlier variables and handle them
check error of data entry
make sure your variable is controlled by design, for example correlation or regression for health and age will lead to wrong result if age is not controlled, that is 20-50 vs. above 50 with health
Then transformation by statistics, and the proper formula is not always the Log 10, but depends on the types and level of skewness.
Thank you very much my colleagues. In fact, Mr Jochen Wilhelm helped me by using QQ plots.
SALUT BILAL?
j'espere que celat'aidera Voir ci joint si non essaye d'utiliser le BOX COX method que tu trouvera dans le logiciel Minitab 17 il te donnera lavaleur de l'exponentiel avec le quel tu trensformera tes données.
Sinon, travail avec les tests non parametriques et la tu a le SPSS 21 qui est bon car il te permet meme d'obtenir une bonne representation graphique des sous ensembles homogenes ce qui a ma connaissane n'est pas possible avec les autres logiciels qui calculent juste la difference entre groupes ou niveaux de variables
voila bon courage et si ya besoin tu a mon tel ca me fera laisir de discuter avec toi
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