So here's my dilemma. I wanted to run multiple 2 and 3 way anovas on various data sets as well as a multiple regression analysis, but most of them don't meet the assumptions of normality and homogeneity of variance. So I know the non parametric test would be to do a Krustal Wallis and run appropriate post hocs from there, but then I can't find out if there are any interactions between my independent variables that has an effect on the dependent variable. I can only compare within groups of the independent variables. I have tried transforming my data and still nada. Any advice would be highly appreciated.
Well you haven't really given much information but I would think about factorial designs with interaction terms. The best current sources are given below:
https://www.amazon.com/Design-Analysis-Experiments-Douglas-Montgomery/dp/1118146921/ref=sr_1_1?keywords=montgomery+design+of+experiments&qid=1559764357&s=gateway&sr=8-1
The best way to deal with lack of normality and nonconstant variance is by transformation using the Box-Cox scheme. See this link:
https://www.google.com/search?q=automated+Box-Cox&rlz=1C1CHBF_enUS847US847&oq=automated+Box-Cox&aqs=chrome..69i57.11630j0j8&sourceid=chrome&ie=UTF-8
Best wishes, David Booth
PS you ignore the assumptions at your peril. Simply saying I have a large sample size almost never works. see:
https://www.amazon.com/Applied-Linear-Statistical-Models-Michael/dp/007310874X/ref=sr_1_2?keywords=Kutner+Applied+Linear+statistical+models&qid=1559766091&s=books&sr=1-2
I can speak more about multiple linear regression than KrusKruskal wallis. I think there are some controversies over how important statistical assumptions are if your sample size is large enough. If you have a giant sample, you could try to make some arguments for why it's okay that you don't meet the normality assumptions. Also, if you have variables that you would expect to be non-normally distributed (i.e., hear rate), you can make that argument too and run the non-normal data... I know that is not the best answer though.... For the multiple linear regression, you could try using weighted least-squares to fix the violated assumptions. Weighted least-squares is used in situations where the homoscedasticity and normality of errors cannot not be correct for by transforming the data. The weighted least-squares approach is meant to heavily weight observations falling at levels of the independent variable that are associated with low variability on the dependent variable and to assign moderate weight to those observations falling at levels for the independent variable having high variability on the dependent variable. See: https://www.youtube.com/watch?v=enPK_SXILnA
There are various options that depend on the details of your data. You have tried transformations, but I would normally consider generalised linear or similar models before transformations and also consider options like robust regressions and/or bootstrapping. What is best depends on your data - and you haven't really explained what the problem is - skew - kurtosis- bounded values?
In addition it may be fine to use regression or ANOVA as these procedures don't assume normally distributed data but residuals sampled from a normal population. The distribution of the residuals might be approximately normal fora given model even if the raw data aren't. For homogeneity of variance you can use the Welch corrected test: https://psyarxiv.com/wnezg/
There are also more flexible approaches such as fitting a bayesian model.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA