Hi, I am completing an assignment on factorial ANOVAs, however my data is not normally distributed and does not have homogeneity of variance, thus not meeting the ANOVA assumptions. This uses a 2x2 independent groups design (two IVs) and am exploring interaction effects. I'm thinking maybe the appropriate test to use would be a Kruskall-Wallis, but I am unsure of whether this test can be performed with two IVs?
Many thanks in advance!
You can have some information regarding the non-parametric test in the link
https://www.researchgate.net/post/Is_there_a_non-parametric_equivalent_of_a_two_way_ANOVA
However, parametric tests are usually the first choice, therefore I suggest to investigate why your data have not homogeneity of variance. Secondly, if you could use the error distribution models different than a normal distribution; or easier, if data can be transformed (but could be a risk in the interpretation: https://www.researchgate.net/post/How_can_we_trust_in_the_back-transformed_confidence_interval_and_statistical_analysis )
Yes, you can use Kruskall-Wallis test because a 2x2 factorial design is a completely random design with 4 treatments.
Dear Sarah Wilton
Information in the following link would be helpful in determining the correct statistical test. Thanks.
https://stats.idre.ucla.edu/other/mult-pkg/whatstat/
you can also use Mann-Whitney if you have two variables.
for more than two variables, Kruskall is appropriate.
if you insist on ANOVA, you can correct normal distribution of your data through omitting those responses, which created the issue. copy your data into excel and find those outliers, then delete them from SPSS.
hope this helps.
I agree completely with my friend Pouya Zargar except on one point and that is don't delete real data. By real I mean not a blunder. If it is not a blunder then it deserves study as any other observation does. See the attached for an example. Best, David Booth Blaine Tomkins since ANOVA and regression are equivalent one cannot handle anything better one way than the other only more conveniently. For details see:https://www.bing.com/search?q=equivalence+of+anova+and+regression+models&FORM=AWRE
Best, David Booth
PS there are nonparametric tests but not nonparametric data
Hello Dear Sarah Wilton
In non parametric tests, it is appropriate to perform Kruskall on more than two variables. If you want to test the difference between the groups, after performing the Kruskall test, in the anova test for the sections that differ, the variances in the post hoc section are not homogeneous; You can choose between Tamhane Test, Dunnetts T3, Games Howel or Dunnetts C (according to number of sample) tests.
Best Regards...
A slightly pedantic response is that there is no such thing as nonparametric data as this is a property of the model not the data. More practically if the main issue is homogeneity of variance I'd suggest the Welch corrected ANOVA:
https://psyarxiv.com/wnezg/
Otherwise, the approach depends on whether the residuals not the data are approximately normally distributed. If it is a repeated measures design its possible for the residuals of the ANOVA and the raw data to have quite different distributions.
Solutions include:
1) Using a generalised linear model that models the outcome as a binomial proportion, Poisson count etc.
2) Using a transformation to handle to non-normality of the residuals. This includes potentially using a rank transformation that would effectively give you a nonparametric model.
3) Using robust regression and bootstrapping
I'd usually favour a generalised linear model type approach.
Thom Baguley Thom, I have asked several people this and gotten strange answers. If only the residuals need to be normal, why does a box-cox transformation on the DV often work.? Isn't it true that the the distribution of the DV and the residuals are related by the fitted model? Thanks very much. Stay safe, David
David Eugene Booth - sorry for delayed response. It is a good question.
In a very simple model such as a one sample t test the residuals and Y will have the same distribution (the difference is just the shift in location). As you increase the complexity of the model this link is more likely to break down and the residuals could have a very different distribution. The simplest illustration is probably a paired t test. The raw data from the paired observations often has a very different distribution from the residuals of the model (which are effectively the same as the distribution of paired differences, not raw scores).
In practice the distribution of residuals and Y even in complex models are related, but sometimes slightly and occasionally very different. The data you work with often matter too. It is more common in my experience to see residuals differ when you have random factors (e.g., repeated measures etc.). This is very common in psychology, health and social sciences. Transformations often work for this reason. So my view is always to plot the residuals when checking assumptions and when considering the need for transformations. One can make simpler points about "outliers" - as these are model dependent.
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