If you had a data set which exhibited both non-normally distributed and non homogeneous,which statistical test would you use compare two sample mean?
if i go with parametric test normality and homogeneity assumption do not fulfill and if i go with non parametric test then homogeneity assumption does not fulfill..please help..i need to compare two independent sample mean ..
Hello Sanjaya,
As long as you are confident that the dependent variable is at least of interval strength (a so-called "metric" variable), then you could use either exact/permutation or bootstrap/resampling methods to evaluate the effects you'd like to assess. As time passes, more of the major statistical software packages offer one or more of these as options to traditional parametric tests.
Here are a couple of links that you may find helpful:
1. https://statweb.stanford.edu/~tibs/stat315a/Supplements/bootstrap.pdf
2. https://machinelearningmastery.com/a-gentle-introduction-to-the-bootstrap-method/
3, https://www.burns-stat.com/documents/tutorials/the-statistical-bootstrap-and-other-resampling-methods-2/
Good luck with your work.
Hello Sanjaya,
As long as you are confident that the dependent variable is at least of interval strength (a so-called "metric" variable), then you could use either exact/permutation or bootstrap/resampling methods to evaluate the effects you'd like to assess. As time passes, more of the major statistical software packages offer one or more of these as options to traditional parametric tests.
Here are a couple of links that you may find helpful:
1. https://statweb.stanford.edu/~tibs/stat315a/Supplements/bootstrap.pdf
2. https://machinelearningmastery.com/a-gentle-introduction-to-the-bootstrap-method/
3, https://www.burns-stat.com/documents/tutorials/the-statistical-bootstrap-and-other-resampling-methods-2/
Good luck with your work.
Hello Sanjaya
This link may enlighten your mind
https://machinelearningmastery.com/statistical-significance-tests-for-comparing-machine-learning-algorithms/
regards
Wilcoxon test, is a non parametric test to compare samples recommended for data of any distribution. it is an equivalent of a t-test but instead of comparing the means of the results it compares the means of the scores or the medians
After thinking a bit more I realize that I am lazier than David Morse . I would probably fix the normality problem and then use the Welch test if possible. I would agree however that David Morse Solution is better
Zandile Nonyana I believe that the Wilcoxen test will not compare both means or medians unless the distribution is symmetirc. Depending on the application I would also consider power. Sometimes we are a bit careless when we say tests are equivalent.
I will use t-test still but apply re-sampling/bootstrap (X1000)
In My data, I have 5 Variable each variable has Muti-Item (i.e. Var 1= 13, Var 2= 12, Var3= 9 etc.) How I test normality? Suppose Var1 = 13 items could run normality in a group.
Hello Manoj,
The recommendations above apply. In particular, if the residuals from a parametric analysis (ANOVA, regression) are non-homogeneous or non normal or non-independent, then a randomization test is appropriate for metric data.
By the way, the statistical literature warns against statistical tests to evaluate assumptions and advocates graphical tools to evaluate the residuals (Montgomery & Peck 1992; Draper & Smith 1998, Quinn & Keough 2002). See also (Chatfield 1998; Gelman, Pasarica & Dodhia 2002). La¨a¨ ra¨ (2009) gives several reasons for not applying preliminary tests for normality, including: most statistical techniques based on normal errors are robust against violation; for larger data sets the central limit theory implies approximate normality; for small samples the power of the tests is low; and for larger data sets the tests are sensitive to small deviations (contradicting the central limit theory).
Good luck with your research,
David S
Gelman, A., Pasarica, C. & Dodhia, R. (2002) Let’s practice what we preach: turning tables into graphs in statistic research. The American Statistician, 56, 121–130.
La¨a¨ra¨, E. (2009) Statistics: reasoning on uncertainty, and the insignificance of testing null. Annales Zoologici Fennici, 46, 138–157.
Montgomery, D.C. & Peck, E.A. (1992) Introduction to Linear Regression Analysis. Wiley, New York.
Quinn, G.P. & Keough, M.J. (2002) Experimental Design and Data Analysis for Biologists. Cambridge University Press, Cambridge, UK
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