ANOVA is fairly robust to violations of normality, particularly if your sample size is large and you have equal variance across groups. Select the 'Levene's test' option in SPSS when conducting the ANOVA to check if the groups have equal variance.

*Remember that ANOVA assumes that your IVs are categorical and your DV is continuous. Is this true of your data?

I thing first of all you should look for regression

Hello Alana,

If distributional assumptions are suspect, you can always evaluate the anova via bootstrap/resampling, which gives an accurate portrayal of differences for the given data set, regardless of normality or homogeneity. SPSS offers this, R offers this (see this link for explanation: https://www.rdocumentation.org/packages/lmboot/versions/0.0.1/topics/ANOVA.boot). Other packages do as well.

As an aside, in a two-way design, note that checking normality amounts to confirming that observations within each cell fit satisfactorily to a normal distribution. Evaluating just the "A" factor levels or "B" factor levels independently is not the appropriate check.

Good luck with your work.

Alana Dyke Here's a nice step by step tutorial on conducting two way ANOVA in spss:

https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics.php

Tariq A Raja I'm not sure how regression solves the problem of nonnormality.

The data has equal variance but one group has

I had a levene value of 0.382 demonststing they are equal ... tried to do a Johnson transformation and got image attached giving me no equation ...

would it be okay to continue with a two way anova ?

The Kruskal-Wallis test is analogous to a one-way anova. There is a traditional non-parametric test for a two-way design with interaction called the Scheirer–Ray–Hare test. Note, too, that these tests are on the ranks of the data, which does change the hypotheses being assessed.

However, there are other, often better, options. One (nonparametric) approach is the aligned-ranks transformation anova. As mentioned, you could use permutation or bootstrap methods, or a permutation approach for general factorial designs. At least in R, these these should be pretty easy to run with custom packages.

I won't give an official opinion on the normality question. It's not clear to me how the software is assessing normality. Is it just pooling all the raw data? Or can you look at model residuals?

One approach on these matters is to use something like the permuation anova and compare the results to those from traditional anova. If there's no meaningful difference, then you know you don't have to worry about it.

Hi Dyke,

Yeh, the normality is one of the assumption for ANOVA and can be tested by different way like Q-Q plot, Kolmogorov-Smirnov Test and the Shapiro-Wilk Test etc.If the variables are not normal you can use transformation to make them normal and if still remains non-normal you can apply non-parametric test.For posthoc tests there are again several approaches which depends upon your experiment like if the replication is same, number of treatments is large or small etc.You can also go for modeling too that again depends upon your data and check the multicollinearity etc. You can use univariate tests as well as multivariate tests that may lead you towards the better approach.

Thank you

Hello Alana,

You being new to statistics, I am wondering if you checked for normality of the response variable. This seem logical but it is not correct. The assumptions for the general linear model (including regression, ANOVA, and ANCOVA) are that the errors (residuals) are normal and homogeneous (Eisenhart 1947, Seber 1966, Neter et al 1983 pp 31& 49, Quinn and Keogh 2002 pp 110 & 280). Evaluation of assumptions in advanced texts, where it occurs, often entails a residual versus fit plot (for homogeneity) and a normal score plot or Quantile-Quantile plot (for normality of the residuals).

The statistical literature warns against statistical tests to evaluate assumptions and advocates graphical tools (Montgomery & Peck 1992; Draper & Smith 1998, Quinn & Keough 2002). Läärä (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). Unfortunately, SPSS tends to promote the practice of checking the response variable.

That preliminary evaluation is not correct can come as a surprise, as can advice against statistical tests to evaluate assumptions. But I think best practice, as in the literature, needs to be put out there.

To check assumptions for residuals see:

https://www.datanovia.com/en/lessons/anova-in-r/#check-assumptions-1

Good luck with your research,

~David S

Chatfield, C. 1995. Problem Solving: A statistician's guide, Second edition (Chapman & Hall/CRC Texts in Statistical Science) 2nd Edition,

Draper, NR and H. Smith 1998 Applied Regression Analysis, 3rd Edition. Wiley

Eisenhart, C. 1947. Biometrics 3:1-21

Gelman, A C Pasarica & R. Dodhia (2002) Let's Practice What We Preach, The American Statistician, 56:2, 121-130, DOI: 10.1198/000313002317572790

Läärä, E. 2009. Statistics: reasoning on uncertainty, and the insignificance of testing null. — Ann. Zool. Fennici 46: 138–157.

Montgomery, DC EA Peck, GG Vining 2012 Introduction to Linear Regression Analysis, 5th Edition. Wiley