Data from the Open science framework
IV1: Sex (male,female), IV2: Perceieved Social Support (low,mod,high)
DV: Identity exploration (continuous data… but scores are 1-4)
the moderation of sex and perceived social support on identity exploration.
Firstly, I have variance in group size - between genders and across the support levels. for example in the female support level low 46, and high is upwards of 1000. Similar In the male groups.
Tutor said it does not matter… which brings me to my next issue:
Normality is violated (Shapiro-wilI, histograms) alongside variance (Levenes test).
data has been cleaned and there are a small number (5) outliers, but not worthy of removal.
lecture notes indicate I can fall on Central limit theorem and run the ANOVA.
my deep dive into research gate and literature says otherwise.
Any advice would be greatly appreciated.
Sal Mangiafico, I won't be able to share my full data set with you but could show a snapshot of some output if you believe it would help.
If ANOVA is acceptable (with n=45 in the least occupied cell) depends on the distribution of the DV. When this is very skewed (many values clustered at lower or upper limit), then the CLT requires much more data to deliver a reasonable normal approximation of the test statistic. If the distribution is more or less symmetric, ANOVA should be ok, but a look at the distribution would be re-assuring. Could you provide a normal-QQ plot of the residuals from your ANOVA model? Also, heteroscedasticity may be a concern, particularily when the variance in the higly occupied cells is smaller. Again, a residual diagnostic plot would be helpful.
A better approach, though, would be a acknowledge that the DV is bounded at a lower and an upper limit. One way to deal with this is to scale the DV into the range (0, 1) and use the logit-transformed values in the ANOVA (compare the normal-QQ plots of the residuals!). You may even avoid the logit-transformation of the DV and use a quasibinomial or beta GLM to fit the logit of the expectation.
Hello Paige Whitelaw
1- "I have variance in group size - between genders and across the support levels." By the way, this is an important issue.
2- See this link. https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics.php
Assumption #5: Your dependent variable should be approximately normally distributed for each combination of the groups of the two independent variables. Whilst this sounds a little tricky, it is easily tested for using SPSS Statistics. Also, when we talk about the two-way ANOVA only requiring approximately normal data, this is because it is quite "robust" to violations of normality, meaning the assumption can be a little violated and still provide valid results.
3- Consider using Heteroskedasticity tests. Like the Breusch-Pagan.
4- In my opinion, think of something called select cases, just to balance the frequency in different groups of independent Variables.
Abolfazl Ghoodjani , I would recommend using a different source to understand the assumptions of a general linear model like anova. Perhaps a textbook on design and analysis of experiments. But also for common nonparametric tests. I consider that site to be pretty bad with how it presents them.
Sal Mangiafico Yes, Sure. Anyway, I'm still learning. Thank you for your attention.
Abolfazl Ghoodjani , more to the point, I think that the Assumption #5 you quote is bad advice.
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