Hi,
I was under the understanding that i would need to test for normality before conducting anova tests. However, i recently read this article by Bruce Weaver @BruceWeaver online and now i'm not so sure:
Presentation Silly or Pointless Things People Do When Analyzing Data: 1. ...
"If means and standard deviations are sensible and appropriate for
description, then t-tests (or ANOVA etc) will likely be just fine for inference."
I have conducted a study with 20 participants, where each participant played the same game three times, using a different control technique each time. In each play through of the game, participants had to complete the same 16 tasks with the time taken for each recorded along with the total game time. i effectively have 48 times per participant. I have all the data in SPSS as a wide case, so i have columns in the following format:
Task 1.1 | Task 1.2 | Task 1.3 | Task 2.1 | Task 2.2 ...
The ".n" represents the version/technique.
I have been testing normality by following a guide on laerd. It looks at the shapiro-wilks sig and divides both kurtosis and skewness by their standard errors and checking it's within the range +/- 2.56, but i have been told i should be using +/- 1.96
I will be perfectly honest, this is the first time I've done statistical analysis on my research, so when reading stuff online the technical jargon can be quite confusing. If it's not too much trouble could answers have a low level/simple explanation in them before proceeding to more complex discussion.
Many thanks to anyone who reads this :)
Hello Adam,
For your two within-subjects design (e.g., two repeated measures factors), there is an assumption that score residuals are normally distributed. The admonition you quote from Bruce Weaver concerns more the scale of the measure used rather than normality.
Why do we assume normality? Because that permits identification of the appropriate reference ("benchmark") distribution against which sample results are compared to determine relative rarity, assuming that the null hypothesis is true. Alternatives would include running an exact test, which is computationally pretty intensive, given the number of levels of the task factor you have.
That said, Micceri's 1989 article, The unicorn, the normal curve, and other mythical creatures (Psychological Bulletin, 105, 156-166, doi: 0.1037//0033-2909.105.1.156) pretty much casts doubt on many "typical" data sets conforming well to the normality assumption. He tested his data sets at the .01 level, there's no reason you can't do likewise.
Good luck with your work!
David Morse Hi David, thanks for your response. Correct me if i'm wrong. I believe your saying that if i use one of the three techniques as a baseline/reference that the others are compared against as well as themselves. I would not need to conduct a normality test?
Hello Adam,
No, I wasn't saying that normality is ignored (for any parametric comparison). Your proposed alternative sounds like paired t-tests, in which the difference scores are presumed to be normally distributed.
With tongue in cheek, you could pray for robustness. The only problem is, short of collecting the entire population, there is no way to know if your prayers have been answered!
Good luck with your work!
David Morse Ok, thanks for clarifying. I'll conduct the normality testing then, so i can conduct my anova and that paired t-test.
Adam Worrallo , I think that the presentation you cited by Bruce Weaver is really good on this question of the assumption of normality.
Let me make a couple of points.
First, he does expand on the quote you cited with, "e.g., reasonably symmetrical distribution with no outliers or extreme scores".
Second, he presents an argument against testing for normality, in that as sample size increases, a test for normality is more likely to find a statistical deviation from normality even for small deviations from normality. But in reality as sample size increases, modest deviations from normality become less and less important.
So what should you do? Plot the residuals from your analysis with a histogram or quantile-quantile plot, and plot the residuals vs. the predicted values. (There are other diagnostic plots, too.) You then have your eyes to judge if the distribution is reasonably normalish or reasonably follows Bruce Weaver's criteria.
Also note that if you are using a form of anova that isn't robust to heteroscedasticity, that unequal variances among groups may be a larger issue than deviations from normality.
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