Timeline for Practically speaking, how do people handle ANOVA when the data doesn't quite meet assumptions?
Current License: CC BY-SA 3.0
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| Jan 30, 2018 at 16:37 | history | edited | Alexis | CC BY-SA 3.0 |
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| Jan 30, 2018 at 16:31 | history | edited | Alexis | CC BY-SA 3.0 |
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| Sep 19, 2017 at 19:38 | history | edited | Alexis | CC BY-SA 3.0 |
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| May 9, 2014 at 22:11 | comment | added | Jas Max | Because, to be blunt, it's not my experiment or study system and I don't have to write the manuscript. I'm not really familiar with the species being studied, so I don't have a strong sense of what effect size would be interesting or important. I'm simply trying to determine if the difference is significant. My goal is just to find and use the best tests that will provide the most powerful results--then the researcher can decide if the difference actually matters and write the paper up. I just don't want to misuse a test, or not use a good one that I was unaware of. | |
| May 9, 2014 at 21:53 | comment | added | Alexis | Why is "any significant statistical difference is fine?" | |
| May 9, 2014 at 21:52 | comment | added | Jas Max | I'm not really worried about effect size at all, any significant statistical difference is fine. The details are too long to go into, but the data/experiment is better described here: stats.stackexchange.com/questions/96154/… My immediate motivation is to avoid a reviewer saying "You used the wrong test" but my real goal is to understand which test to use when, and why. Stats textbooks talk about these things in ideal/abstract terms and most scientists I ask just use the tests they learned in grad school, and don't know why. | |
| May 9, 2014 at 21:11 | comment | added | Alexis | To be pedantic, we don't know anything about the population variance, we merely infer. As I wrote. I think your inference on Levene's test is sound. I don't have an answer as to transformation preference. $\alpha$ is the researcher decision, perhaps informed by editorial or funder guidelines. How worried about power are you given your sample size, and magnitude of effect size that you consider relevant? | |
| May 9, 2014 at 20:59 | comment | added | Jas Max | Also, is Levene's test, p<.05 the appropriate test and cutoff for this decision? What about O'Brien's, Bartlett's...the results of these test can differ substantially and I don't really know which to use--so I go with Levene because it seems to be the most conservative. But perhaps that's overkill--maybe by being too quick to abandon ANOVA, I'm switching to a test that unnecessarily reduces the statistical power of my analysis. | |
| May 9, 2014 at 20:56 | comment | added | Jas Max | How do you know anything about the population variance if not by evaluating the sample variance? I interpret a Levene's test p-val as "assuming the population variances are equal, what are the odds your sample variances would differ this much." If I get a low p-val I reject the hypothesis that the population variances are equal and can't use ANOVA. Kruskal-Wallace seems like a good alternative, but is it preferable to transforming data to meet ANOVA assumptions and if so why? | |
| May 9, 2014 at 20:21 | history | edited | Alexis | CC BY-SA 3.0 |
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| May 9, 2014 at 20:19 | comment | added | Alexis | Ah, the assumption of equal variances is the population variances not the sample variances. You can infer that the population variances are equal... via eyeball test, or by some other, say, statistical test. | |
| May 9, 2014 at 20:07 | comment | added | Jas Max | What I'm really trying to discuss is the gap between textbook stats and the real world. Every textbook says "variances must be equal for ANOVA" but of course they never are. So, do we arbitrarily cutoff at a particular point and switch to a different test--if so, at what point? In my field (plant biology) most people just use whatever test they were trained to use without much thought. I'm not really satisfied with that. I'd love any suggestions for books/websites that discuss 'practical' use of statistics--i.e. which test to use when, and why. Thanks for the Dunn's suggestion, that helps. | |
| May 9, 2014 at 19:58 | comment | added | Jas Max | Ok, thanks for this answer, but I'm not completely clear on what you're saying. As far as 'heteroscedasticity' I thought I was using the word in the ordinary sense: "a collection of random variables is heteroscedastic if there are sub-populations that have different variabilities from others. Here "variability" could be quantified by the variance or any other measure of statistical dispersion."-Wikipedia. In my data the variances of sub-groups are unequal (according to Levene's test) so I described them as heteroscedastic. Is this not right? | |
| May 9, 2014 at 19:40 | history | answered | Alexis | CC BY-SA 3.0 |