HOV tests

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    I need a few clarifications on HOV & ANOVA
    1. What do we do first – HOV or ANOVA?
    2. If HOV is done first and it fails, then do we still need to do ANOVA?
    3. In HOV, which result we need to consider – Bartlett or Levene’s?


    Robert Butler

    The first thing you do is plot your data – in the case of running an HOV or an ANOVA my first choice would be histograms and boxplots.  Once you have estabilished that the data you are examining looks “reasonable” – (no bimodality, no tails-wagging-dogs, etc.) then, depending on what you want to examine you could run either one. 
      If your focus is on differences of means you would probably choose ANOVA and, since lack of homogenity of variance can be an issue with this test you might want to check for this.  Bartlett’s test is very sensitive to lack of normality in the sample populations and I don’t know of any current text that recommeds running it.  Levene’s test is the test of choice.
      If your data fails Levene’s you can still run the ANOVA – the worst case will be that, because of the lack of variance homogenity, ANOVA won’t see a difference. If the differences in variances aren’t “too bad” ANOVA may still report a significant difference.  If you just absolutely have to run a test on means in the presence of variance inhomogenity then you could use Welch’s test. 
      If, in fact you don’t have variance homogenity it has been my experience that the investigation of the this lack of homogenity pays far greater dividends in terms of understanding, discovery, and money to the bottom line than does the simple detection of a means difference when one or more of the variances are significantly different from one another.

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