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I am also a little bit confused about the assumption of independence.

I have the following situation:

  • one continuous dependent variable (radiant power of a medical device)
  • a few independent variables [age of the device (categorized), ...]

The researcher went to a lot of doctors' surgeries to investigate the radiant power of their device[s]. The issue is, that some practices had more than one device.

My question is whether it is still meaningful to apply a multi-factor ANOVA? Because I doubt that the observations taken from the same surgery are independent from each other.

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  • $\begingroup$ How many practices are there? Did you get multiple measurements of each device? $\endgroup$ – gung - Reinstate Monica Jan 31 '16 at 13:59
  • $\begingroup$ I would say you might want to model it in the framework of ANCOVA or random effects. Such a situation is often referred to as "pseudo-replication", since your doubt is correct, the obs from the same surgery seem to be correlated. You might want to check mechanism to overcome this problem of pseudo-replication before trying to choose an analysis. If the data is not collected yet, this design should not be adopted. $\endgroup$ – Henry.L Jan 31 '16 at 14:26
  • $\begingroup$ Because a user has been kind enough to answer, please do not destroy your question. $\endgroup$ – whuber Jan 31 '16 at 20:31
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Your data won't be independent. That means your confidence intervals will appear narrower than the correct width and your p-values will be incorrect. If the radient power is conditionally normal, you should use a linear mixed effects model to assess this.

One other note, you would do best not to categorize the age of the devices. Use the actual ages as a continuous variable and use a continuous regression rather than an ANOVA. This will give you more statistical power and a clearer answer to your question of interest.

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