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.

  • $\begingroup$ 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

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.