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I'm having a dataset where I've measured the decay of a certain drug at different time intervals.

I have on measurement for each time interval, and I want to test if there is a correlation.

Straight forward is the use of a Simple Linear Regression. However I've read somewhere that a t-test (paired/unpaired) or ANOVA would work too. However in my case I have a hard time seeing this as I only have one dependent variable and one independedent variable and both are continous.

Data could look like this:

Time     Conc
  1      1000
  2       750
  3       250
  4       75
  5        0

Hope that someone can get me out of the loop my head is in after having read so much about the relationsship between these three methods.

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  • $\begingroup$ T-test and ANOVA are best used when you have groups, so all the measurements from each time interval can be considered as a group. In your example you have 5 time intervals so you'd have 5 groups. If your time intervals are equally spaced, then it also makes sense to use simple linear regression. $\endgroup$ – Sheep Apr 26 '16 at 14:49
  • $\begingroup$ @Sheep So, for this data, I need to divide the data into groups depending on the time, eg. the mean of the time variable? $\endgroup$ – Nicolai Apr 26 '16 at 14:50
  • $\begingroup$ Yes, you can divide the data into groups based on the time intervals but it's not advised to do so unless if you have prior knowledge that it's advantageous to do so. (You've seen similar data from a previous experiment). If you have direct time and concentration measurements, a linear regression on the continuous time variable should be sufficient. $\endgroup$ – Sheep Apr 26 '16 at 14:53
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Looking for a correlation between time and drug concentrations in this case is not at all helpful. Correlations look for linear associations between variables. These seem to be drug concentrations in vivo, which typically have time courses that are more like exponential than linear decays. The interest in these situations is more in the rate constants for loss of drug concentration and how those rate constants are associated with other biological variables.

Think about this: if you give a single dose of a drug in a living individual, do you expect anything other than an eventual drop to a concentration of 0? What you care about is how quickly that happens, as that almost certainly will be the result.

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