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I'm trying to model data as a 2nd degree polynomial, but the data is unpaired and each data point of average values has a standard error for each axis.

My data:

  1. A time series in minutes (time tissue is exposed to cryoprotectant)
  2. A % value of tissue survival after liquid nitrogen storage (3 replicates for each time point)
  3. A % value for the uptake of cryoprotectant in tissue directly after exposure to cryoprotectant (3 replicates for each time point)

The tissue used for the uptake is of the same type but is from a different source, as the uptake measuring protocol is destructive.

So there are 2 sets of 3 values for each time point. However, a scatterplot of this data does not make sense because the survival and the regrowth values are not paired - I could mix and match my values within each time point.

At low levels of cryoprotectant, survival is low because of ice formation. At high levels of cryoprotectant survival is low because of cryoprotectant toxicity. Therefore:

  • I would like to model survival vs. uptake to find the maximum survival value's corresponding cryoprotectant uptake.

I can:

  • Perform a polynomial fit on survival vs. uptake using the average values for each time point
  • Use that fit to find a predicted optimum uptake %

I cannot:

  • Get a p-value for the fit that is valid (i.e. one that assesses the error at each time point for both variables)

Therefore is it possible to model such data with a valid p-value, or does the fact that it is unpaired mean it doesn't make sense? I'm currently carrying this out in R.

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    $\begingroup$ please explain this "However, a scatterplot of this data does not make sense because the survival and the regrowth values are not paired" in more detail (without the use of subject specific jargon, of course). You say the uptake measurement is not from the same source, this is not enough detail. $\endgroup$ – WetlabStudent Jun 9 '14 at 14:52
  • $\begingroup$ My apologies. The samples that give the values for the survival are not the same samples that give the values for the uptake. So for each time point there are 3 values for survival (A,B,C) and 3 values for uptake (1,2,3), but those values are not paired i.e. A-1, B-2, C-3 is as valid as A-2, B-3, C-1. Does that make sense? Sorry for the lack of clarity! $\endgroup$ – AcerMouse Jun 9 '14 at 15:45

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