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In my biology class we were doing a lab on respiration rates of peas. We used a respirometer with a small pipet tube (markings up to 1 mL) to measure the volume of gas; by immersing in water, the gas and water would remain separate and the level of water could be measured on the pipet, giving the amount of gas inside and therefore the respiration rates. However, at one point, the water level went beyond the highest mark on the pipet; the peas had used more than 1 mL of air for respiration. Now I'm supposed to find the average gas usage (other class groups did the same thing but none had peas use more than 1 mL of gas). How do I compute the class average? Do I exclude my data point for those trials?

In short, I couldn't measure the amount of gas used by peas because they used more than the pipet could measure. Other groups doing the same experiment didn't have this problem, so how do I find the average gas usage?

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  • $\begingroup$ How many measurements / peas were there? Is it reasonable to assume that the measurements followed a normal distribution, or a symmetrical distribution? $\endgroup$ – gung - Reinstate Monica Jan 31 '16 at 22:25
  • $\begingroup$ There were 4 other class groups who made the measurements. This makes it really difficult to decide. $\endgroup$ – Faraz Masroor Jan 31 '16 at 22:28
  • $\begingroup$ Each respirometer had 25 peas in it but the respiration rate was taken as the sum of all of the 25 peas. We didn't measure the rates of each individual peas, just all 25 as a whole. $\endgroup$ – Faraz Masroor Jan 31 '16 at 22:28
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    $\begingroup$ So you have 1 measurement per 25 peas, & there were 5 measurements (of which 1 was above the scale), is that right? Is there any good / theoretical reason to assume the data follow a symmetrical distribution? $\endgroup$ – gung - Reinstate Monica Jan 31 '16 at 22:48
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    $\begingroup$ Then I'd recommend first reporting the average as if there was no censoring. Then note directly afterwards that using that average as an estimate of the true mean will be downward biased, but that its not possible for you to say how far down without doing more statistics than you currently know how to do. You now have the preview for what those statistics would be, so you're a little bit ahead of the game. And if you ever eventually need to do a censored analysis - well - you know where to find us... :-) $\endgroup$ – conjugateprior Jan 31 '16 at 23:39
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Since it's for a class I'd recommend the following:

  • Report the average as if there was no censoring, treating the censored value as 0.1.
  • Note that this average is, as an estimator of the true mean, downward-biased, so you'd expect the true mean to be a bit higher.
  • Also note that it's not possible to say how far the average will be biased without doing a more sophisticated statistical analysis that takes into account the censoring.
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