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This is the problem:

Some nerve cells have the ability to regenerate. Researchers think that these cells may generate creatine phosphate (CP) to stimulate new cell growth.

To test this hypothesis, researchers cut the nerves emanating from the left side of the spinal cord in a sample of rhesus monkeys, while the nerves on the right side were kept intact. They then compared the CP levels (mg/100g) in nerve cells on both sides.

I think this is the study, but that's an aside, it does not actually help.

This study problem is the basis of many statistics courses. I have no questions about those problems, they are completely simple one-line problems with R!

However, I doubt the basis for all those questions, which is that they claim that a paired test should be used.

Here is an example: http://www.stat.wisc.edu/~larget/stat371/exam2e-sol.pdf

Q: State whether this data should be analyzed using paired sample techniques or two independent sample techniques. Provide a brief justification of your response.

Solution: A paired analysis is more appropriate because there are two observations taken on each individual. There is a paired design. Comparisons between measurements on the same individual better control for extraneous factors.

I'm completely baffled by this "reasoning": With that justification everything is a paired test - after all, everything happens in the same universe! The test is about the neurons, not about the monkeys. And the neurons are different ones (I'm taking a neurology course, so just believe me :-) ).

Now, I'm not certain that a paired test may not be justified in the end, but I'm quite certain the justification above is completely bogus. It uses the individual - but the tests is about cells inside the individual, completely different.

May I ask for your opinion(s)?


Thanks guys, I appreciate the answers I got. I feel as before: The paired test may be justified, but I'd say that for how this is used as a test in stats courses its use IMHO is at the very least not the best choice, at least if the question is as above and the reasoning as quoted.

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  • $\begingroup$ Might help to consider an alternative experiment in which one sample of monkeys had all the neurons cut & another sample none. Could that be construed as a paired t-test? What are the "extraneous factors" here? $\endgroup$ Jan 23, 2015 at 14:33
  • $\begingroup$ That's different monkeys. Paired is when you test smokers who give up smoking, and you test something on them before and after the quit. The SAME individual. $\endgroup$
    – Mörre
    Jan 23, 2015 at 14:37
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    $\begingroup$ "The test is about the neurons, not about the monkeys. And the neurons are different ones" - Right, but it's reasonable to assume that CP production in neurons belonging to the same individual ought to be correlated due to genetic differences or extraneous circumstances. $\endgroup$
    – RobertF
    Jan 23, 2015 at 14:40
  • $\begingroup$ But that is background knowledge that a stats student should not be assumed to have, no? I don't consider it "common sense" to make such an assumption. $\endgroup$
    – Mörre
    Jan 23, 2015 at 14:42
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    $\begingroup$ With apologies to those who have kindly offered answers, I'm voting to close this question as off-topic because it appears to have a pedagogical focus rather than a statistical one and is not phrased with sufficient clarity to permit a definite interpretation. $\endgroup$
    – whuber
    Jan 23, 2015 at 16:10

2 Answers 2

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A paired t-test was suggested in the exam question because creatine phosphate production within nerve cells from the spinal cord may be closely correlated among cells collected from the same rhesus monkey.

A standard Student's t-test, which assumes the samples from each monkey are completely independent, may not have sufficient power to detect a small but consistent difference in creatine phosphate production between nerve cells from the severed & intact spinal cord sections if the measurements are swamped by the observed variation between rhesus monkeys.

A paired t-test may not be the most efficient statistical test in this case given the small sample sizes. Instead, the nonparametric Wilcoxon signed-rank test would be more appropriate.

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  • $\begingroup$ So all in all, I think this is a horrible case to use for statistics classes. Here a lot of background knowledge and thinking seems to be required. I come back to that ridiculous justification that I quoted... $\endgroup$
    – Mörre
    Jan 23, 2015 at 14:38
  • $\begingroup$ That depends - the exam question may be making the assumption that students have been exposed to case-control experiment methodology during the course. $\endgroup$
    – RobertF
    Jan 23, 2015 at 14:46
  • $\begingroup$ Not really, I found this in UTAustinX: UT.7.01x Foundations of Data Analysis on edX.org. (But as I said, I've no questions about the results so no worries that you helped me with homework, I managed to enter the single line t.test(...) line into R myself :) - that this is a paired test was provided). $\endgroup$
    – Mörre
    Jan 23, 2015 at 14:50
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The issue is that CP levels naturally vary across individuals. Some individuals will tend to have high CP levels and some will tend to have low CP levels.

This will tend to make a pair of CP measurements from the same individual more similar than the corresponding measurements from two different individuals would be.

This dependence between measurements on an individual is what makes them paired measurements.

This is different from "everything happens in the same universe" because "being in the same universe" would not tend make one pair of measurements more alike than another.

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Essentially the same reasoning (though less clearly explained) is in the answer you quoted. They don't state my first sentence, but the fact that there's variation across individuals is rather obvious - is that really necessary to state? The consequence of that obvious fact - that two measurements on an individual are paired is stated.

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  • $\begingroup$ But that is not part of the reasoning that is given for the question by those testing their students on it. As I said, I'm willing to accept the judgment - but I utterly reject the justification. The question should include that CP levels in neurons in the same individual are very similar, shouldn't it? $\endgroup$
    – Mörre
    Jan 23, 2015 at 14:36
  • $\begingroup$ "I reject the justification in the answer, what do you think" is not a question in the form required here. If that's really all you're saying, your question would need to be closed. $\endgroup$
    – Glen_b
    Jan 23, 2015 at 14:47
  • $\begingroup$ To be more specific, in the help page what type of questions should I avoid asking there are two relevant items: (1) "there is no actual problem to be solved: “I’m curious if other people feel like I do.”" and (2) "your question is just a rant in disguise". If you're not actually interested in understanding why they're paired, then you have no actual stats problem and your issue with the answer is effectively a rant. On either of those criteria your question should be closed. $\endgroup$
    – Glen_b
    Jan 23, 2015 at 14:54
  • $\begingroup$ I answered your question because I made the mistake of thinking you needed an explanation of why it was paired. You made it clear you don't, in which case, my answer doesn't apply -- and you made it quite clear that you think so too. Your response makes it 100% clear it's not a real question. $\endgroup$
    – Glen_b
    Jan 23, 2015 at 14:55
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    $\begingroup$ The justification seems clear to me. You have two measurements made on the same body part (the spinal cord) on the same subject (the monkey) under two different conditions (normal and regenerating). This should make it clear that there will be dependence between the two measurements and therefore a paired t-test is appropriate. I do not perceive a need for specific subject matter expertise to appreciate this $\endgroup$
    – NickB2014
    Jan 23, 2015 at 15:29

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