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I've an ongoing experiment. We're trying to determine if it's possible to detect if a bunny is infected with a disease through an electronic device over a period of time of 1 month. Since we couldn't get a higher volume of the virus we have to work with 3 control subjects and 3 infected subjects.

The problem is that we didn't realize that the subjects involved had two different blood types( A & B). So now we have Group A (2 control & 1 infected) and Group B (1 control & 2 infected).

The difference between blood types changes the magnitude obtained from the instrument.

My questions are, what type of analysis should I use (Specially for small samples/Data-sets)? Am I still able to divide them into control and infected groups? Is this problem reliable (in terms of statistics)? Is a test of standard deviations the best way to approach this?

Thanks in advance

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  • $\begingroup$ Yes you can apply probability and statistical analysis, but you'll have to make some assumptions that variables follow a certain distribution etc.... (eg. error term is normally distributed or something like that). Various statistical arguments that are based upon asymptotic results, arguments that require large samples (eg. that the sample mean converges to a normal random variable as $n \rightarrow \infty$) will almost certainly be inapplicable. $\endgroup$ – Matthew Gunn Sep 27 '16 at 21:43
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Most significance tests would have very low power in this situation, but that's just one of many problems with significance tests. I would recommend confidence intervals, but some of your groups have only 1 subject, in which case most confidence intervals will probably be undefined. I think the best thing to do is just report your data literally, since you only have 6 numbers.

If you have more than one measurement per subject (and hence more than 6 numbers), things are different. The more measurements you have, the more you can get out of conventional longitudinal methods. Of course, you'll still have an at best extremely imprecise estimate of between-subject differences, which could be big.

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  • $\begingroup$ I took measurements over 4 weeks, essentially I have 28 measurements for each subject. I tried some standard deviation tests and ANOVA, both differentiated between infected and healthy subjects, but only if I grouped them by blood type. Do you think the number of measurements is too low to try to do some analytics with it? $\endgroup$ – Diego Corona Sep 27 '16 at 18:22
  • $\begingroup$ @DiegoCorona You could try a mixed model with a random intercept for each rabbit and fixed effects for blood type and infection status. $\endgroup$ – Kodiologist Sep 27 '16 at 18:33

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