I have two experiments from the last two years in the field. The experiments are supposed to be the same, but different environmental conditions slightly skewed the exposed conditions relative to what was experience last year. I am now attempting to analyze both these data sets to determine if the experimental conditions were close enough to last year's or if the experiment will need to be repeated. I'm currently attempting to analyze the data based on a phenotypic scoring system, physiological and biochemical measurements. However, the two data sets are comprised each of 40 individuals with only 10 overlapping in both experiments (so 70 total). Statistically, what would be the best way to compare these two data sets given the minimal overlap of individuals? I have already run those 10 overlapping individuals through a PCA, Chi-Squared test, as well as a single linear regression and have seen a relatively good correlation, but now need to be able to compare all individuals and see if i can normalize a single score based on these two data sets. How might one proceed with establishing a single platform from which to asses these two experiments?
you have a hybrid repeated measures and independent set up. It may be best to keep what you have done for the repeated measures (overlap) separate and analyse the 30 non-overlapping individuals as two independent unpaired sets.
You say the repeated measures are correlated, that implies a trend, a measurable difference between the first and second years. The first concern is that this suggests that the two sets of conditions are not comparable. However, it may also be due to ageing of the individuals involved. Are your subjects different ages? Have you independent variables that would allow you tease out if the differences arise do to the different years or due to some other variable that is changing too? This will be important to help understand what exactly is different between the two populations.
In the unpaired data you could assess if the two experiments show differences significantly and any variables that contribute to the paired set should be taken into account. However, you will not be testing two populations that you expect to be the same, but two populations that you expect to differ based on your paired sample examination. It means the data would not be able to answer the same hypotheses that a true replication with no skew or bias would. All data would need interpreted in light of the differences between years.
Do you have baseline variables that allow you to check the status of the individuals at the start of each set of observation?
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in addition to James' answer above, you might be interested in reading
http://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=2251&context=jmasm
Derrick, B., Russ B., Toher, D., and White, P. (2017), "Test Statistics for the Comparison of Means for Two Samples That Include Both Paired and Independent Observations" Journal of Modern Applied Statistical Methods, May, Vol. 16, No. 1, 137-157
https://arxiv.org/pdf/1603.00214.pdf
Lubna Amro and Markus Pauly, "Permuting Incomplete Paired Data: A Novel Exact and Asymptotic Correct Randomization Test"
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Is it really that you want to compare the data sets between the two years, or -as I suppose- to analyze the impact of the experimental factors on the responses (scoring, physiological and biochemical measurements, if I am right)?
If the latter is the case, you may use a mixed effects model that adjusts for systematic differences between the years (co-factors) and accounts for the partial replication (those 10 individuals).
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