Assuming 12 varieties are evaluated in 4 replicates in Randomized Complete Block Design (RCBD) where 20 variables are measured, is it appropriate to run correlation and principal component analysis on such replicated data or on the mean value of those varieties across the replicates? Which is the better approach? That is, there would 12*4 =48 observations if the analysis is based on replicate values while there would be 12 observations having computed the mean prior to correlation and principal component analysis.
Dear all,
it has just occurred to me that doing PCA on the replicated data may not be appropriate. Take for example, if we are to plot the PC1 vs PC2, we would have 48 data points i.e. four data points for each variety. I think running PCA on average value is better. What of pearson correlation analysis?
It depends on the nature of your data. Normality assumption must be hold, your data must be metric/continuous and kindly note that outliers make your results unstable...
First principal component is created in such way to describe maximum of variance in data set, second pc is orthogonal to first and describe maximum of the rest variance and so on.
In my opinion replication better represent variance in data set. In other hand using means the scatter is decreased so less number of PC's will be needed to describe data. In my opinion findings for both ways will be similar.
When you use correlation coficient you should be very careful because Simpson's paradox can occur.
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