[R] Is the PC1 in PCA always a "size effect"?

[asako Ishii]

Hi

Im a beginner to R or statistics in general.

I am comparing our products(6 in all) and competitive products(2). These products have a similar chemical formulation, but slightly different to each other. I chose the quantity of each chemicals as the variables and did a PCA to extract the characteristics of the products. The result was a PC1 which could be interpreted as the difference between us and the competitive. In my previous experience, PCA always gave me a PC1 that is a linear combination of the same sign, which is called more or less a "size effect" as is explained in statistics textbooks. Is there anything wrong in my PCA or in my interpretation of the result? Does the same thing often happen in other field too?

Thanks in advance!
-- 
Yukihiro Ishii <yukiasais at ybb.ne.jp>