Can a non sequitur be between premises rather than the conclusion?

Being an engineer who has dabbled in other fields of science, I think the critical flaw is that P3 is not necessarily true. For instance, I've been reading a lot on supplements recently, and have seen conclusions that read something like "After receiving a 1mg/kg daily dose of the supplement for 2 weeks, 50% of participants self-reported increased feelings of alertness, vs. 10% who received placebo."

In this case, the dose, the time frame, and the numbers of participants are quantified and objectively measurable. Your eyesight might be bad, but any other person looking at the same set of data would get the same conclusion. On the other hand, increased feelings of alertness is a subjective perception. This doesn't necessarily sink the whole study, you would just need to get a sufficiently large sample size that would give you the statistical confidence to assert that, for an average person taking this supplement, it is X% likely to cause feelings of increased alertness. While their is some subjectivity involved, it has a much more solid foundation than an uninformed opinion.

Hi, Jason! 

A non sequitur cannot occur between premises unless those premises are part of a complex argument. A complex argument is an argument that has a smaller argument contained within it, and the premises and conclusion of the smaller, contained argument are all premises of the larger, containing argument. If there is a non sequitur between the premises and conclusion of the smaller argument, then technically, relative to the larger argument, there is a non sequitur between premises! 

Other than that quasi-loophole, it is not possible. You're feelings about the logical connection could still be on to something or other. Perhaps your emotions are detecting some equivocation, ambiguity, or tricky falsehood in the premises. But not a non sequitur (which is what my “no fallacies” mark refers to), unless there is a premise-conclusion relationship. 

Thank you, Jason

From, Kaiden 

P.S. I have not weathered the voluminous comment discussion, so cannot help it if I missed certain information relevant to my Answer.

It wouldn't be a 'non sequitur', but you could make an inference objection to contest the connection between two premises. That seems odd, until you realise that by doing this, you're basically contesting a hidden premise.

P:3 Perception is subjective.

(Implicit premise): There is no right or wrong perception

P:4 Evidences are subjective.

(implicit premise): there is no right or wrong interpretation of evidence

C: Therefore science is subjective. 

Which brings us to the problem with this argument. The word 'subjective' is doing a lot of work here. Indeed, there is a subjective aspect to human perception, so different perceivers may weigh evidence differently. But 'subjective' does not mean 'there is no right or wrong', 'anything goes', or 'all viewpoints are equally valid' - some are based on mistaken interpretations, and others are irrelevant - they have nothing to do with the evidence presented. 'Subjective' here means there are general boundaries but there is still some room for interpretation.

Also, according to this logic everything is subjective. Maybe that's what they were trying to argue so that their opinions can be equally as valid as evidence based science? 

As for science itself being subjective, it is true that there is subjectivity in the scientific method, which is really more like a set of principles than concrete instructions. The principles still have to be coherent, though, however they're interpreted, or it's simply not science anymore.