Objectivism is not defined by rational empiricism. ... ["For the New Intellectual" p. 30]
I believe this is a significant distinction (the hub of misunderstanding among Objectivists as well as non-O'ists) in that while the scientific method of inquiry and experiment (empirical) does have value within Objectivism - qua methodology, a tool ; rational empiricism, qua philosophy, is anti-conceptual. Therefore, it was completely rejected by Rand, and cannot be even a partial definition of O'ism.
I agree that in seeking to explain our understanding of everything in the universe by a one-sided theory simply left us all a lot worse off. The mind-body dichotomy is as old as the Greeks. In the previous century, fascists and communists caused horrible wars with their Idea and their Materialism. But that is the point. Neither side is enough to understand reality.
We live by "common sense." David Kelley has explained how free will derives from the brain's need to filter incoming sensora and order them into understanding. But we always test that with experience. As Rand said, reality is the final arbiter of the correctness of our ideas. In discussing the phony disease of dyslexia, I point out that nothing about letters is natural and that people who do not read books well probably could learn to read animal tracks quite well. Animal tracks have a reality to them. In a muddy trail behind an apartment complex in the suburbs last weekend, I saw the tracks of a deer and a large canine. They cannot be confused like P R and B because they were made by an entire animal fitted to an ecological niche. It is why we can tell the animal from a tooth.
The so-called "problem of induction" defines the limit of strict empiricism: lacking any consisten theory to explain a fact like sunrise or the whiteness of swans, you never know if the sun will come up in the East or anywhere tomorrow and a black swan invalidates your concept of swanness.
I point out, though, that the animals were immediately identified for what they are: swans, not some other thing entirely. That is because rational-empiricism works.
The scientific method is not strict empiricism. You can learn this and teach it as maybe three steps or as many as 14 (see the Edmund website here), but the basic 5 to 9 steps of the scientific method depend on creating a causal theory to test. It is not the mere accumulation of instances.
Objective knowledge of the universe requires thinking logically about the evidence of your senses and testing your syllogisms (and sorites) both by repeating previous engagements (replicating an experlment) and also seeking new ones. That last is "falsification" and some Objectivists misunderstand it.