empirically
By testing or observing something in the real world.
Empirically means through direct observation or experience rather than through theory or speculation. When scientists test a hypothesis empirically, they conduct actual experiments and gather real data. When a doctor says a treatment works empirically, she means she's seen it work in actual patients through direct observation.
The word comes from empirical, which describes knowledge gained through the senses: seeing, hearing, touching, measuring. If your friend claims that dropping a basketball makes it bounce higher than dropping a tennis ball, you could test this empirically by dropping both balls from the same height and measuring the results. That's empirical evidence, something you can observe and verify yourself.
This approach contrasts with pure reasoning or guesswork. Ancient philosophers sometimes made claims about nature based only on logic, like insisting that heavier objects must fall faster. When Galileo tested this empirically by dropping objects from towers and rolling balls down ramps, he discovered the philosophical reasoning was wrong. The empirical evidence revealed the truth.
Scientists value empirical methods because they let anyone repeat the observations and check the results. When something is proven empirically, it means the real world has demonstrated it through observable evidence.