The nuances of chemical confirmation

For a chemical hypothesis to gain credibility, empirical evidence must somehow be invoked to support it. For example, when during the 1660s chemist Robert Boyle experimented on gases, the observations he published proved decisive for the acceptance that the pressure of a gas is inversely proportional to its volume. We still call this relationship Boyle’s law, even though he was not the first to conceive of it.

The central role of experimentation in science was decisively established during the scientific revolution by Francis Bacon. Bacon promoted the rigorous examination of nature through repetitive and reproducible experiments that should be performed and checked by an organised community of scientists. To this day, the idea that inferences should be based on a careful analysis of empirical observations remains a defining feature of science. 

But how does confirmation work exactly? That is, how should empirical data and observations be used to support a hypothesis?