First: Watch a phenomenon that is of interest for you:
“Wow, here on the Galapagos Islands there are many different birds. Why is that so?”
Second: Try to find a pattern:
“Hey, it seems that on every single island there are quite different birds.”
Third: This pattern leads you to a model of what we have seen:
“It seems that on different islands different species have evolved.”
Forth: This model is now what helps us to draw a hypothesis:
“I hypothesize that out of few birds on a newly emerged island new species have evolved over time. Maybe, different species have evolved from one species by both variations within the population and different selective pressures that have worked.”
Fifth: Perform in the best case controlled randomized experiments with replicates to test your hypothesis and use statistics to estimate how likely this event of interest may occur just by chance. If we find that it is very unlikely to happen just by chance then we are saying that this is statistically significant.
OK, Darwin (and Wallace) had only observational studies to build their evolutionary theory. We can not wait for several million of years to see whether our experiment resulted in new species on a set of islands. However, what we can do is to perform experiments with species that have a much higher generation time such as insects or even better with microbes that can have generation times of only 20 min! For example, we could just rear bacteria in a flask with controlled conditions in the lab and see after thousands of generations whether the isolated populations evolve differently. This is exactly, what the lab of Richard Lenski did. After ten thousands of generations they observed the evolution of a novel trait, aerobic citrate utilization, in an experimental population of Escherichia coli (see Long-term Experimental Evolution Project Site url:http://myxo.css.msu.edu/ecoli/).
However, it is much easier to perform controlled randomized experiments with replicates with for example emerging antibiotic resistance of microbes, which have a huge fitness advantage over non-resistant clones or maybe aphids, which when more red coloured are more prone to be eaten by birds or ladybugs than more green coloured ones. With such data we than can perform statistical analyses, which allows us to estimate whether the observed differences are very unlikely to happen (small p value) under the hypothesis that there is no difference (so-called null hypothesis). This would indicate that observed differences are statistically significant.
Appreciate your comments and suggestions.