So far, we have touched upon observations, questions, hypotheses, and experimentation. Next is analysis of experimental data. It is this statistical analysis that may help to determine the validity of our hypothesis, and may lead us to a theorem. After data is collected, statistical analysis can begin. Statistical analysis may be able to tell us if results are significant or merely the product of chance.
Experimental design determines the type of analysis employed.
Not all experiments will lead us to conclusions. It may simply be that we discover inadequacy of our current methods to evaluate the problem. Ideally, the whole population should be studied, but this is usually not possible. Instead, representative samples must be taken. Sampling can be the downfall of experiments.