The biggest role of statistics in experimental analysis involves using mathematical concepts to evaluate differences in results among groups. This includes ruling out other possibilities that may have led to perceived differences between a control group and a experimental group. Testing error, incorrect sampling methods and chance can affect the results. Scientists use statistics to rule these out and make sure the difference results from the treatment effect.
Statistics also help determine what level of probability is apparent from an experimental analysis. In other words, statistics measure how likely something is to happen given the parameters of the experiment. To determine probability, researchers define an "alpha level," which separates probable occurrences from those that may be vagaries of chance or simply outliers.
Statistics help researchers determine causal relationships present in experimental data. Scientists may find it challenging to view a set of data and determine what--if any--relationships exist among the numbers. Using statistics and then plotting findings on a bell curve can show whether or not the experimental change affected the participants. Even without a direct correlation, statistics may show relationships that the researcher wouldn't have suspected.
Blaine Pascal is considered the father of many mathematical concepts we use today, including probability theory. Probability theory drives the use of statistics in experimental analysis. While it might serve a high function today, it actually came about as Pascal and Pierre de Fermat studied games of chance.
Statistics become worthless if incorrect sampling techniques are used. For samples to be pertinent, they must truely represent the population studied. Statistics can provide ways to curb sampling errors but to a limited extent.