Statistical thinking, the basic idea

Understand the simple chain of thinking below, then enlist or hire a statistician who will use the appropriate recipe for the data at hand.

1. There is a population of individuals. (Population = individuals subject to the same foreground causes of interest. There may also be background, non-manipulatable causes that vary among these individuals.)
2. For some measurable attribute the individuals have varying responses to the foreground causes (possibly because of the background causes).
3. You have observations of the measurable attribute for two or more subsets (samples) of the populations.
4. Central question of statistical analysis: Are the subsets sufficiently different in their varying responses that you doubt that they are from the one population (i.e., you doubt that they are subject to all the same foreground causes)? Statisticians answer this question with recipes that are variants of a comparison between the subset averages in relation to the spread around the averages. For the figure below, the statisticians' comparison means that you are more likely to doubt that subsets A and B are from the same population in the left hand situation than in the right hand one.

The central question of statistical analysis: Are the averages far apart relative to the spread (left hand picture) or not (right hand picture)?

5. If you doubt that the subsets are from the same population, investigate further, drawing on other knowledge about the subsets. You hope to expose the causes involved and then take action informed by that knowledge about the causes.