BUILDING A LOGICAL MIND---Episode 4

 RANDOM OR REPRESENTATIVE SAMPLING IN 
                     STATISTICAL INDUCTIONS 

   Assume you are in a business economics class of a hundred students. One day the teacher asks how many in the class favor the tax exemption for business lunches. All but two students raise their hands. The teacher concludes that most students at the university are in favor of tax exemptions for business lunches. This is the inductive method, but it's neither fair nor accurate since the selected sample is not representative of the student body as a whole. It excludes students in art, drama, physics, philosophy,  many of whom might oppose the tax exemption for business lunches. So what is the right way to arrive at an accurate conclusion ? There are two ways : (1) We can randomly select a large enough number of students---say 300 in a school made up of a thousand students --- and solicit their opinions. Random sampling prevents any bias from influencing the outcome. (2) We can select a group of students representative of the entire population. Let's assume, for example, that the university breaks down the following way : 35 percent business ; 15 percent engineering ; 20 percent liberal arts ; 15 percent physical sciences ; 10 percent fine arts ; 5 percent other. If you wanted to find out what the students as a whole think about tax-exempt business lunches, but couldn't interview every student, you could select a hundred out of the thousand students at the school, keeping the percentages in this group the same as the percentages of students in the various colleges : 35 percent from business ; 15 percent from engineering ; 20 percent from liberal arts, and so on. Such a method will lead you to a fairly accurate conclusion about the student body's opinion on tax-exempt business lunches. If statistics are to have any relevance at all, they must be a result of random or representative sampling. 
   Although induction leads to truths, especially in science, for the most part it leads to a high probability. So we must use induction cautiously. After all, it was not that long ago that people thought frogs fell from the clouds since they appeared out of nowhere every time it rained. 

                                              DEDUCTION 

   Induction helped our remote forebears take control of their destiny and make sense out of a bewildering world. Each truth established by observation became a small step on the stairway human beings were building to lift themselves out of the purely animal world. Induction also made possible something else --- another way to create steps, another way to arrive at reasonable conclusions about the world : DEDUCTION.  Fr the first time, they could make reliable generalizations about the natural world; they could begin classifying it. Some things were animals ; some were plants ; some were minerals. Among those things that were animals, some were insects, some were reptiles, some were mammals. Among the mammals, some were land-dwelling, some were water-dwelling. And the classification would continue until there were 15,000 species of mammals alone. Creatures with x characteristics belong in this species ; creatures with y characteristics belong in that species. Humans were, in effect, putting their world into categories ---categories that eventually led to biological classification of shared characteristics. Grouping creatures into various classes can be very useful, for it enables humans to reason deductively --- that is, to draw an accurate conclusion from two general premises. 
   Assume for example that you, as a biologist, know very well that "all warm-blooded, egg-laying, winged and feathered vertebrates are birds. " Then one day you come across a penguin, the first one ever seen. Upon examination you discover that even though it doesn't resemble any bird you've ever seen, it is a warm-blooded, egg-laying, winged and feathered vertebrate. You conclude : "This creature must be some kind of bird." The creature is now less mysterious since you can name it, which is another way of saying categorize it. Induction led us to the generalization about birds ; deduction led you to the conclusion that this new-found creature is also a bird.