[I've never been happy with this note and often thought of dropping it, but I never did. I couldn't shake the feeling that there was a critically important idea buried inside that was struggling to get out. Lately, and you'll see this reflected in my web pages, I had the insight that what I was really trying to do was show how a statistician thinks rather than what a statistician does. It struck me that this was an early attempt to get at it. Tools are what we use, what we do. Tasks are what we're trying to accomplish.
Switching metaphors, this note points out that what's important is knowing where we're going. How we get there is of little consequence, as long as we get there safely. To get anywhere we have to learn to use various forms of conveyance and we should be proud of having mastered them. However, we shouldn't confuse learning how to travel with having made a journey.]
Tools can have many different uses. The screwdriver that attaches a handle to a drawer can be used to connect a wire to an electrical outlet. In a pinch, it can be used as a pry bar to open a can of paint. Some tasks can be performed by any number of tools. A bolt can be tightened with a pair of pliers, a vice grip, socket wrench, or ratchet. Should you use a hammer and nails join two pieces of wood? In some cases, yes, but in other cases it might be better to use nuts, bolts, washers, and a drill. In other cases, wooden dowels and a good glue may be the best choice.
Statistics is a set of tools. What you do with them will be determined by the research question under investigation. Questions like "What test should I use?" are common as students begin to apply the statistical techniques they've just learned because a first course tends to focus on the tools themselves and what they can do rather than on the larger ends for which the tools are just the means. In some ways, this is unavoidable, just as novices cannot be expected to be able to use hand tools effectively without being given some knowledge of tools and practice using them divorced from any specific task. As with hand tools, there are many statistical techniques that will achieve a particular result. However, some are better suited than others, perhaps because they make different assumptions of the data or because available software makes then easier to use. ("We are prisoners of our software!" -- a theme you will hear repeated often.) With experience, the question will change to, "I have conducted this research in order to answer this question. What types of analyses can help me achieve my goal?" Once it is understood what each method can accomplish, the question will just about answer itself.
Not all questions can be answered with the statistical tools an analyst currently has at his/her disposal. A true understanding of statistical methods has begun when analysts begin to realize that their toolkits are inadequate and that additional tools must be added.
A similar view is expressed by RP Ableson in Statistics As Principled Argument (Hillsdale, NJ: Lawrence Erlbaum Associates, 1995):
Despite many new developments and the intensity of statistical training offered in several university departments, students generally seem as bemused as ever. From long observation of student struggles with statistics, I conclude that the difficulties lie not so much with computational mechanics as with an overall perspective on what they are doing. For many students, statistics is an island, separated from other aspects of the research enterprise. Statistics is viewed as an unpleasant obligation, to be dismissed as rapidly as possible so that they can get on with the rest of their lives. Furthermore, it is very hard to deal with uncertainty, whether in life or in the little world of statistical inference. Many students try to avoid ambiguity by seizing upon tangible calculations, with stacks of computer output to add weight to their numbers. Students become rule-bound, thinking of statistical practice as a medical or religious regimen. They ask questions such as, "Am I allowed to analyze my data with this method?" in the querulous manner of a patient or parishioner anxious to avoid sickness or sin, and they seem to want a prescriptive answer, such as, "Run an analysis of variance according to the directions on the computer package, get lots of sleep, and call me in the morning."
There is only one way to get past this point: PRACTICE! Once you have to tools, the only way to learn to use them effectively is by using them. One exercise I will institute this year in the hope of moving things along more quickly will have students invent 3 research situations where a newly introduced technique could be used effectively.
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