Published on March 20th, 20130
How Statistics is Useful in Social Science – An Example from the Kalmar War
By Tor G. Jakobsen, NTNU
The goal of scientific research is to make conclusions that go beyond the collected data. With large-N studies it is possible to make generalizations about the causal effects of different phenomena, if one has established the direction of causality.
As a tool of the positivist tradition, the statistical method is a way of identifying patterns and regularities in the observable world. Statistics involve the systematic collection of data with the aim of achieving knowledge by induction, that is, making inferences from observed regularities to general theories.
This systematic inductive use of statistics can be traced back to John Graunt, Sir William Petty, and Hermann Conring. In the 17th century they brought the use of descriptive statistics to science. Yet, the phrasing of social-science questions in variable terms did not happen until the 19th century.
Francis Galton introduced the correlation coefficient, the scatter plot, and also regression analysis, the prime tool of modern social-science statistics. Karl Pearson carried on Galton’s work, and later on Émile Durkheim placed statistics in the center, finding covariance between suicide and religion, in addition to other variables. Before Durkheim introduced the use of statistics into the social sciences, researchers relied on a more philosophical procedure, based on reasoning and facts of experience.
This can be illustrated by an event that took place in Norway in the 17th century. The background for this was the Kalmar War (1611–1613) which was fought between Sweden and Denmark. The root of the war was the Swedish wish to establish a trade route through northern Norway (Norway was then a part of the Danish kingdom).
The Fate of the Scottish Mercenaries
In 1612 a following of more than 300 mercenaries left Aberdeen in Scotland and sailed across the sea, eventually reaching the coast of Norway. Their plan was to cross the Norwegian interior in order to join their Swedish employers in the Kalmar War. The Scotsmen went through Romsdalen, and after a while they reached the valley of Gudbrandsdalen, located in the heart of the Norwegian inland.
When the entourage had reached the narrowest part of the valley, they discovered an unaccompanied, but armed, Norwegian farmer. The Scottish mercenaries, led by their Captain George Sinclair, pursued this lone peasant. Suddenly the peasant was out of sight. All the Scotsmen could see was a secluded linden tree. There was no place there to hide, except for in the tree.
The Norwegian could not have reached the sides of the valley without being noticed. The only logical explanation was that the farmer was covering himself in-between the branches of the linden. Thus, Captain Sinclair concluded that the peasant had climbed up and was hiding in the tree.
The conclusion made by Sinclair was, of course, a valid scientific inference. This is because the Scotsmen’s background experience summoned that the farmer had no other escape than to climb up the linden, taking into account that, as far as the mercenaries knew, no man could fly or disappear into the earth. In the same manner as Captain Sinclair reached this conclusion, the great thinkers of all sciences have reached their conclusions. One has a background experience which one uses as a basis when interpreting the facts. All in all, science involves a large degree of systematized common sense.
Yet, in today’s social science tradition many researchers would not have accepted Sinclair’s conclusion. They would have demanded further evidence, preferably with 95 percent certainty. Today’s quantitative researcher would have insisted that Sinclair’s men had thrusted pointy sticks or spears through at least 19/20 of the linden, to ensure that one with enough statistical significance could conclude whether the frightened peasant actually was hiding in the tree. One would not have trusted the Captain’s experience and common sense alone, one now wants numbers and facts on the table before deciding whether or not the Norseman is hiding in the linden or not.
Well, Captain Sinclair was of course right in his conclusion, even though this was not based on numbers or tests of significance. Yet, this was of little help, as about 500 Norwegian farmers came down from above the path, ambushing the mercenaries. The whole incident ended with the defeat of the Scottish troops, the death of George Sinclair, and the tragic fate of the surviving Scotsmen in a barn in the deep interior of Norway.
Still, this is not what is important with this story. The main point is that the social sciences need to be receptive to all facts, and also to all methods in which one can discover facts that can be useful for understanding social processes.
The Statistical Method
Using the statistical method, social scientists are able to make generalizations about the empirical world, whether operating with samples of a population, or the population as a whole.
There are many pitfalls to avoid before making statistical generalizations. One must define the population correctly, taking into account what the sample should constitute, and which time period to investigate. The researcher needs to be aware of the context and disposition of their data, which are the assumption that underlie statistical models. Sampling error is not the only source of error when it comes to survey data. Other problems include interviewer variability, non-response, problems connected to the questionnaire etc.
It is commonplace to operate with p-values, which denotes the probability of being mistaken when we reject a null hypothesis. The closer a p-value is to 0; the more certain we can be of not rejecting a true null hypothesis when accepting our own alternative hypothesis.
Even so, one also needs the backing of sound theory to say something about the relationship between variables. Statistical correlations should not be mistaken as being causal explanations. As such, observed relations must be interpreted with basis in theories about human action. The results from a regression analysis essentially only provide us with correlations between variables, just as Hume tells us that we can only observe patterns and regularities, not causality. Hume thoroughly states that science needs to be careful with regards to causal claims.