8 Data Analysis Techniques


Chapter Four, Appendix One – Analysis Techniques

For those interested, earlier webpages lay out how Dr. Lott put together a well-reasoned research design and compiled a comprehensive database of relevant information. Those details are important for showing why Dr. Lott’s research has really not been overturned in over two decades. Now we turn toward his core research questions and findings in Chapters Four, Five, and Six. But first, we’ll go through an overview of the kinds of statistical techniques he used to process the data and answer his research questions.


Dr. Lott’s main research question could be stated, What kind of relationship is there between crime and gun ownership by law-abiding citizens? If we increase the number of in guns, will that mean more crime, less crime, or does this variable have no influence on crime? To study the kind of relationship and the degree of influence, Dr. Lott uses the statistical technique of regression analysis to “control for” (i.e., screen out) some factors so he can focus on measure the impact that other specific “variables” have on one another.


What does this term regression analysis mean? The short answer is that this research technique lets you find a “best-fit line” for a set of data you’ve graphed out related to your research question, and the coefficient (a number which represents the direction and steepness of that line) helps you determine the kind of relationship between the variables involved.

If you’re more a visual thinker, then picture this illustration: Suppose you shoot a bunch of buckshot at a bulls-eye target, and that the target is sitting with its left and lower edges just touching the lines on a graph. The buckshot scatter pattern is sort of clustered together, but spread out enough that it’s not all in the bulls-eye. If you stand close enough to the graph to see where the concentration points of the pattern are, that’s an informal type of regression analysis. It’s figuring out where a line goes through the cluster in a way that it is as close as possible to touching the largest number of individual shot points.

From there, the direction of the slope on the best-fit line tells you the kind of relationship between the variables.

  • If one variable increases while the other decreases, it is an inverse relationship and has a positive coefficient. For instance, the title of Dr. Lott’s book illustrates an inverse relationship: the more guns law-abiding citizens have, the less crime will be committed. The number of crimes goes down when the number of guns goes up.
  • If both variables increase or decrease together, it is a direct relationship and has a negative coefficient. For instance, if crime conviction rates decrease, you’d expect prison occupancy rates will decrease.

The steepness or flatness of the slope tells us how much one variable rises or falls when the other variable is changed.

All of the above is about using a standard form of regression analysis. But in his research, Dr. Lott also applied some even more complicated research analysis techniques. Here the descriptions get even more dense, but the important thing to remember is that there is no way to pinpoint and measure how various possible factors in the deterrence of crime interact, unless we use empirical research with a clear research design, applied to the right kinds of data sets, and using appropriate kinds of analysis techniques. This gives us concrete conclusions to consider about the effects of gun control. Otherwise, all we have to go on are people’s abstract assumptions and potentially very emotional stories. Which are the most useful for figuring out wise legislation?


One other research technique Dr. Lott uses is called two-stage least squares analysis. This is used to separate out the influences of interdependent variables. For example, with gun control research, Dr. Lott notes that with gun control research, “… crime rates influence whether the nondiscretionary concealed-handgun laws are adopted at the same time as the laws affect crime rates. Similar issues arise with arrest rates. Not only are crime rates influenced by arrest rates, but since an arrest rate is the number of arrests divided by the number of crimes, the reverse also holds true.” (Page 338.)

If you’ve heard the term standard deviation, that is where this element comes in. Standard deviations are a way of “normalizing” the variables so you can do the equivalent of comparing apples and oranges. You can’t compare them directly because they are different items. But you could calculate the “average” apple and the “average” orange in your fruit orchards, for instance. (That average is called the mean.) Then you could compare the typical percentage of weight change to apples and to oranges when you apply fertilizers to the orchards.

Put another way, standard deviations are a way of measuring typical changes. For instance, an evenly distributed (symmetrical) bell curve has the mean (center point/average) in the very middle, and 68% of all the data are within one standard deviation unit from that center line, and 95% of all the data are within two standard deviations from the center line.

In another technique called multiple regression analysis, other variables that are not under examination (what are called the exogenous or outside variables) help explain how and why the variables that are under examination (i.e., the endogenous or inside variables) work.

Those are some of the core concepts that Dr. Lott uses throughout his studies. Appendix One of his book explains and explores other kinds of more complicated regression techniques. And while these techniques are technical, the key thing to see is that he runs different types of analyses so he can explore the dynamics of linkages between private ownership of guns and their effects on crime. The goal is to get research findings that have high statistical significance. Significance measures the level of certainty about the impact a variable has. The higher the significance, the better the research conclusions we have, and the more objective we can be about thinking through the connections between gun-control laws and crime.

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