Abstract
When we Make Inferences to a population, we rely on a statistic in our sample to make a decision about a population parameter. At the heart of our decision is a concern with Type I error. Before we reject our null hypothesis, we want to be fairly confident that it is in fact false for the population we are studying. For this reason, we want the observed risk of a Type I error in a test of statistical significance to be as small as possible. But how do statisticians calculate that risk? How do they define the observed significance level associated with the outcome of a test?
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Notes
- 1.
See Anthony Braga, “Solving Violent Crime Problems: An Evaluation of the Jersey City Police Department’s Pilot Program to Control Violent Crime Places,” unpublished dissertation, Rutgers University, Newark, NJ, 1996.
- 2.
Problem-oriented policing is an important new approach to police work formulated by Herman Goldstein of the University of Wisconsin Law School. See H. Goldstein, Problem-Oriented Policing (New York: McGraw-Hill, 1990).
- 3.
The correction factor adjusts your test to account for the fact that you have not allowed individuals to be selected from the population more than once. Not including a correction factor makes it more difficult to reject the null hypothesis. That is, the inclusion of a correction factor will make it easier for you to reject the null hypothesis. One problem criminal justice scholars face in using a correction factor is that they often want to infer to populations that are beyond their sampling frame. For example, a study of police patrol at hot spots in a particular city may sample 50 of 200 hot spots in the city during a certain month. However, researchers may be interested in making inferences to hot spots generally in the city (not just those that exist in a particular month) or even to hot spots in other places. For those inferences, it would be misleading to adjust the test statistic based on the small size of the sampling frame. For a discussion of how to correct for sampling without replacement, see Paul S. Levy and Stanley Lemeshow, Sampling of Populations: Methods and Applications (New York: Wiley, 1991).
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Weisburd, D., Britt, C. (2014). Steps in a Statistical Test: Using the Binomial Distribution to Make Decisions About Hypotheses. In: Statistics in Criminal Justice. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-9170-5_8
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