Defining the Observed Significance Level of a Test

Abstract

It is probably clear to you now that research in criminal justice is often concerned with making inferences to a population based on a sample statistic. During the course of our research, we may often use tests of statistical significance to determine whether we can safely reject a null hypothesis as being true for our population of interest. But, when we conduct these tests, we will always have some risk of what is called a type I error (mistakenly conclude that an intervention or strategy is effective or efficacious). This chapter will illustrate some of the basics of probability theory in R that demonstrates how we identify the risk of type I error. In doing so, you will be posed with scenarios where you will compute binomial probabilities of a criminal court judge delivering a guilty verdict in bench trials using for loops and while loops. This chapter will be using binomial probabilities as an example (covering the multiplication rule and arrangements, specifically).

Key Terms

Arrangements

The different ways events can be ordered and result in a single outcome. For example, there is only one arrangement for gaining the outcome of ten heads in ten tosses of a coin. There are, however, ten different arrangements for gaining the outcome of nine heads in ten tosses of a coin.

Binomial formula

The means of determining the probability that a given set of binomial events will occur in all its possible arrangements.

Independent

Describing two events when the occurrence of one does not affect the occurrence of the other.

Multiplication rule

The means for determining the probability that a series of events will jointly occur.

Sampling distribution

A distribution of all the results of a very large number of samples, each one of the same size and drawn from the same population under the same conditions. Ordinarily, sampling distributions are derived using probability theory and are based on probability distributions.