Abstract
Many people involved in criminology and criminal justice research spend time making predictions about populations in the real world. These predictions tend to be based on a theoretical framework and are formally stated as hypotheses in order to answer a specific research question. Using inferential statistics (see Chap. 6), we can test to what extent our data support these hypotheses and provide empirical evidence to support (or reject) our expectations in R. This chapter uses a simulated dataset of results from a crime reduction intervention for at-risk youth to explore how the binomial distribution allows us to generalize from a sample of 100 participants in a study to the wider population.
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References
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Key Terms
- Binomial distribution
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The probability or sampling distribution for an event that has only two possible outcomes.
- Directional hypothesis
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A research hypothesis that indicates a specific type of outcome by specifying the nature of the relationship that is expected.
- External validity
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The extent to which a study sample is reflective of the population from which it is drawn. A study is said to have high external validity when the sample used is representative of the population to which inferences are made.
- Non-directional hypothesis
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A research hypothesis that does not indicate a specific type of outcome, stating only that there is a relationship or a difference.
- Nonparametric tests
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Tests that do not make an assumption about the distribution of the population, also called distribution-free tests.
- Null hypothesis
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A statement that reduces the research question to a simple assertion to be tested by the researcher. The null hypothesis normally suggests that there is no relationship or no difference.
- Parametric tests
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Tests that make an assumption about the shape of the population distribution.
- Type I error
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Also known as alpha error and false-positive. The mistake made when a researcher rejects the null hypothesis on the basis of a sample statistic (i.e., claiming that there is a relationship) when in fact the null hypothesis is true (i.e., there is actually no such relationship in the population).
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Wooditch, A., Johnson, N.J., Solymosi, R., Medina Ariza, J., Langton, S. (2021). Hypothesis Testing Using the Binomial Distribution. In: A Beginner’s Guide to Statistics for Criminology and Criminal Justice Using R. Springer, Cham. https://doi.org/10.1007/978-3-030-50625-4_8
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DOI: https://doi.org/10.1007/978-3-030-50625-4_8
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