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Summary
The construction of confidence intervals refers to the development of value ranges estimated to contain the valid population parameter. Each sample has its descriptive statistics, such as the mean or proportion. The scholars set the level of confidence based on their assessment of the relative costs of a loss of 252 confidence versus compromised precision (Gau, 2019). The trade-off between trust and accuracy must be considered when deciding on a degree of certainty: The estimate’s consistency degrades as confidence rises.
In criminal justice and criminology studies, confidence levels are expressed in percentages, with 95 percent and 99 percent being normal. Confidence levels are determined in advance, so one must decide whether to use 95 percent or 99 percent before creating the interval (Gau, 2019). The explanation for this is that the degree of trust affects the interval measurement.
Small-Sample Confidence Intervals for Means
As N reaches 99, however, this presumption falls apart, necessitating the use of different distribution. The CI formula for small samples is almost similar to that for large models; the only difference is that instead of using the critical value of z, the essential importance of t is used (Gau, 2019). Researchers typically err on the side of caution, so if you have to choose between inflating or shrinking the measured CI, increase it. This is standard practice in criminology and criminal justice science.
Confidence Intervals With Proportions and Percentages
The process for proportions is identical to that for percentages; percentages must simply be converted to ratios before being entered into the CI formula. Since a sample proportion cannot be assumed to equal the population proportion due to sampling error, confidence intervals must be generated to approximate population values with a high degree of certainty.
Critique
The chapter provides an extensive explanation of the proposed framework by giving numerous examples and visual representations of formulas. The authors provide examples of each proposed procedure and a broad description of each variable, facilitating a better understanding of the material. For example, using the Confidence Intervals With Proportions and Percentages formula, researchers discovered that accidental pregnancy significantly increased women’s chances of suffering physical violence during pregnancy, which has important implications for the criminal justice system (Gau, 2019).
Reference
Gau, J. M. (2019). Statistics for criminology and criminal justice. Sage.
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