[ORDER SOLUTION] Sampling and Estimation

Analytical Methods

Module 3: Sampling and Estimation

Scientists rarely collect data from the entire group or population they want to study. For example, if researchers want to study characteristics of individuals serving prison sentences in state and federal correctional institutions, they will find that the most recent data collected was at year-end 2016 and that 1,505,400 individuals were incarcerated at that time (Bureau of Justice Statistics, 2018). Because 1.5 million people is a large group or population which would be impractical and expensive to collect data of interest, researchers need to break the sample down into smaller sample groups that, hopefully, are representative of the larger population. From the smaller samples, researchers can estimate population information using inferential statistics.

A great deal of thought, planning, and attention to procedural detail is necessary when sampling from a larger population. Study samples must not only generate a sample that is likely to be representative of the larger population but must also generate a sufficient number of cases/observations that will provide enough statistical power to produce meaningful data. In criminal justice recidivism studies, researchers interested in specific types of recidivism are often faced with sampling difficulties because base rates (the rate at which some phenomena are observed in the real world—such as sex offender recidivism—is relatively low). Medical researchers face the same challenges when studying the causes of certain diseases that may have low base rates of occurrence.

Module 3 lays important groundwork for understanding sampling, probability sampling, normal distributions, and inferential statistics. It also provides important information on the degree of confidence researchers strive for (confidence intervals) in their estimates or predictions.

Learning Outcomes

Distinguish probability sampling from non-probability sampling.
Understand sampling distribution and the central limit theorem.
Comprehend the relationships among sample size, confidence level, and confidence intervals.
Interpret confidence intervals.

Please take note that the Module 3 Discussion (initial post due on Thursday at 11:59PM) is an evaluation of a published research study dealing with predictors of satisfaction between police-prosecutor relationships. Take some time to read the study so that you can provide a thorough answer to the discussion question. Also, be aware that the Module 3 Portfolio Project Milestone focuses on identifying at least one published research study on your topic of interest, and the creation of a research question and hypothesis. This is worth up to 25 points and is due Sunday at 11:59PM. Again, ask your instructor if you need guidance in any of the above areas and they will be glad to help.

For Your Success & Readings

In data analysis, we need both descriptive statistics and inferential statistics. Remember that descriptive statistics summarize the attributes of the unit(s) of measurement in your sample (e.g., age, race, education, income, gender). In criminal justice, nearly every research study (whether the study examines offenders, victims, or criminal justice personnel) contains data on group differences relative to the variables measured. Module 2 covered how to generate descriptive statistics in SPSS, and how to describe and summarize data utilizing tables, graphs, and histograms.

Module 3 covers inferential statistics, which are appropriate when analyzing relationships among variables or assessing population parameters. For example, if we want to know the extent to which mandatory sentencing guidelines have influenced time served in prison vs. the extent to which discretionary sentencing by judges has influenced time served in prison, we would utilize statistical tests that produce data on how the variable of sentencing guidelines is correlated with prison time served. Another example relates to the extent to which correctional treatment completion (or a lack of correctional treatment completion) predicts recidivism.

Understanding the concept of sampling is important to learning inferential statistics, because inferential statistics aim to judge a population using sample data. Module 3 covers the groundwork, evolving from the types of samples, to sampling distribution, to the relationship between sample size, and confidence intervals. Type of sample determines a sample’s representativeness of the target population; sampling distribution provides a major simplification en route to statistical inference based on a probability sample; and sample size determines the preciseness, or the level of confidence, of the sample estimates.

Required

Chapters 6 & 7 in Social Statistics for a Diverse Society
Chapter 9 in Logic of Hypothesis Testing in Online Statistics Education: A Multimedia Course of Study

Recommended

Kuang, K., & Liang, B. (2015). Efficiency and justice and fairness: An empirical analysis of criminal appeals in hunan province, China. European Journal on Criminal Policy and Research, 21(4), 565-590.
Williamson, E. J., Stricker, J. M., Irazola, S. P., &Niedzwiecki, E. (2016). Wrongful convictions: Understanding the experiences of the original crime victims.Violence and Victims, 31(1), 155-166.

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References

Bureau of Justice Statistics. (2018). Prisoners in 2016. 

United States Census. (2017). A basic explanation of confidence intervals.