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Chapter 10: Problem 28

Kidnapping in southern and eastern European countries The following data on kidnapping offences in countries of east and south Europe in 2014 were obtained from https://data.unodc.org. (Crime and Criminal Justice \(\rightarrow>\) Crime \(\rightarrow>\) Kidnapping \(\rightarrow\) Filter by Region and Sub Region as appropriate) \(\begin{array}{ll}\text { Eastern Europe: } & 31,95,12,3,292,88,369,10\end{array}\) Southern Europe: \(\quad 2,1,3,1,58,297,22,376,11,5,99,8\) Using statistical software, a. Construct and interpret a plot comparing responses by region. Kidnapping in southern and eastern European countries The following data on kidnapping offences in countries of east and south Europe in 2014 were obtained from https://data.unodc.org. (Crime and Criminal Justice \(->\) Crime \(\rightarrow>\) Kidnapping \(->\) Filter by Region and Sub Region as appropriate) Eastern Europe: 31,95,12,3,292,88,369,10 Southern Europe: 2,1,3,1,58,297,22,376,11,5,99,8 Using statistical software, a. Construct and interpret a plot comparing responses by region.

Short Answer

Expert verified
Construct a box plot comparing both regions' kidnapping data to highlight differences.

Step by step solution

01

Organize the Data

Collect and organize the dataset for Southern and Eastern European countries. Eastern Europe includes values [31, 95, 12, 3, 292, 88, 369, 10] and Southern Europe includes values [2, 1, 3, 1, 58, 297, 22, 376, 11, 5, 99, 8].
02

Choose an Appropriate Plot

For comparing distributions of the two regions, we can use a box plot or a histogram. These plot types allow us to see the spread and any outliers for each region.
03

Input Data into Statistical Software

Enter the data sets into statistical software like R, Python, or Excel. For example, if using R or Python, use the commands that specify the datasets for plotting.
04

Plot the Data

Create a box plot by using the statistical software's plotting function. This will visually display the median, quartiles, and potential outliers for both the Eastern and Southern European regions.
05

Analyze the Plot

Examine the box plot: compare the median values and quartile ranges to understand differences in distributions. Look for any outliers that may indicate unusually high or low values within each region.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Box Plot
A box plot is a convenient way to display the distribution of data through five major summary statistics: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It visually depicts how your data is spread and identifies possible outliers.
For our dataset on kidnapping offenses in Southern and Eastern Europe, a box plot will provide an immediate snapshot of how each region's kidnapping rates differ. It not only presents the central 50% of data points within a 'box' but also uses 'whiskers' to extend out to the smallest and largest values within 1.5 times the interquartile range (IQR). Any data points outside this range can be considered outliers.
Creating a box plot in statistical software like R or Python involves entering your dataset and using simple commands to generate the plot. This will aid in understanding the central tendency, variability, and potential anomalies within the regional kidnapping data.
Data Visualization
Data visualization is a powerful tool that transforms raw datasets into comprehensible charts and graphs. It allows us to see patterns, trends, and anomalies at a glance, providing insights that may not be immediately apparent from the raw numbers.
In the context of our kidnapping dataset, visualizing the data through a plot such as a box plot or histogram helps in comparing the two regions. It's a crucial step because it aids in drawing conclusions about the regional differences in kidnapping offenses.
  • This visual comparison is key in understanding if certain regions have consistently higher or lower numbers of kidnappings.
  • It allows us to identify outliers that might indicate anomalies or data entry errors.
  • By understanding the spread through visualization, we can target specific areas for policy intervention or further research.
Data visualization makes it easier for stakeholders to make informed decisions based on clear, visual data trends.
Regional Comparison
Comparing regions requires analyzing the data to tease out differences and similarities. Full comprehension of regional differences in the kidnapping data requires a well-grounded statistical approach.
A box plot provides a comparative overview of the Eastern and Southern European regions. By examining the plot, we can look for key elements:
  • Compare the medians of the two regions to understand which typically has higher or lower rates of kidnapping.
  • Observe the interquartile range (IQR) to see the spread of mid-range data, indicating variability within each region.
  • Review the range of the data to understand the overall spread and any outliers that suggest unusual data points.
For the given dataset, such a comparison might reveal whether Southern Europe or Eastern Europe experienced more variability in kidnapping cases. This analysis is essential for policy makers and law enforcement agencies to allocate resources effectively.
Crime Statistics
Crime statistics like our kidnapping data offer valuable insights into public safety issues within different regions. They serve a critical role in shaping crime prevention efforts and public policy.
Kidnapping statistics for Southern and Eastern Europe provide quantitative backing for understanding the extent of this crime in these areas. The value of crime statistics lies in:
  • Identifying trends over time, helping in forecasting and preventive measures.
  • Supporting law enforcement and policy-making through data-driven decisions.
  • Revealing regional disparities that might necessitate targeted interventions.
By studying these statistics, governments and organizations can formulate strategies to mitigate such crimes. It also provides the public with awareness of the safety landscape, influencing societal behaviors and expectations.

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Most popular questions from this chapter

Refer to Example 10 on whether arthroscopic surgery is better than placebo. The following table shows the pain scores one year after surgery. Using software (such as MINITAB) that can conduct analyses using summary statistics, compare the placebo to the debridement group, using a \(95 \%\) confidence interval. Use the method that assumes equal population standard deviations. Explain how to interpret the interval found by using software. $$\begin{array}{lccc} \hline & & {\text { Knee Pain Score }} \\ { 3 - 4 } \text { Group } & \text { Sample Size } & \text { Mean } & \text { Standard Deviation } \\ \hline \text { Placebo } & 60 & 48.9 & 21.9 \\ \text { Arthroscopic }- & 61 & 54.8 & 19.8 \\\\\text { lavage } & & & \\ \begin{array}{l}\text { Arthroscopic }- \\ \text { debridement }\end{array} & 59 & 51.7 & 22.4 \\ \hline\end{array}$$

A study of the death penalty in Kentucky reported the results shown in the table. (Source: Data from \(\mathrm{T}\). Keil and \(\mathrm{G}\). Vito, Amer. \(J\). Criminal Justice, vol. \(20,1995,\) pp. \(17-36 .)\) a. Find and compare the percentage of white defendants with the percentage of black defendants who received the death penalty, when the victim was (i) white and (ii) black. b. In the analysis in part a, identify the response variable, explanatory variable, and control variable. c. Construct the summary \(2 \times 2\) table that ignores, rather than controls, victim's race. Compare the overall percentages of white defendants and black defendants who got the death penalty (ignoring, rather than controlling, victim's race). Compare to part a. d. Do these data satisfy Simpson's paradox? If not, explain why not. If so, explain what is responsible for Simpson's paradox occurring. e. Explain, without doing the calculations, how you could inferentially compare the proportions of white and black defendants who get the death penalty (i) ignoring victim's race and (ii) controlling for victim's race. $$\begin{array}{llrrr}\hline \begin{array}{l} \text { Victim's } \\\\\text { Race } \end{array} & \begin{array}{l} \text { Defendant's } \\\\\text { Race } \end{array} & \begin{array}{l}\text { Death Penalty } \\\\\text { Yes } \end{array} & \begin{array}{r} \text { No } \end{array} & \text { Total } \\ \hline \text { White } & \text { White } & 31 & 360 & 391 \\ & \text { Black } & 7 & 50 & 57 \\ \text { Black } & \text { White } & 0 & 18 & 18 \\ & \text { Black } & 2 & 106 & 108 \\\\\hline\end{array}$$

Multiple choice: Sample size and significance If the sample proportions in Example 4 comparing cancer death rates for aspirin and placebo had sample sizes of only 1000 each, rather than about 11,000 each, then the \(95 \%\) confidence interval for \(\left(p_{1}-p_{2}\right)\) would be (-0.007,0.021) rather than \((0.003,0.011) .\) This reflects that a. When an effect is small, it may take very large samples to have much power for establishing statistical significance. b. Smaller sample sizes are preferable because there is more of a chance of capturing 0 in a confidence interval. c. Confidence intervals get wider when sample sizes get larger. d. The confidence interval based on small sample sizes must be in error because it is impossible for the parameter to take a negative value.

Annual income of CEOs A study analyzes the total annual pay of CEOs (in pounds) for a sample of UK companies over the period \(2003-2006\) categorized according to the number of compensation consultants employed. The sample included 311 firms having one consultant and 203 firms having two consultants. Software output shows the following results: Two sample T hypothesis test: \(\mu_{1}:\) Mean of CEO total pay in firms with one compensation consultant \(\mu_{2}:\) Mean of CEO total pay in firms with two compensation consultants a. Does it seem plausible that income has a normal distribution for each firms' category? Explain. b. What effect does the answer to part a have on inference comparing population means? What assumptions are made for the inferences in this table? c. A \(95 \%\) confidence interval for the difference in the population means for CEOs (men and women) is \((拢-370.19, 拢 128.19) .\) Interpret, indicating the relevance of \(拢 0\) falling in the interval.

Risky behaviors among HIV positive female sex workers In 2014 , questionnaire surveys were administrated among 181 female sex workers in the Yunnan province of China who confirmed themselves to be HIV positive (www.ncbi.nlm. gov/pubmed/26833008). The participants were divided into two age groups -76 cases were below 35 years and 105 cases were 35 years old and above. 26 females below 35 years and 54 females of ages 35 years and above reported using drugs. Let \(p_{1}\) and \(p_{2}\) denote the population proportions of females below 35 years and of females 35 years or above who took drugs, respectively. a. Report point estimates of \(p_{1}\) and \(p_{2}\). b. Construct a \(95 \%\) confidence interval for \(\left(p_{1}-p_{2}\right),\) specifying the assumptions you made to use this method. Interpret. c. Based on the interval in part b, explain why the proportion using drugs may have been quite a bit larger for females of ages 35 years or above, or it might have been only moderately larger.
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