Statistics concepts and applications

Statistics are the tools to describe the systematic body of information that assist policy makers or managers to make decision about important issues. Statistics provide the accurate methodology to draw the accurate inference from the sample of data to the full population. Despite the benefits derived from applied statistics, there are challenges that policy makers face in measuring social issues.

Answer to Question A

In public sector, statistical approach is used to carry out the measurement. Measurement is the process of assigning number to the issue that policy makers are interested in studying or analyzing. There are various methods to go about measuring social problem. First, the attitude of the total population to a social problem could be measured by sampling the opinion of the population towards the issue. Meier et al. (2011) reveal the method in measuring complex issue such as measuring the religion preference of a particular racial group, or attitude of population towards particular government or agency. While these particular issues could not be measured quantitatively, the only method to measure these issues are to measure them in term of category: white vs. non-white, male vs. female, or favor tax increase, favor no change, or favor no tax increase.

Total number of daily arrest of prostitutes could be used to measure the issue of social problem such as level of the prostitution in a certain community. Thus, the total number of arrest could be related to the level of prostitution activity in a given community, and with the data produced from the arrest, the population or policy maker will be able to conclude whether there is an increase or decrease in the prostitution activity in a community. Typically, the more number of prostitutes arrested the high level of prostitution activity. For example, the city council of Prudeville in New York was very concerned about the increase in the level of prostitution in the city. The data produced by the police made policy makers to pass anti-sex zoning law to enhance the quality of life in the city.

Despite the benefits policy makers may derive from measuring social problems, there are still challenges in measuring social problem in a given community. One of the challenges in measuring social problem is inability to measure the issue directly. For example, it is not possible to measure the poverty level within a community or the level of intelligent of the people in a community. The only approach is to measure these issues indirectly. Meier et al. (2011) argue that the operational definition is a method these concepts could be measured. For example, poverty level could be measured if there is a general increase in the purchasing power parity of people within a given time. Moreover, the level of students' intelligence could be measured by the grade of students within an academic year.

While there is no comprehensive way of measuring social problem, the method to enhance perfect measurement is to calculate the number of error in a given measurement. A good measurement is accomplished, if there is a little error. To ensure that the issue of social problem is being addressed is to use multiple indicators to measure the problem being addressed. "For example, success of a neighbourhood revitalization program would require several indicators. The decrease in crime, reduction of in vandalism, willingness to walk outside at night, and general physical appearance might be other indicator." ( Meier et al., 2011 P. 17).

Answer to Question B

The concept valid is the extent, which a test is able to measure what it claims to measure. Data validity reveals that the finding truly represents the phenomenon that a researcher is claiming to measure. There are four types of validity: Face validity, correlational validity, consensual validity, and predictive validity. Law School Admission Test (LSAT) has both face validity and consensual validity because LSAT is used to screen candidate. Additionally, LSAT has correlational validity because it can be used to correlate law school grade. However, LSAT is not effective to be used as a predictor of law school performance.

The feature of good data is its reliability and validity. Data are good when they are able to provide the same results to a phenomenon in number of times. For example, the data is good if they can be used to determine the effectiveness of police in a number of times and producing the same results. However, bad data are characterized by unreliability and non-validity. A researcher will not be able to deduce the inference of phenomenon from such data.

To determine whether the results of the 5 students are reliable and valid, there is a need to determine the precision of students' measurements. The results of 5 students are reliable if all of them produce the same results or nearly the same results. However, the data produced by 5 students could be valid or reliable if they could not provide the same results.

Answer to question C.

The highest level of measurement for the listed variables is as follows:

1

Race

Nominal

2

Age

Interval

3

Income

Interval

4

Age

Interval

5

Highest educational degree achieved

Interval

6

Job status

Nominal

7

Perceived crime level

Interval

8

Client Satisfaction

Ordinal

9

No of arrests

Interval

Race and job status could be measured at more than one level of measurement. The best level of measurement is interval level of measurement because it is the most precise highest level of measurement. The interval level of measurement could produce identical results for repeated applications. Thus, it produces data quality and able to provide validity with reference to level of measurement.