A third kind of sampling design is systematic random sampling. The systematic random sampling procedure is the easiest one. This sampling scheme is particularly useful in manufacturing processes, when the sampling is done from a continuously operating assembly line. Under this scheme, a first item is selected randomly and thereafter every
The fourth and last sampling design is cluster random sampling. In cluster sampling, each sampling unit is a group of smaller units. In the manufacturing environment, this sampling scheme is particularly useful since it is difficult to prepare a list of each part that constitutes a frame. On the other hand, it may be easier to prepare a list of boxes in which each box contains many parts. Thus, in this case, a cluster random sample is merely a simple random sample of these boxes. Another advantage of cluster sampling is that by selecting a simple random sample of only a few clusters, we can in fact have quite a large sample of smaller units. Such sampling is achieved at minimum cost, since both preparing the frame and taking the sample are much more economical. In preparing any frame, we must define precisely the characteristic of interest or variable, where a variable may be defined as follows:
Definition 2.1.7
A variable is a characteristic of interest that may take different values for different elements.
For example, an instructor is interested in finding the ages, heights, weights, GPA, gender, and family incomes of all the students in her engineering class. Thus, in this example, the variables (characteristics of interest) are ages, heights, weights, GPA, gender, and family incomes.
2.2 Classification of Various Types of Data
In practice, it is common to collect a large amount of nonnumerical and/or numerical data on a daily basis. For example, we may collect data concerning customer satisfaction, comments of employees, or perceptions of suppliers. Or we may track the number of employees in various departments of a company or check weekly production volume in units produced and sales dollars per unit of time, and so on. All the data collected, however, cannot be treated the same way as there are differences in types of data. Accordingly, statistical data can normally be divided into two major categories:
Qualitative
Quantitative
Each of these categories can be further subdivided into two subcategories each. The two subcategories of qualitative data are nominal and ordinal, whereas the two subcategories of quantitative data are interval and ratio. We may summarize this classification of statistical data as in Figure 2.2.1.
The classification of data as nominal, ordinal, interval, and ratio is arranged in the order of the amount of information they can provide. Nominal data provide minimum information, whereas ratio data provide maximum information.
Figure 2.2.1 Classifications of statistical data.
2.2.1 Nominal Data
As previously mentioned, nominal data contain the smallest amount of information. Only symbols are used to label categories of a population. For example, production part numbers with a 2003 prefix are nominal data, wherein the 2003 prefix indicates only that the parts were produced in 2003 (in this case, the year 2003 serves as the category). No arithmetic operation, such as addition, subtraction, multiplication, or division, can be performed on numbers representing nominal data. As another example, jersey numbers of baseball, football, or soccer players are nominal. Thus, adding any two jersey numbers and comparing with another number makes no sense. Other examples of nominal data are ID numbers of workers, account numbers used by a financial institution, ZIP codes, telephone numbers, sex, or color.
2.2.2 Ordinal Data
Ordinal data are more informative than nominal data. When the ordering of categories becomes important, the data collected are called ordinal. Examples include companies ranked according to the quality of their product, companies ranked based on their annual revenues, the severity of burn types, or stage of cancer among cancer‐afflicted patients. Again, no addition, subtraction, multiplication, or division can be used on ordinal‐type data.
Other examples of ordinal data are represented by geographical regions, say designated as A, B, C, and D for shipping purposes, or preference of vendors who can be called upon for service, or skill ratings of certain workers of a company, or in electronics engineering, the color‐coded resistors, which represent ascending order data.
2.2.3 Interval Data
Interval data are numerical data, more informative than nominal and ordinal data but less informative than ratio data. A typical example of interval data is temperature (in Celsius and Fahrenheit). Arithmetic operations of addition and subtraction are applicable, but multiplication and division are not applicable. For example, the temperature of three consecutive parts A, B, and C during a selected step in a manufacturing process are
2.2.4 Ratio Data
Ratio data are also numerical data that have the potential to produce the most meaningful information of all data types. All arithmetic operations are applicable on this type of data. Numerous examples of this type of data exist, such as height, weight, length of rods, diameter of a ball bearing, RPM of a motor, number of employees in a company, hourly wages, and annual growth rate of a company. In ratio data, the number zero equates to nothingness. In other words, the number zero means absence of the characteristics of interest.