Like all fields of learning, statistics has its own vocabulary. Some of the words and phrases encountered in the study of statistics will be new to those not previously exposed to the subject. Other terms, though appearing to be familiar, may have specialized meanings that are different from the meanings that we are accustomed to associating with these terms.
Data The raw material of statistics is data. For our purposes we may define data as numbers. The two kinds of numbers that we use in statistics are numbers that result from the taking—in the usual sense of the term—of a measurement, and those that result from the process of counting. For example, when a nurse weighs a patient or takes a patient’s temperature, a measurement, consisting of a number such as 150 pounds or 100 degrees Fahrenheit, is obtained. Quite a different type of number is obtained when a hospital administrator counts the number of patients—perhaps 20—discharged from the hospital on a given day. Each of the three numbers is a datum, and the three taken together are data.
Statistics The meaning of statistics is implicit in the previous section. More concretely, however, we may say that statistics is a field of study concerned with (1) the collection, organization, summarization, and analysis of data; and (2) the drawing of inferences about a body of data when only a part of the data is observed.
The person who performs these statistical activities must be prepared to interpret and to communicate the results to someone else as the situation demands. Simply put, we may say that data are numbers, numbers contain information, and the purpose of statistics is to investigate and evaluate the nature and meaning of this information.
Sources of Data The performance of statistical activities is motivated by the need to answer a question. For example, clinicians may want answers to questions regarding the relative merits of competing treatment procedures. Administrators may want answers to questions regarding such areas of concern as employee morale or facility utilization. When we determine that the appropriate approach to seeking an answer to a question will require the use of statistics, we begin to search for suitable data to serve as the raw material for our investigation. Such data are usually available from one or more of the following sources:
- Routinely kept records. It is difficult to imagine any type of organization that does not keep records of day-to-day transactions of its activities. Hospital medical records, for example, contain immense amounts of information on patients, while hospital accounting records contain a wealth of data on the facility’s business activities. When the need for data arises, we should look for them first among routinely kept records.
- Surveys. If the data needed to answer a question are not available from routinely kept records, the logical source may be a survey. Suppose, for example, that the administrator of a clinic wishes to obtain information regarding the mode of transportation used by patients to visit the clinic. If admission forms do not contain a question on mode of transportation, we may conduct a survey among patients to obtain this information.
- Experiments. Frequently the data needed to answer a question are available only as the result of an experiment. A nurse may wish to know which of several strategies is best for maximizing patient compliance. The nurse might conduct an experiment in which the different strategies of motivating compliance are tried with different patients. Subsequent evaluation of the responses to the different strategies might enable the nurse to decide which is most effective.
- External sources. The data needed to answer a question may already exist in the form of published reports, commercially available data banks, or the research literature. In other words, we may find that someone else has already asked the same question, and the answer obtained may be applicable to our present situation.
Biostatistics The tools of statistics are employed in many fields—business, education, psychology, agriculture, and economics, to mention only a few. When the data analyzed are derived from the biological sciences and medicine, we use the term biostatistics to distinguish this particular application of statistical tools and concepts. This area of application is the concern of this book.
Variable If, as we observe a characteristic, we find that it takes on different values in different persons, places, or things, we label the characteristic a variable. We do this for the simple reason that the characteristic is not the same when observed in different possessors of it. Some examples of variables include diastolic blood pressure, heart rate, the heights of adult males, the weights of preschool children, and the ages of patients seen in a dental clinic.
Quantitative Variables A quantitative variable is one that can be measured in the usual sense. We can, for example, obtain measurements on the heights of adult males, the weights of preschool children, and the ages of patients seen in a dental clinic. These are examples of quantitative variables. Measurements made on quantitative variables convey information regarding amount.
Qualitative Variables Some characteristics are not capable of being measured in the sense that height, weight, and age are measured. Many characteristics can be categorized only, as, for example, when an ill person is given a medical diagnosis, a person is designated as belonging to an ethnic group, or a person, place, or object is said to possess or not to possess some characteristic of interest. In such cases measuring consists of categorizing. We refer to variables of this kind as qualitative variables. Measurements made on qualitative variables convey information regarding attribute.
Although, in the case of qualitative variables, measurement in the usual sense of the word is not achieved, we can count the number of persons, places, or things belonging to various categories. A hospital administrator, for example, can count the number of patients admitted during a day under each of the various admitting diagnoses. These counts, or frequencies as they are called, are the numbers that we manipulate when our analysis involves qualitative variables.
Random Variable Whenever we determine the height, weight, or age of an individual, the result is frequently referred to as a value of the respective variable. When the values obtained arise as a result of chance factors, so that they cannot be exactly predicted in advance, the variable is called a random variable. An example of a random variable is adult height. When a child is born, we cannot predict exactly his or her height at maturity. Attained adult height is the result of numerous genetic and environmental factors. Values resulting from measurement procedures are often referred to as observations or measurements.
Discrete Random Variable Variables may be characterized further as to whether they are discrete or continuous. Since mathematically rigorous definitions of discrete and continuous variables are beyond the level of this book, we offer, instead, non rigorous definitions and give an example of each.
A discrete variable is characterized by gaps or interruptions in the values that it can assume. These gaps or interruptions indicate the absence of values between particular values that the variable can assume. Some examples illustrate the point. The number of daily admissions to a general hospital is a discrete random variable since the number of admissions each day must be represented by a whole number, such as 0, 1, 2, or 3. The number of admissions on a given day cannot be a number such as 1.5, 2.997, or
3.333. The number of decayed, missing, or filled teeth per child in an elementary school is another example of a discrete variable.
Continuous Random Variable A continuous random variable does not possess the gaps or interruptions characteristic of a discrete random variable. A continuous random variable can assume any value within a specified relevant interval of values assumed by the variable. Examples of continuous variables include the various measurements that can be made on individuals such as height, weight, and skull circumference. No matter how close together the observed heights of two people, for example, we can, theoretically, find another person whose height falls somewhere in between.
Because of the limitations of available measuring instruments, however, observations on variables that are inherently continuous are recorded as if they were discrete. Height, for example, is usually recorded to the nearest one-quarter, one-half, or whole inch, whereas, with a perfect measuring device, such a measurement could be made as precise as desired.
Population The average person thinks of a population as a collection of entities, usually people. A population or collection of entities may, however, consist of animals, machines, places, or cells. For our purposes, we define a population of entities as the largest collection of entities for which we have an interest at a particular time. If we take a measurement of some variable on each of the entities in a population, we generate a population of values of that variable. We may, therefore, define a population of values as the largest collection of values of a random variable for which we have an interest at a particular time. If, for example, we are interested in the weights of all the children enrolled in a certain county elementary school system, our population consists of all these weights. If our interest lies only in the weights of first-grade students in the system, we have a different population—weights of first-grade students enrolled in the school system. Hence, populations are determined or defined by our sphere of interest. Populations may be finite or infinite. If a population of values consists of a fixed number of these values, the population is said to be finite. If, on the other hand, a population consists of an endless succession of values, the population is an infinite one.
Sample A sample may be defined simply as a part of a population. Suppose our population consists of the weights of all the elementary school children enrolled in a certain county school system. If we collect for analysis the weights of only a fraction of these children, we have only a part of our population of weights, that is, we have a sample.
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