Chapter One: Foundations of Biostatistics 1/9

Transcription

1 Chapter One: Foundations of Biostatistics 1/9

2 1.1 Introduction 2/9 1.1 Introduction There are many definitions for the terms statistics and biostatistics. The following are two such definitions. Statistics is a discipline concerned with (1) the organization and summarization of data, and (2) the drawing of inferences about the characteristics of some collection of persons or things when only a portion of these characteristics are available for study. Biostatistics is that branch of statistics that deals primarily with the biological sciences and medical/health-related disciplines.

3 1.2 Populations and Samples 3/9 1.2 Populations and Samples There are conflicting ideas as to what constitutes a population. Consider the following statements from two popular statistics texts A population is a set of persons (or objects) having a common observable characteristic. Note that the word population refers to data and not to people.

4 1.2 Populations and Samples 4/9 1.2 Populations and Samples (continued) In point of fact, we use the term population in two different ways. The following definitions will be helpful in understanding the concepts of populations and samples. A popular population is a collection of persons or things in which we have an interest. For example, the collection of persons living in Florida who test positive for hepatitis C or the collection of deer in some county of Michigan that carry the tick responsible for Lyme disease might be two such examples. A statistical population is a collection of some characteristic of a set of persons or things in which we have an interest. Examples would include the blood pressures of some set of students or an indicator as to whether each student had experienced some form of sexual abuse during her/his lifetime.

5 1.2 Populations and Samples 5/9 1.2 Populations and Samples (continued) A sample is a subset of a population and may be consist of persons/things or characteristics of persons/things depending on whether the sample is from a popular or statistical population. Thus, we may refer to a sample of 50 men over age 65 who suffer from hypertension or to a sample of 50 blood pressures taken on 50 men over age 65 who suffer from hypertension

6 1.2 Populations and Samples 6/9 1.2 Populations and Samples (continued) Two related concepts are defined as follows. When a characteristic is measured and recorded, the result is termed data. Thus, if a series of blood pressures is recorded on a piece of paper or in a computer file, the recordings are referred to as data. A characteristic that takes on more than one value is termed a variable. Thus, if a sample consists of 50 males, gender is not a variable in this sample but rather is termed a constant. If the sample is made up of males and females, then gender is a variable in this sample.

7 1.3 Parameters and Statistics 7/9 1.3 Parameters and Statistics Closely related to the concepts of populations and samples are the concepts of parameters and statistics. A parameter is any summarization of the elements of a population. Thus, if the average of the blood pressures that make up a population is calculated, the result is one example of a parameter. A statistic is any summarization of the elements of a sample. Thus, if the average of the blood pressures that make up a sample is calculated, the result is one example of a statistic.

8 1.4 Descriptive and Inferential Statistics 8/9 1.4 Descriptive and Inferential Statistics The discipline of statistics may be conceived of in a number of different ways. Among the most common of these is to characterize the discipline as being made up of two (related) components. Descriptive statistics is made up of various techniques used to summarize the information contained in a set of data. Inferential statistics is made up of various techniques used to provide information about parameter values based on observations made on the values of statistics.

9 Summary Depiction 9/9 Summary Depiction The relationship between populations and samples, parameters and statistics, and descriptive and inferential statistics is depicted in this figure. Population (Parameter) Sample Inferential statistics x x X 121 x (Statistic) x Descriptive statistics used to produce value of x from data