Statistics - Week 1 Learning Objectives Colour Code: Definitions Descriptions Explanations 1. Define the terms population, sample, parameter, and statistic, and describe the relationships between them. · Population is the set of all the individuals of interest in a particular study. · A sample is a set of individuals selected from a population, usually intended to represent the population in a research study. Relationship between a population and a sample: (Figure 1) THE POPULATION All of the individuals of interest The results from the sample are generalized to the population The sample is selected from the population THE SAMPLE The individuals selected to participate in the research study · A parameter is a value, usually a numerical value, that describes a population. A parameter is usually derived from measurements of the individuals in the population. · A statistic is a value, usually a numerical value, that describes a sample. A statistic is usually derived from measurements of the individuals in the sample.
Other definitions: . A variable is a characteristic or condition that changes or has different values for different individuals. · Data are measurements or observations. A data set is a collection of measurements or observations. A datum is a single measurement or observation and is commonly called a score or raw score. 2. Define descriptive and inferential statistics and describe how these two general categories of statistics are used in a typical research study. · Descriptive statistics are techniques that take raw scores and organise or summarise them in a form that is more manageable. Often the scores are organised in a table or graph so that it is possible to see the entire set of scores. Another technique is to summarise a set of scores by computing an average. . Inferential statistics are methods that use sample data to make general statements about a population. Important Description Below Because populations are typically very large, it usually is not possible to measure everyone in the population. Therefore, a sample is selected to represent the population. By analyzing the results from the sample, we hope to make general statements about the population. Typically, researchers use sample statistics as the basis for drawing conclusions about population parameters. One problem with using samples, however, is that a sample provides only limited information about the population. Although samples are generally representative of their populations, a
sample is not expected to give a perfectly accurate picture of the whole population. There usually is some discrepancy between a sample statistic and the corresponding population parameter. This discrepancy is called sampling error, and it creates the fundamental problem inferential statistics must always address. 3. Define sampling error and describe the concept of sampling error and explain how this concept creates the fundamental problem that inferential statistics must address. . Sampling error is the naturally occurring discrepancy (or error) that exists between a sample statistic and the corresponding population parameter. The concept of sampling error: sample statistics vary from one sample to another and typically are