Introduction to statistics

Statistics n Plays an important role in many facets of human endeavour n Occurs remarkably frequently in our everyday lives n Is often incorrectly thought of as just a collection of data, graphs and diagrams

Definition of statistics n Statistics is the scientific method that enables us to make decisions as responsibly as possible.

The decision-making process: 1. Collecting pertinent information that is as reliable as possible. 2. Selecting the parts of the available information that are most helpful to make rational decisions. 3. Making the actual decisions as sensibly as possible on the basis of the available evidence. 4. Perceiving the risks entailed in the particular decision made, and evaluating the corresponding risks of alternative actions.

Statistics can be split into two broad categories: 1. Descriptive statistics 2. Statistical inference

Descriptive statistics n The meaningful presentation of data such that its characteristics can be effectively observed.

Descriptive statistics n Encompasses the following: –Graphical or pictorial display –Condensation of large masses of data into a form such as tables –Preparation of summary measures to give a concise description of complex information (e.g. an average figure) –Exhibition of patterns that may be found in sets of information

Statistical inference n Relates to decision making and is the subject that leads to future action rather than an inspection of the past. It refers to decisions.

Statistical inference n Especially relates to: –Determining whether characteristics of a situation are unusual or if they have happened by chance –Estimating values of numerical quantities and determining the reliability of those estimates –Using past occurrences to attempt to predict the future

Variability n Virtually everything varies n Variation occurs among individuals n Variation occurs within any one individual as time passes

Variability n Affects the reliability of information: –Conclusions reached from one set of people may or may not carry over to a different set. –Conclusions made today may not be valid in the future.

Statisticians statistician n A statistician can be defined as a person who can collect, present, and analyse data, and draw inferences from them.

Statisticians statistician n A statistician may: –be a consultant for an organisation or individual –lecture or teach –undertake research (e.g. at the CSIRO) –supervise research projects –be involved in the application of statistical method –develop mathematics required for theory –design statistical methodology for best effect in fields such as economics

Statistics in economics and commerce n Statistics n Statistics are used to draw inferences and predict the future in both economics and commerce. n This requires knowledge of: –techniques to detect trends and cycles –the ability to distinguish between genuine structural changes and the results of random fluctuation –methods of extrapolation.

Publications in statistics n These are numerous and include: –General statistical journals (e.g. International Statistical Review) –Journals in specific areas (e.g. Journal of Statistical Physics) –Australian journals (e.g.The Australian and New Zealand Journal of Statistics)

Types of data n Statistical data can be obtained in a number of ways. These include: –Measurements using an instrument (e.g. a simple ruler) –Counts (e.g. the number of employees absent each day)

Types of data n Rank data n Rank data (e.g. where individuals or objects are ranked according to a criterion) n Categorical data n Categorical data or classification data involves placing observations into categories (e.g. eye colour or gender) n Primary data n Primary data are information collected by the person or organisation that will be using the information n Secondary data n Secondary data are information already collected by someone else