Statistics I: data and correlations

Statistics is the mathematical science dealing with the presentation, analysis, and interpretation of numerical information (data). In descriptive statistics, raw data are simplified as tables, graphs, and summary statistics such as mean and standard deviation. Inferential statistics is used to analyse and draw conclusions about a population of interest using data taken from a sample of the population, according to the laws of probability theory. Investigators are usually interested in populations rather than samples. For example, it is more useful to know the average arterial pressure in the UK adult population as a whole rather than in a much smaller sample in whom it is actually measured during the course of an investigation. As the study of entire populations is generally not possible, statistical methods are used to extrapolate from measured (known) sample characteristics to unmeasured (unknown) population characteristics. Three key terms are often used in statistics: parameter, variable, and sample statistic. A parameter is a measurable characteristic or attribute of a population or model (e.g. the average height or weight of the UK population). It has a fixed and usually unknown value. A variable is a measurable attribute of a sample (e.g. height or weight in a sample data set); variables vary from individual to individual. Variables may be either quantitative (interval or ordinal data) or qualitative (nominal data). A dependent variable is simply measured, whereas an independent variable is manipulated or controlled experimentally. For example, in an investigation of a new neuromuscular blocking agent, the dose of neuromuscular blocking agent received by patients is an independent variable, whereas the length of time before return of the first twitch in a train-of-four count is a dependent variable. A sample statistic is a mathematical quantity calculated from sample data variables, and is used as an approximation to a corresponding population parameter. Types of data