Book Report

statistics Definition 1 Branch of mathematics concerned with collection, classification, analysis, and interpretation of numerical facts, for drawing inferences on the basis of their quantifiable likelihood (probability). Statistics can interpret aggregates of data too large to be intelligible by ordinary observation because such data (unlike individual quantities) tend to behave in regular, predictable manner. It is subdivided into descriptive statistics and inferential statistics. Descriptive statistics are used to describe the main features of a collection of data in quantitative terms. Descriptive statistics are distinguished from inductive statistics in that they aim to quantitatively summarize a data set, rather than being used to support statements about the population that the data are thought to represent. Even when a data analysis draws its main conclusions using inductive statistical analysis, descriptive statistics are generally presented along with more formal analyses, to give the audience an overall sense of the data being analyzed. Contents [hide] Statistical inference or statistical induction comprises the use of statistics and random sampling to make inferences concerning some unknown aspect of a population. It is distinguished from descriptive statistics. Two schools of statistical inference are frequency probability and Bayesian inference. History Main article: History of statistics Some scholars pinpoint the origin of statistics to 1662, with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.[5] Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its stat- etymology. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and the natural and social sciences. Because of its empirical roots and its focus on applications, statistics is usually considered to be a distinct mathematical science rather than a branch of mathematics.[6][7] Its mathematical foundations were laid in the 17th century with the development of probability theory by Blaise Pascal and Pierre de Fermat. Probability theory arose from the study of games of chance. The method of least squares was first described by Carl Friedrich Gauss around 1794. The use of modern computers has expedited large-scale statistical computation, and has also made possible new methods that are impractical to perform manually.

Statistics is the most widely used branch of mathematics in quantitative research outside of the physical sciences, and also finds applications within the physical sciences, such as in statistical mechanics. Statistical methods are used extensively within fields such as economics, social sciences and biology. Quantitative research using statistical methods starts with the collection of

data, based on the hypothesis or theory. Usually a big sample of data is collected - this would require varification, validation and recording before the analysis can take place. Software packages such as PSPP and R are typically used for this purpose. Causal relationships are studied by manipulating factors thought to influence the phenomena of interest while controlling other variables relevant to the experimental outcomes. In the field of health, for example, researchers might measure and study the relationship between dietary intake and measurable physiological effects such as weight loss, controlling for other key variables such as exercise. Quantitatively based opinion surveys are widely used in the media, with statistics such as the proportion of respondents in favor of a position commonly reported. In opinion surveys, respondents are asked a set of structured questions and their responses are tabulated. In the field of climate science, researchers compile and compare statistics such as temperature or atmospheric concentrations of carbon dioxide. Empirical relationships and associations are also frequently studied by using some form of General linear model, non-linear model, or by using factor analysis. A fundamental principle in quantitative research is that correlation does not imply causation. This principle follows from the fact that it is always possible a spurious relationship exists for variables between which covariance is found in some degree. Associations may be examined between any combination of continuous and categorical variables using methods of statistics.

Qualitative data The term qualitative is used to describe certain types of information. Qualitative data are described in terms of quality (that is, 'informal' or relative characteristics such as warmth and flavour). This is the converse of quantitative, which more precisely describes data in terms of quantity and often using a numerical figure to represent something in a statement. Quantitative data falls into two broad categories: Discrete (or attribute) data and Continuous (or variable) data. Discrete data generally falls into three categories: Category data (eg. car type), Bi-nomial data (eg. pass/fail), and Count / Poisson data (eg. # of hairs on your head). Qualitative data are generally (but not always) of less value to scientific research than quantitative data, due to their subjective and intangible nature. It is possible to approximate quantitative data from qualitative data - for instance, asking people to rate their perception of a sensation on a Likert scale.