Basic Statistical Concepts

There are numerous texts on basic statistics, some of them oriented towards chemists. It is not tire aim of this section to provide a comprehensive background, but simply to provide the main definitions and tables that are helpful for using this text. 

Conventionally a bar is placed above the letter. Sometimes the letter m is used, but in this text we will avoid this, as m is often used to denote an index. Hence tire mean of tire measurements 

Statistically, this sample mean is often considered an estimate of the true population mean sometimes denoted by /i. The population involves all possible samples, whereas only a selection are observed. In some cases in chemometrics this distinction is not so 

The estimated or sample variance of a series of measurements is defined by 

This equation is useful when it is required to estimate the variance from a series of samples. However, the true population variance is defined by 

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Use of multiple regression techniques in the study of functional properties of food proteins is not new I76) Most food scientists have some familiarity with basic statistical concepts and some access to competent statistical advice. At least one good basic text on statistical modelling for biological scientists exists (7 ). A number of more advanced texts covering use of regression in modelling are available (, ). ... 

This formulation may look somewhat unfamiliar, but we shall see that both the weighting factor and the quantity being averaged can mean many different things in colloid science. Appendix C presents a more detailed presentation of basic statistical concepts for both discrete and continuous distributions for those who desire more information on these topics. 

Some basic statistical concepts are defined in this section. For a more comprehensive treatment, the reader is directed to standard statistical texts. ... 

The purpose of this chapter is to review some basic statistical concepts. Statistical calculation and algorithms are not covered since, as has already been explained, they do not form part of the subject matter of this book. I shall, however, attempt an illustration of the nature of an important divide in statistics that between Bayesian or subjectivist statistics on the one hand and classical or frequentist on the other. 

It is impossible to evaluate model fitting without some basic statistical concepts. But do not be alarmed. You wiU not have to become a master statistician to benefit from the techniques presented in this book. A few notions derived from the (deservedly) famous normal distribution will suffice. These, presented in Chapter 2, are very important if we wish to understand and to correctly apply the methods scussed in the rest of the book. In an effort to lighten the dullness that often plagues the discussion of such concepts, we base our treatment of the normal distribution on solving a practical problem of some relevance to the culinary world. 

REM IT ALSO APPLIES BASIC STATISTICAL CONCEPTS TO FIND THE SLOPE, Y-INTERCEPT AND CORRELATION COEFFICIENT FOR THE LEAST SQUARES REGRESSION. 

Mullins, E. 2003. Statistics for the Quality Control Chemistry Laboratory, Royal Society of Chemistry, Cambridge. (Despite the title this text contains a good deal of material on basic statistical concepts, and many worked examples.)... 

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