Introduction to Statistics for Engineers

The second group, i.e. at a slightly lower level, is the one where all factors that are part of an observed phenomenon are known, but we know or are only partly aware of their interrelationships, i.e. influences. This is usually the case when we are faced with a complex phenomenon consisting of numerous factors. Sometimes we can link these factors as a system of simultaneous differential equations but with no solutions to them. As an example we can cite the Navier-Stokes simultaneous system of differential equations, used to define the flow of an ideal fluid  

An an even lower level of knowledge of a phenomenon is the case when only a certain number of factors that are part of a phenomenon are known to us, i.e. there exists a large number of factors and we are not certain of having noticed all the variables. At this level we do not know the natural law, i.e. the mathematical model by which these factors act. In this case we use experiment (empirical research) in order to reach the noticed natural law. 

Design of Experiments in Chemical Engineering. Zivorad R. Lazic Copyright 2004 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 3-527-31142-4 

As an example of this level of knowledge about a phenomenon we can cite the following empirical dependencies Darcy-Weisbah s law on drop of fluid pressure when flowing through a pipe [1]  

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Introduction to Statistics for Engineers A useful calculation formula is ... 

Introduction to Statistics for Engineers Table 1.30 Analysis of variance... 

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