. Elementary biophysics: selected topics. Biophysics. CHAPTER 1 The Mathematical Treatment of Data. INTRODUCTION With a given set of data, the problem is always to extract the maximum amount of information. This in no sense relieves the investigator of the problem of designing better and more extensive and inclusive experi- ments. But the existing data surely deserve to be analyzed as fully as warranted. The word warranted is the problem word, and it is to this problem that the mathematical analysis of data is directed. We would like to know the information that can be gotten from some data in
. Elementary biophysics: selected topics. Biophysics. CHAPTER 1 The Mathematical Treatment of Data. INTRODUCTION With a given set of data, the problem is always to extract the maximum amount of information. This in no sense relieves the investigator of the problem of designing better and more extensive and inclusive experi- ments. But the existing data surely deserve to be analyzed as fully as warranted. The word warranted is the problem word, and it is to this problem that the mathematical analysis of data is directed. We would like to know the information that can be gotten from some data includ- ing the most likely values of the various quantities measured and, equally importantly, the probable uncertainty of the values thus ob- tained. A measurement of any property of a system is, by itself, almost with- out significance, because we do not know the uncertainty in the measure- ment. A statement as extreme as this needs some justification. We feel intuitively that the purpose of a measurement is to know something accurate about a property. If we are greatly uncertain about the result, then we have learned little. For we then have to say that the measure- ment might be some particular number but that it also might be, say, 1000 times greater or less than that number. Thus, not even knowing the uncertainty in the measurement is equivalent to changing the number 1000 to any number you may wish to insert. The whole purpose of statistical analysis is to show us how to maximize the relevance of the measurements we make. MEASUREMENTS AND THEIR VARIATION As a simple first example, let us take a series of n individual measure- ments of something: x1,x2, . . , xn. Why do we take more than one measurement? What have we gained by taking, as we usually do, the arithmetic average of these n measurements? If we consider that the sources of uncertainties in measurements act randomly, then in a set of measurements we are as likely to get an individual result higher than the "
Size: 1589px × 1573px
Photo credit: © The Book Worm / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookcollectionbiodiversi, booksubjectbiophysics
