Uncertainties in Data and Results

This part of the chapter is concerned with the evaluation of nncertainties in data and in calculated results. The concepts of random errors/precision and systematic errors/accuracy are discussed. Statistical theory for assessing random errors in finite data sets is summarized. Perhaps the most important topic is the propagation of errors, which shows how the error in an overall calculated result can be obtained from known or estimated errors in the input data. Examples are given throughout the text, the headings of key sections are marked by an asterisk, and a convenient summary is given at the end. 

Faced with the inevitability of random error, the observer customarily makes several measurements of a given physical quantity and then averages them to obtain a value that is expected to be more reliable than any single measurement. The average or mean of N measurements of an experimental variable x is 

The observer also customarily reports in some manner the scatter of the measurements that go into this expression in order to give an indication of the precision A erode way is to state the range of measured values  

For several reasons this does not give a very clear measure of the precision of the individual measurements but can be used as the basis of quick estimates of more sophisticated measures. Very commonly the average deviation is cited  

Traditionally this has been cherished for its arithmetic simplicity, a virtue of declining value in this age of computers. Its usefulness for quantitative comparisons is limited because under given experimental conditions its value depends sensitively on sample size (the value for a pair of measurements being, on the average, about 30 percent smaller than the value calculated with a large group of measurements). 

---