![]() (Prentice Hall, Upper Saddle River 2006)Ī. Agresti, C. Franklin: Statistics: The Art and Science of Learning from Data (Prentice Hall, Upper Saddle River 2006) J.T. McClave, T. Sincich: Statistics, 10th edn. R.M. Bethea, R.R. Rhinehart: Applied Engineering Statistics (Dekker, New York 1991) This process is experimental and the keywords may be updated as the learning algorithm improves. These keywords were added by machine and not by the authors. , x n and the functional relationship y = f( x 1, x 2. These methods provide a means for determining error in a quantity of interest y based on measurements of related quantities x 1, x 2. Accurate predictions can be made only if the proper probability function has been selected.įinally, statistical methods for accessing error propagation are discussed. EXPERIMENTS ER STATISTICAL CALCULATIONS SERIESOnce a probability function has been selected to represent a population, any series of measurements can be subjected to a chi-squared ( χ 2) test to check the validity of the assumed function. Many probability functions are used in statistical analyses to represent data and predict population properties. The increase in complexity is not a concern, because computer subroutines are available that solve the tedious equations and provide the results in a convenient format. In principle, these methods are identical to linear regression analysis however, the analysis becomes much more complex. Methods for extending regression analysis to multivariate functions exist. The adequacy of the regression analysis can be evaluated by determining a correlation coefficient. Regression analysis provides a method to fit a straight line or a curve through a series of scattered data points on a graph. Even though the functional relationship between quantities exhibiting variation remains unknown, it can be characterized statistically. Regression analysis can be used effectively to interpret data when the behavior of one quantity y depends upon variations in one or more independent quantities x 1, x 2. This is a useful technique that improves the data base by providing strong evidence when something unanticipated is affecting an experiment. Statistical methods can also be employed to condition data and to eliminate an erroneous data point (one) from a series of measurements. Studentʼs t distribution also permits a comparison to be made of two means to determine whether the observed difference is significant or whether it is due to random variation. ![]() Use of Studentʼs t distribution function, which characterizes sampling error, provides a basis for determining sample size consistent with specified levels of confidence. Sampling error can be controlled if the sample size is adequate. The effects of sampling error are accounted for by placing confidence limits on the predictions and establishing the associated confidence levels. In engineering applications is the ability to predict the occurrence of an event based on a relatively small sample. The most significant advantage resulting from the use of a probability distribution function A normal or Gaussian probability distribution is by far the most commonly employed however, in some cases, other distribution functions may have to be employed to adequately represent the data. Usually, the data are represented with a statistical distribution function that can be characterized by a measure of central tendency (the mean x ¯ ) and a measure of dispersion (the standard deviation S x). Statistical methods are extremely important in engineering, because they provide a means for representing large amounts of data in a concise form that is easily interpreted and understood. ![]()
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