Statistical Analysis of Experimental Data
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. Usually, the data are represented with a statistical distribution
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Statistical An
11. Statistical Analysis of Experimental Data
James W. Dally
characterized statistically. Regression analysis provides a method to fit a straight line or a curve through a series of scattered data points on a graph. The adequacy of the regression analysis can be evaluated by determining a correlation coefficient. Methods for extending regression analysis to multivariate functions exist. In principle, these methods are identical to linear regression analysis; however, the analysis becomes much more complex. 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. Many probability functions are used in statistical analyses to represent data and predict population properties. Once 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. Accurate predictions can be made only if the proper probability function has been selected. Finally, statistical methods for accessing error propagation are discussed. These methods provide a means for determining error in a quantity of interest y based on measurements of related quantities x1 , x2 , ..., xn and the functional relationship y = f (x1 ‚x2 ‚ ..., xn ).
11.1
Characterizing Statistical Distributions ... 11.1.1 Graphical Representations of the Distribution........................ 11.1.2 Measures of Central Tendency ........ 11.1.3 Measures of Dispersion .................
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11.2 Statistical Distribution Functions ........... 263 11.2.1 Gaussian Distribution ................... 263 11.2.2 Weibull Distribution ..................... 265 11.3 Confidence Intervals for Predictions ....... 267 11.4 Comparison of Means............................ 270
Part A 11
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. 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 Sx ). 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. The most significant advantage resulting from the use of a probability distribution function in engineering applications is the ability to predict the occurrence of an event based on a relatively small sample. The effects of sampling error are accounted for by placing confidence limits on the predictions and establishing the associated confidence levels. Sampling error can be controlled if the sample size is adequate. Use of Student’s t distribution function, which characterizes sampling error, provides a basis for determining sample size consistent with specified levels o
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