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ludoviceStatisticsHandout - Experimental Statistics P J...

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© 1996 and 2002 P. J. Ludovice Experimental Statistics P. J. Ludovice School of Chemical & Biomolecular Engineering Georgia Institute of Technology Atlanta, Georgia 30332-0100 Contents Introduction 1 Statistical Inference & the Normal Distribution 4 Confidence Limits or Confidence Intervals 8 t-Tests for Differences of Means 12 Generalized Least Squares Regression 14 Propagation of Error 18
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© 1996 and 2002 P. J. Ludovice 1 Introduction The purpose of this guide to experimental statistics is to familiarize the student with a few useful techniques in experimental statistics that will assist in the analysis of experimental data. After introducing the critically important concept distributions we will discuss the concept of statistical inference for analyzing data. This concept is used to infer something about the distribution of all possible data (population) from a single small set (sample) of data. We will learn how to place error bars on data as well as determine of two measurements are statistically different. Next we carry out correlation to see if the behavior of one variable of interest changes in a fashion similar to another variable (correlates). Since many of the parameters of interest to us come from fitted parameters as a result of some correlation we will also learn how to put an error bar on these fitted parameters. Finally we will learn how to propagate error through a calculation to determine the error on a derived parameter that utilizes a measured parameter and its associated error. In general the goal of most experiments is to summarize the data in single quantity and then associate some statistical error with this quantity. These summary quantities are typically called measures of central tendency and the include averages and fitted parameters of from correlations. The most commonly used measure of central tendency is the arithmetic mean ( X ), which is the average of various X values or all N values N X X N i i = = 1 . [1] Because this measure of central tendency is derived from several points, there is a spread of the data that is also associated with this measure. The spread or width of the data describes the precision of the data and is called the dispersion. The most commonly used measure of dispersion is the standard deviation ( σ ) which measures the root mean square deviation from the mean of a population ( µ ) averaged over all the data in the population (N p ) p N j j N X p = = 1 2 ) ( µ σ . [2] Note that that equation 2 describes the standard deviation for an entire population or a complete set of elements. In science and engineering we rarely have this complete set or entire population so we often use a sample or subset of the population. When the entire population is accessible then it is preferable to use this, however often this is not the case. For example if one wishes to take data on an entire school this is usually accessible, while accessing the population of an entire country is often cost prohibitive (this is why the U.S. census costs so much).
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ludoviceStatisticsHandout - Experimental Statistics P J...

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