Statistics
A Brief Introduction to the Gaussian Distribution, Sample Statistics, and the Student's t Statistic JCE
Scott Van Bramer, Widener University
This document provides students with an brief introduction to the gaussian distribution, sample statistics, and the student's t statistic. It was designed for quantitative analysis, instrumental analysis, and physical chemistry courses.
Gaussian Distributions
Kevin Lehmann, Princeton University
The author generates a set of data from a Gaussian distribution to illustrate the properties of the distribution such as the mean of a set of data, the confidence level for the mean, the chi-squared function, and the Student t Distribution The document concludes with a discussion of the mean absolute deviation and a survey of the Moments of a distribution and how the mean absolute deviation and the moments are used to characterize the shape of the distribution. Variance, skew, and kurtosis are the three moments discussed in this document.
Introduction to the Propagation of Error
Peter J. Hansen, Northwestern College
This document presents a systematic development of the basic principles of propagation of error using the area of a rectangle and the density of a substance.
Linear Least Squares Regression JCE
Sidney H. Young, University of South Alabama
Andrzej Wierzbicki, University of South Alabama
Linear least-squares regression is the workhorse mathematical tool of the physical chemistry laboratory. This Mathcad worksheet and its accompanying data files demonstrate various implicit and explicit methods for determination of slope and intercept of a regressed line.
Mean Versus Median
Kevin Lehmann, Princeton University
This worksheet provides a comparison of the mean and median values for both theoretical distributions and for data sets sampled from Gaussian and Lorentzian distribution functions. The document shows that the mean value provides a moderately better estimate of the central value than the median for the case of a Gaussian. However, in the case of a Lorentzian, due to its slow fall off for large displacements from the central value, the mean is almost useless as a statistic, while the median functions quite well. The document also introduces the idea of finding the optimal estimate by using the method of maximum likelihood. This document requires Mathcad 6.0+ including upgrade through patch 'e' .
Non-Linear Least Squares Regression JCE
Sidney H. Young, University of South Alabama
Andrzej Wierzbicki, University of South Alabama
Nonlinear least-squares regression is often required in the physical chemistry laboratory. It is especially important for fitting functions that cannot be linearized. This template demonstrates various implicit and explicit methods for determining the parameters of the regressed curve obtained by nonlinear curve-fitting.
Rejection of Data
Kevin Lehmann, Princeton University
The document provides a detailed presentation to the theory of rejection of data using a Gaussian distribution. The document discusses the conditions under which the Q-test is used. The exercises in the document give students opportunities to practice the concepts. The document provides a numerical example of how statistical methods can reduce the errors in information extracted from measurements with real, as oppose to Gaussian, noise characteristics.