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A Brief Introduction to the Gaussian Distribution, Sample Statistics, and the Student's t Statistic

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Abstract

Statistics is an important part of the chemistry curriculum, and small-sample statistics are critical to interpreting experimental results. Most students, however, have a very poor understanding of how small data sets behave and how statistical tests are used with small data sets. This set of Mathcad documents is designed to develop students’ understanding of normal distributions, small sample sets, and Student’s t statistic. Gaussian.mcd allows students to explore the area under a Gaussian distribution to understand one- and two-sided distributions. Sample_statistic.mcd allows students to observe how the average and standard deviation depend upon the number of samples taken from a normal population. They also explore how robust these variables are for a small number of samples. Students_t_statistic.mcd then goes on to show the importance of using Student’s t with small sample sets. Two additional documents, descriptive_stats.mcd and comparative_stats.mcd, are included for use as calculation templates. They are designed for the user to enter a data set and they calculate a number of statistical parameters for the data. The documents are suitable to use in physical chemistry, analytical chemistry, or instrumental analysis. They require Mathcad 11, Mathcad 12, or later and expect students to have minimal experience using Mathcad. If students are proficient with Mathcad, the instructor may increase the degree of interaction by removing some equations or graphs.

Figure 1. Sample standard deviation (+) and standard deviation (x) as a function of N, the number of samples taken from a population and used to calculate an average that represents the total population.

Downloads

Version	Download
All Files	StatisticsCollection.zip
Mathcad 12 XML	comparative_stats.xmcd
Mathcad 12 XML	descriptive_stats.xmcd
Mathcad 12 XML	gaussianxmcd.xmcd
Mathcad 12 XML	sample_statistics.xmcd
Mathcad 12 XML	students_t_statistic.xmcd
Mathcad 12	comparative_stats.mcd
Mathcad 12	descriptive_stats.mcd
Mathcad 12	gaussian.mcd
Mathcad 12	sample_statistics.mcd
Mathcad 12	students_t_statistic.mcd
Mathcad 11	comparative_stats_mcd11.mcd
Mathcad 11	descriptive_stats_mcd11.mcd
Mathcad 11	gaussian_mcd11.mcd
Mathcad 11	sample_statistics_mcd11.mcd
Mathcad 11	students_t_statistic_mcd11.mcd

Version	Download
Mathcad 12	comparative_stats.pdf
Mathcad 12	descriptive_stats.pdf
Mathcad 12	gaussianxmcd.pdf
Mathcad 12	sample_statistics.pdf
Mathcad 12	students_t_statistic.pdf

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Keywords

Audience: Upper-Division Undergraduate;

Domain: Analytical Chemistry; Laboratory Instruction; Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Chemometrics; Mathematics / Symbolic Mathematics; Statistical Mechanics;

JCE Citation