Statistics for Analysis of Experimental Data
Catherine A. Peters
Department of Civil and Environmental Engineering
Princeton University
Princeton, NJ 08544
Published as a chapter in the
Environmental Engineering Processes Laboratory Manual
S. E. Powers, Ed.
AEESP, Champaign, IL
2001
Statistics is a mathematical tool for quantitative analysis of data, and as such it serves as the means by which we extract useful information from data. In this chapter we are concerned with data that are generated via experimental measurement. Experimentation often generates multiple measurements of the same thing, i.e. replicate measurements, and these measurements are subject to error.
Statistical analysis can be used to summarize those observations by estimating the average, which provides an estimate of the true mean. Another important statistical calculation for summarizing the observations is the estimate of the variance, which quantifies the uncertainty in the measured variable.
Sometimes we have made measurements of one quantity and we want to use those measurements to infer values of a derived quantity. Statistical analysis can be used to propagate the measurement error through a mathematical model to estimate the error in the derived quantity.
Sometimes we have measured two different things and we want to know whether there really is a difference between the two measured values. Analysis of variance (t-tests) can be used to estimate the probability that the underlying phenomena are truly different. Finally, we may have measured one variable under a variety of conditions with regard to a second variable. Regression analysis can be used to come up with a mathematical expression for the relationship between the two variables. These are but a few of the many applications of statistics for analysis of experimental data. This chapter presents a brief overview of these applications in the context of typical experimental measurements in the field of environmental engineering.
This chapter is necessarily brief in presentation. Students who seek a deeper understanding of these principles should study a textbook on statistical analysis of experimental data. The bibliography at the end of this chapter lists some useful textbooks, some of which are directly aimed at environmental engineers and scientists.
Read and download
ليست هناك تعليقات:
إرسال تعليق