Graduation Year

2012

Document Type

Thesis

Degree

M.S.

Degree Granting Department

Geology

Major Professor

H. L. Vacher

Co-Major Professor

Mark C. Rains

Keywords

Geometric Mean, Nitrogen, Nutrient Concentration, Phosphorus, Quantitative Literacy, Skewness

Abstract

ABSTRACT

It may be of no surprise that water quality data is right-skewed, but what appears to be overlooked by some is that the arithmetic mean and standard deviation most often fail as measures of central tendency in skewed data. When using the arithmetic mean and arithmetic standard deviation with nutrient data, one standard deviation about the arithmetic mean can capture nearly all of the data and extend into negative values. Representing nutrient data this way can be misleading to viewers who are using the statistics, and making assumptions, to understand the characteristics of those waters. Through an in-depth statistical analysis of Florida's nitrogen and phosphorus data, I have found the geometric mean and multiplicative standard deviation capture a better representation of the central region of skewed data. Including the geometric mean and multiplicative standard deviation in the descriptive statistics of nutrient data is relatively simple with today's tools and helps to better describe the data. Adding these statistics can contribute to more effective understanding of nutrient concentrations, better application of data, and the development of better data-derived policy. While the suggestions of this paper are by no means original, it is with added evidence provided by the study of the skewness, distributions, and central regions of 53 nutrient data sets that I intend to help reiterate the argument that a few additional descriptive statistics can greatly empower the communication of data, and because of the ease with which they can now be calculated, there is no excuse to ignore them.

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