You may have heard someone say “You can prove anything you want with statistics!” However, this is not true, unless the audience is ignorant of how statistics works, or unless the audience is not given essential information showing the validity—or not—of important conditions and assumptions behind the statistical techniques involved. In particular, you cannot be deceived, unless you do not know how statistics works! Furthermore, statistics cannot actually prove a particular conclusion, such as a difference among different groups. The best statistics can do for you is to tell you, within a formal, probabilistic framework, that an observed difference among samples is probably different—or not—from what would be expected to occur by chance if the samples came from different groups having the same characteristics. Even though statistics does not give you a proof, statistics does provide friendly tools that give you conclusions based on real data and valid techniques, so that, overall, you can be reasonably confident about the final conclusions (while admitting the possibility of being wrong). However, no matter how elegant the statistical analyses are, the conclusions of the research may still be false, unless the data collected are valid representations of the real world and all the components of the study are properly designed and carried out.
of the Measures of Variation and Their Associated Concepts,
This 55-page "handbooklet"
is intended for anyone at any level who wishes to have more intuitive
explanations of the concepts of standard deviation and variance, as well
as a better understanding of their formulas and associated concepts.
(Total of 66 pages.)
About the Author
Ray L. Winstead has a bachelor’s degree
in mathematics (with an additional concentration beyond a minor in
biology) from Atlantic Christian College (now Barton College in Wilson,
North Carolina), a master’s degree in mathematics (with a minor in
applied mathematics) from Duke University (Durham, North Carolina), and
a Ph.D. in Zoology (with a minor in ecology) from North Carolina State
University (Raleigh, North Carolina). He was also a Postdoctoral Fellow
for two years in biomathematics and statistics at North Carolina State
University. He was a Professor of Biology at Indiana University of
Pennsylvania in Indiana, Pennsylvania, where he taught graduate courses
in biostatistics and ornithology, as well as undergraduate courses in
general biology and ornithology. He retired in June 2013 from IUP after
teaching there for thirty-seven years. He is the editor of the book
Our First Sixteen Presidents: 110 Portraits, Paintings, and Lithographs
with Biographical Narratives by Franklin P. Rice (1882) and Henry W.
Rugg (1888) published in January 2014 and also the editor of the book
The Development of Law Pertaining to Desegregation of Public Schools in
North Carolina: Circumvention of the Supreme Court’s 1954 Brown v. Board
of Education Ruling for Ten Years in North Carolina (1966
dissertation) by Elton D. “E. D.” Winstead published in September 2014.