Statistical Inference and Evidence-Based Science

International Journal of Aquatic Research and Education Volume 5 | Number 2 Article 2 5-1-2011 Statistical Inference and Evidence-Based Science Stephen J. Langendorfer Bowling Green State University, Follow this and additional works at: https://scholarworks.bgsu.edu/ijare Recommended Citation Langendorfer, Stephen J. (2011) "Statistical Inference and Evidence-Based Science," International Journal of Aquatic Research and Education: Vol. 5 : No. 2 , Article 2. DOI: 10.25035/ijare.05.02.02 Available at: https://scholarworks.bgsu.edu/ijare/vol5/iss2/2 This Editorial is brought to you for free and open access by ScholarWorks@BGSU. It has been accepted for inclusion in International Journal of Aquatic Research and Education by an authorized editor of ScholarWorks@BGSU. Langendorfer: Statistical Inference and Evidence-Based Science International Journal of Aquatic Research and Education, 2011, 5, 143-146 © 2011 Human Kinetics, Inc. Statistical Inference and Evidence-Based Science I presume that many readers may have heard some variation of the quote, attributed to British Prime Minister Benjamin Disreali and popularized by American humorist, Mark Twain (a.k.a., Samuel Clemens), when referring to confusion generated by the use and misuse of quantitative figures. “There are three kinds of mistruth: lies, damned lies, and statistics” (Twain, 1906). One of the “rites of passage” associated with obtaining a graduate degree is being required to complete multiple statistics classes. I try to sympathize with my current students when I reflect on how little I could recall after finishing my first course in tests and measurements as an undergraduate. During my Masters program at Purdue University, I gained a completely undeserved reputation for being a “statistics whiz,” bestowed upon me by my fellow student and oft co-conspirator, Larry Bruya (who fulfills my personal definition of a “true friend” wherein a “friend” is said to be one who will bail you out of jail, while a “true friend” is one who sits in the jail cell with you and proclaims, “Golly, that was fun!”). Larry and I took the same first-level statistics class together at Purdue and in the evenings while studying, he would quiz me about what each day’s topic meant. I was too dumb to realize that Larry wasn’t asking rhetorical questions to challenge me, but that he really didn’t know the answers. I figured I didn’t want to appear stupid, so I started concocting answers and in the process figured out how to actively learn statistics! Thanks, Larry. There is a sequel to this story decades later. Whenever I make some kind of pronouncement in his presence, Larry has learned to inquire, “Do you really know the answer or are you just making that up?!” Such an inquiry never fails to result in gales of laughter while Larry explains to whoever is gathered our personal story about what he affectionately calls “making up crap about statistics.” An important realization to come from any discussion about statistics, with or without any notion of lying or even just “making up crap,” is that comprehending statistics can legitimately be quite confusing, even to those with some basic knowledge. They can be utterly mystifying to those without a degree of quantitative literacy in probability, laws of chance, and elementary statistical procedures. Worse, when statistics have been misused (say it ain’t so!) simply to support one’s preconceived opinion, all trust in them can go right out the window so that the validity of all statistics becomes suspect. Statistics as Tools There are all sorts of numbers that pass for statistics, rightly or wrongly: Individual scores, percentages, percentiles, standard scores, means, medians, modes, ranges, standard deviations, variances, T scores, t tests, analysis of variance, correlation, multivariate analysis of variance, analysis of covariance, and multiple regression, ad infinitum. An important first realization is that any statistic is merely a tool like Published by ScholarWorks@BGSU, 2011 143 1 International Journal of Aquatic Research and Education, Vol. 5, No. 2 [2011], Art. 2 144   Langendorfer a hammer, screwdriver, shovel, or rake. Like any tool, a statistic can be both used and misused. Applying the appropriate statistic to the right research question is critical in scientific study. That necessitates fundamental knowledge about many kinds of statistics. As the old saying goes, “If your only tool is a hammer, everything begins to look like a nail!” I cannot possibly and do not intend to overview everything that is important about statistics in these several editorial pages. I am addressing several notions that do apply to the scientific rigor associated with research papers submitted to and published by this particular scholarly journal. For more sophisticated understanding of statistics, I encourage readers to seek out various print and online statistical sources including the Publication Manual of the American Psychological Association (6th ed., 2010). Chapter 5, “Displaying Results” (pp. 125-167) presents an important summary of how to analyze and present the statistical results of many different kinds of study. Descriptive Vs. Inferential Statistics It may be helpful to consider that all statistics (remember that does not mean all numbers) can be categorized into one of two groups: descriptive statistics and inferential statistics. I realize that there are also parametric and nonparametric statistics, subcategories of inferential statistics, and I am certain there are other ways to categorize different statistics. For my discussion purposes, I think these two groupings will suffice. Descriptive Statistics. For most individuals the most straightforward way to summarize or capture the essence of a group of numbers is by using descriptive statistics. Examples of descriptive statistics include measures of central tendency (i.e., mean, median, mode) and measures of variability (i.e., range, standard deviation, variance, standard errors) along with simple percentages, percentiles, standard scores, and correlations. The purposes of descriptive statistics are to summarize for a reader the score characteristics of a group or sample of numbers as well as to provide some insight into the scores achieved by individuals within that group. True to their name, they simply describe and summarize the group of numbers: what the distribution of numbers looks like, where its middle score lies, how spread out the scores are, and whether scores are related or associated with other scores. Importantly, individual descriptive statistics do not, by themselves, give one enough information to generalize those numbers or scores to other groups beyond the immediate sample. They also can be misleading when used in isolation or inappropriately. For example, knowing the mean of a group of scores tells the reader only where the arithmetic average of those scores falls. If the sample of scores is skewed (i.e., (...truncated)