The Endangered Manatee Population vs. Florida Watercraft

Keith Greiner, Ed.D.

August 9, 2020

The West Indian Manatee is an endangered mammal that lives in areas from Florida to Guyana. The large herbivores are unique in that they are able to be in both salt water and fresh water. They move along under the surface in search of vegetation. The Nature Conservancy continues to list manatees as endangered because of their frequent collisions with watercraft. In 2015, collisions with Florida watercraft amounted to 21% of the Florida manatee deaths. Twenty-two percent of the deaths were perinatal.

The relationship between the number of watercraft and manatee deaths from collisions with watercraft is the subject of an analysis that has been included in several high school and college statistics texts. One such text is:

Moore, W. H. (2010). The basic practice of statistics (5^th ed.). New York, NY: W. H. Freeman & Company, Table 4.1, Page 101.

When teaching with the text, I found that it lacked two important items that were related to the manatee topic. First, the tables and graphs in the text did not include references for the source of the data. Such lack of reference was found throughout the text and indicates a profound lack of attention to scholarly quality. It is a poor example for students and is a poor example of the need for high quality scholarly work. The lack of references leaves the learner wondering if the data are real or if they were assembled out of thin air in an effort to have a data set that demonstrate a calculation. When the publisher was told about the problem, they were unresponsive. Second, there was insufficient discussion of the meaning and interpretation of the data and the example analysis in Table 4.1 of that edition.

This essay addresses both issues. First, the easy one: references to the source data.

The analysis of watercraft vs. manatee deaths comes from several sources.

1. Watercraft data are published by the Florida Department of Motor Vehicles. Annual reports from 2000 through 2015 are available at http://www.hsmv.state.fl.us/dmv/vslfacts.html on November 23, 2016 only those years of data were available. The textbook example uses data that includes the years from 1977 through 2013. These will undoubtedly be updated in years to come, although the DMV website will likely not add years from 1977 through 1999. An inquiry to the Florida Department of Motor Vehicles brought a set of data that did not match either the published book or the data published on the agency's website. Most likely the source of that data set has a different definition that is unknown to me. Therefore, I have not included it in this analysis.

2. Manatee deaths data comes from three sources: 1) the statistics book referenced above, 2) a website (http://www.chegg.com/homework-help/questions-and-answers/table-41-gives-37-years-data-boats-registered-florida-manatees-killed-boats-data-set-figur-q10249733 ) that appears to use the textbook as its source. The chegg.com site includes updates that are likely included in post-2010 editions of the text. Like the textbook, chegg.com does not adequately mention its source. The primary source for the data is from the Florida Fish and Wildlife Commission (http://myfwc.com/research/manatee/rescue-mortality-response/mortality-statistics/yearly/) where annual reports have been posted for years ranging from 1974 through 2015. Fortunately, the same categories of tabulations were used for all those years. This source lists county-level details of manatee deaths and the historical data used for the analysis must be compiled by selecting the annual totals for the watercraft category.

3. The textbooks' lack of an in-depth discussion is likely due to the emphasis on the techniques of calculation that we see in many texts. However, calculations without adequate scholarly references, critical thinking, and full understanding of the data, are of little value for those who might use the statistical analyses for policy decisions. As a result, we see large numbers of people who have taken statistics classes, but who do not use the knowledge in everyday life.

For this analysis, we first line up the number of watercraft (in thousands) in a left-hand column, along side the number of manatee deaths from watercraft (in whole numbers) in a right-hand column. Be sure to put the year in the far left. The arrangement of the watercraft and manatee deaths columns will put watercraft on the x axis, as the independent (explanatory) variable, and manatee deaths on the y axis as the dependent (response) variable. The selection of independent and dependent variables suggests causality; that the presence of watercraft may cause manatee deaths. Next, create an Excel scatter chart from the watercraft and manatee deaths columns. Under the options, select the on-screen equation and the R² value. Graph 1 shows the result. Here we see the equation, and most importantly, we see the R² value. This value is the square of the linear correlation between the two variables. It indicates the proportion or percentage of variation between the two, that is explained by the regression line. Graph 1 shows an R² value of 0.90914 or 90.914% That’s very good.

As a comparison, lets look at another variable. Lets compare watercraft (in thousands) to perinatal deaths. The term “perinatal” refers to deaths around childbirth. Graph 2 shows that comparison. There, we see the linear equation is clear, and the R² value is 0.73981 or 73.981%. That is very high, but not as high as the watercraft accidents. Notice how the variation from the line becomes more disperse on the high end numbers of watercraft. That dispersion results in the lower R² value. Declaring a high relationship between watercraft and perinatal deaths, then, becomes a bit more subjective; unless some other supporting data are available.

Graph 3 shows a time-series of Florida watercraft over the years of this analysis. Notice that the number of registered watercraft peaked in 2007. That is important, if it coincides with a change in manatee deaths.

Graph 4 shows a time-series of manatee deaths from watercraft. Notice how that number peaked in 2008. There was some variation in the number of deaths, but a polynomial trend line of order 6, tracks along the variation and seemingly peaks in 2007: the same year as the peak in watercraft. The equation for the polynomial trend line is shown, and the R² value of the line is 0.90578 or 90.578%. That’s very close to the R² value shown in Graph 1.

Graph 5 shows the annual perinatal deaths of Florida manatees. Notice how it continues to increase over time, and the increase appears to be linear, with larger variations in the most recent years. Unlike the number of watercraft and unlike the number of manatee deaths from watercraft, it does not show a decline after 2007. Still, the R² value is high, at 0.86351, which is the same as 86.351%.

Now, an appropriate question is whether there is a causal relationship between the number of watercraft and perinatal manatee deaths? I don’t know. In addition to the nice graph and the high level of R² there must be some other logical indicator of causality. Is there some form of interaction between watercraft and manatees that would cause a disruption of manatee birth. There are many things that could have high correlations with manatee deaths. Without some other meaningful causal connection, such comparisons are meaningless. So, without further evidence, I cannot say that there is a causal relationship between watercraft and perinatal deaths of manatees. What I do know that another comparison to a constantly rising value is highly unlikely to have a causal relationship, and it is fairly easy to find a set of data that rise in the same way over time, but have no relationship. For example, it is possible to do the calculation of Consumer Price Index CPI-U as the independent variable vs. manatee deaths. Over the range of years 1977 to 2013 the R² value is 0.8452 or 84.52%. That is a high level of R² and a suggestion that a regression line would account for 84.52% of the variation. But the calculation is illogical. I’d include a graph of that, here, but the internet being what it is, someone might extract such a graph indicates a causal relationship.

(c) 2016 by Keith Greiner