Roadless America: Using Google Maps and R to Estimate Population Parameters Through Sampling Yue Cao1 Sara Stoudt1 Dana Udwin1 Nicholas J

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Roadless America: Using Google Maps and R to Estimate Population Parameters Through Sampling Yue Cao1 Sara Stoudt1 Dana Udwin1 Nicholas J. Horton1 1 Department of Mathematics and Statistics Smith College

Pedagogical Purpose Mapping the Results Conﬁdence Interval Comparisons

We sought a way to teach students in an advanced high school or undergraduate level statistics class that is more compelling and effective than rolling die or studying M&Ms. The Roadless blue-individual group red-class as a whole America activity asks students to sample random latitude and longitude coordinates from the contiguous United States, display these locations on a Google map, and determine whether or not the point is within one mile of a road. A worksheet template to be opened in RStudio streamlines this process for students.

Each group of students data can be used to calculate an estimate of the proportion of the United States within one mild of a road, as well as a 95% conﬁdence interval. When an entire class sections data is pooled, the consequent 95% conﬁdence interval is much narrower.

Students thereby observe how different samples, generated by various groups in a class, will yield different sample proportions and different confidence intervals. They will learn how increasing the sample size by pooling groups data impacts the width of a confidence interval. They will be able to interpret a confidence interval in the context of our original question: how much of America lies within one mile of a road? Environmental Purpose

Part of what makes the Roadless America activity engaging is its relevance: roads affect the ecology of at least 22% of the land area of the continental United States. Among other consequences, roads and traffic eliminate forest canopy, elevate the temperature, introduce vehicular noise and pollution and facilitate humans breeching the landscape. Figure 2- Map of Class Data Blue- Outside of the Continental US A policy called “Roadless Area Conservation” aims to limit road construction in order to halt Red- Within 1 Mile of a Road negative environmental impact on designated public lands. The United States Forest Service has Figure 5- Confidence Intervals Generated Per Group and For Combined Class Data Green- Roadless begun denoting certain regions as “Inventoried Roadless Areas that are both without nearby roads and potential candidates for roadless area conservation. According to the U.S. Forest Service, Conclusions Inventoried Roadless Areas comprise only 2% of the land in the continental United States. GoogleMaps For the test run of this activity completed in the three class sections of MTH241: Practice of Methodology Figure 3- Example of a Location Within 1 Mile of a Road in Texas Statistics, a total of thirty four groups of two students each produced thirty four proportion estimates and thirty four confidence intervals. A confidence interval was generated from the thirty The MOSAIC package in R enables random geographic location generation. We set the four groups pooled data: these 680 sampled locations suggested that 81.8% of the United States parameters within which our forty numbers must lie (twenty longitude, twenty latitude) to between is within one mile of a road with a 95% confidence interval of (77.6%,85.5%). 65 and 125 degrees for longitude and 25 to 50 degrees for latitude. This is a rectangle within Many students seemed to benefit from the activitys interactive nature and relevant content. which the contiguous United States lies. Students then utilize the getLocation function, provided However, several groups data contained errors in data input, ranging from incorrectly classifying a in the RStudio worksheet, to display a Google map for each of their twenty locations. The location as within one mile of a road, to bungling the csv so badly as to warrant tossing the data following function takes a pair of coordinates from the randomly generated list “myroadless” and (thirty four groups data was used, but the class sections altogether had thirty five groups). This opens a new browser window that displays that random point on a Google map with a circle of limitation suggests a need for improved directions in the R template and guidance during the radius equal to 1 mile. class session. googleMap(myroadless[counter,"latitude"] myroadless[counter,"longitude"], Extensions mark=TRUE, maptype="terrain", radius=1, browse=TRUE) The Google map allows the students to determine: This code can be utilized to determine many things about many regions. For example, the longitude and latitude coordinates framing the United States could be changed to frame New 1. if the location is within the continental United States Zealand. A different parameter could also be measured. For example, instead of “roadlessness,” 2. if it is within one mile of a road we might measure how much of the United States is Texas, or zoom into Michigan and determine how much of the state is near a lake. Students then edit a cvs file that contains information about each coordinate: latitude, longitude, within continent i.e. on land (1 if yes, 0 if no), location (e.g. state, body of water, Mexico, Canada, Acknowledgements etc.), within one mile of a road (1 if yes, 0 if no). We would like to thank Professor Daniel Kaplan of Macalester College for the original “Roadless They are given a template that can be run in RStudio and simplifies this process. When they are America” idea. We would also like to thank Randall Pruim of Calvin College for the specific uses done collecting information, they run a final set of code in the R template that uses their twenty of googleMap(). More personally, thank you to those MTH241 students who patiently made sample locations to produce both an estimate of the proportion of the United States within one possible “Roadless America’s maiden voyage. Above all, we thank Professor Nick Horton for his mile of a road and a confidence interval for this estimate. enduring support and knowledge, as well as Professor Ben Baumer for his Beamer poster Figure 1- Example of a Location More Than 1 Mile From a Road in Colorado template and technological savvy.

Figure 4- Example of a Location Outside the Continental US Off the Coast of California References

1. “Distance to Nearest Road in the Conterminous United States,” US Department of the Interior, US Geological Survey, 2005. 2. “Roadless Area Conservation,” US Department of Agriculture, US Forest Service, 2013. 3. Gelman, Andrew, and Deborah Nolan. Teaching Statistics: A Bag of Tricks. New York, NY: Oxford University Press, Inc, 2002.