# Statistics: Predicting Temperature

## Summary

Students apply statistical tools to polar research and data. This includes creating scatterplots in RStudio of temperature with time for the modern Arctic and the modern global average, demonstrating polar amplification; computing coefficients of linear regression to reconstruct the temperature record for the past 800,000 years from the isotopic record in ice cores; and computing correlation coefficients between CO2 and temperature.

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## Learning Goals

**Part I**

- Learn consequences of climate change, including how polar ice melt contributes to sea level rise and how thawing permafrost releases methane and leads to damaged Arctic infrastructure.
- Learn about polar amplification and the role played by positive feedback loops.
- Gain experience using RStudio to create scatter plots.
- Be familiar with what questions are asked in statistics and understand that the researcher has the role of interpreting the results.
- Know the terminology related to scatterplots(e.g. explanatory and response variables)and the types of scatterplot (strength, direction, and form of the association).

**Part II.**

- Understand that isotopic composition in ice cores can be used as a thermometer.
- Be able to interpret the coefficients of simple linear regression.
- Learn about identifying and dealing with outliers.
- Be able to use RStudio to determine the coefficients of simple linear regression.
- Gain practice reading peer-reviewed journal articles.

**Part III.**

- Be familiar with how temperature has changed in the past.
- Be able to use a linear regression model to make a prediction.

**Part IV.**

- Know that temperature has varied between ice ages and warm stable periods and that these variations are enhanced by CO2 through the greenhouse effect.
- Be able to recognize differences between how CO2 and temperature are correlated in the ice core record, for the modern global average, and in the modern polar regions.
- Gain experience computing sample correlation and understand what it is.
- Know that correlation does not prove causation, and that a predictive physical model is needed.

## Context for Use

This activity is designed to be used in an introductory statistics course. Students must have in-class access to computers with R and RStudio installed. Problems can be mitigated by having students work in pairs and having an extra laptop or two available as needed, equipped with the software.

The activity is meant to take about two weeks of class time, assuming three hours per week. It could also be taught in two 3-4 hour lab sessions. It has been taught to class sizes of up to 30. Application in larger classes could be fostered by additional support, if available; e.g. through teaching assistants. The activity includes four presentations for the instructor to give the class, which teach the polar and statistics concepts, as well as in-class activities, a homework assignment and a test. No previous computational or coding experience is required.

## Description and Teaching Materials

**Overview**

In this module, students will work actively with polar data through computer programming in R, using RStudio. The lecture presentations and instructions are designed so that no prior coding experience is necessary. This module includes four PowerPoint presentations, which can be taught sequentially or divided between class periods. All materials needed to implement the activity are provided below. Links to online resources used are provided and digital backups are included in case data is moved or removed. The following describes activities and the materials used for each.

**Materials**

- Polar Data ( 175kB Jul31 23) (used throughout)
- Materials for Part 1 (part1.zip (Zip Archive 5.3MB Aug1 23)). After unzipping, this includes:
- Pre-module homework: Install RStudio and R.
- Presentation: stats_part1_scatterplots.pptx
- Handout for student activity: part1_student_activity.docx

- Materials for Part 2 (part2.zip (Zip Archive 10.1MB Aug1 23)). After unzipping, this includes:
- Presentation: stats_part2_coefficients.pptx
- Handout for student activity: part2_student_in_class_activity.docx
- Homework assignment: part2_homework_simple_linear_regression.docx
- Journal article: Dahe_1994.pdf

- Materials for Part 3 (part3.zip (Zip Archive 2.8MB Aug1 23)). After unzipping, this includes:
- Presentation: stats_part3_making_predictions.pptx
- Handout for student activity: part3_student_activity.docx

- Materials for Part 4 (part4.zip (Zip Archive 4.1MB Aug1 23)). After unzipping, this includes:
- Presentation: stats_part4_correlation.pptx
- Handout for student activity: part4_student_activity.docx
- stats_exam.pages

- Assessment (assessment.zip (Zip Archive 695kB Aug1 23)) -- educator-only file. After unzipping, this includes:
- key_part1_student_activity.R
- key_part2_Homework_more_simple_linear_regression.docx
- key_part2_Homework_simple_linear_regression.R
- key_part2_student_activity.docx
- key_part3_student_activity.R
- key_stats_exam.pages

**Instructor Preparation**

- Download materials above and unzip files.
- Install RStudio and R (instructions are given in the Part 1 homework assignment).
- Follow the workflow below, practicing giving the presentations and the demonstrations in RStudio. Work through the student in-class activities, homework assignment, and exam.
- Compare the completed exercises and the exam to the provided keys and review as needed.
- You may optionally choose to use the Climate Change videos in References and Resources.

**Workflow**

**Part I**

- Pre-module homework: using the Part 1 Homework, students install R and RStudio before the start of the module.
- The instructor may optionally have students watch climate change videos to help transition students to the topic (see references and resources below; note that if done in class this would require additional time beyond the planned ~6 hours of in-class time).
- The instructor delivers the Part 1 presentation to the students, which starts with an explanation of why polar research is being taught in a statistics class.
- Partway through the presentation, the instructor gives a demo, using RStudio to create scatterplots. The commands are given in the presentation.
- Later in the presentation, students complete an in-class activity using RStudio to create and compare scatterplots of Arctic and global temperature. The instructions are available as handouts.

**Part II.**

- The instructor delivers the Part 2 presentation to the students.
- Partway through the presentation, the instructor gives a demo using RStudio to determine the coefficients of simple linear regression. The commands are given in the presentation.
- Later in the presentation, students complete an in-class activity with a small-group discussion, following the questions given in the presentation.
- Students are assigned the homework assignment: they read the journal article by Dahe et al and use RStudio to perform the linear regression and interpret the coefficients for delta18O vs temperature from the article.

**Part III.**

- The instructor delivers the Part 3 presentation to the students.
- Partway through the presentation, students complete an in-class activity in RStudio, determining and plotting the temperature anomaly over the ice core record.

**Part IV.**

- The instructor delivers the Part 4 presentation to the students.
- Partway through the presentation, the instructor may (optionally) demonstrate in RStudio how to determine the correlation between height and volume of trees.
- Later in the presentation, students complete an in-class activity creating plots and compute the correlation coefficient of CO2 vs temperature.
- The instructor completes the presentation.
- The students take the exam.

## Teaching Notes and Tips

**Computer lab vs personal laptops**

While students can use a computer lab or work on individual laptops, we suggest the latter. Installing R and RStudio on laptops is straightforward, gives the students a valuable experience, and allows them to complete work at home, if needed. Furthermore, the student has the computational tool available to them after completion of the activity.

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## Assessment

We recommend the in-class assessments be assessed in class on a pass/fail basis, and suggest 20 points each for a total of 60 points. The suggested point totals for the homework and exam are 50 and 100.

Keys and rubrics are provided for the homework assignment and exam (in the file "assessment.zip" above). Suggested scores are given for all questions in the homework assignment and exam, but the instructor may choose to grade only selected questions or to assign different values. In particular, the instructor may choose to make the polar science-related questions worth extra credit.

## References and Resources

**Climate change videos (optional):**

- Climate Change: Lines of Evidence, from the National Academies of Science, Engineering and Medicine. Options include a 26 minute video or any of 7 videos of about 4 minutes each. To allow for varying levels of available class time, video content was ranked as follows, from most to least relevant:
- Chapter 1: From the 18 second mark to the 1 minute mark, Chapter 3, Chapter 5 (8 minutes total). - or -
- Chapters 1-5 (about 20 minutes).

- Climate Change in 60 Seconds from The Royal Society.
- Effect of climate change on hurricanes, by Vox, 3 minutes 22 seconds.

**References**

- R and RStudio: https://posit.co/download/rstudio-desktop/.
- Dahe, Q., Petit, J. R., Jouzel, J., & Stievenard, M. (1994). Distribution of stable isotopes in surface snow along the route of the 1990 International Trans-Antarctica Expedition.
*Journal of Glaciology*,*40*(134), 107-118. - References and resources contained within the presentations include figures from the literature and open-license images, which are attributed within the notebook.