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Statistics Content in Other AP Courses

Adam Shrager has taught AP Statistics at Hopewell Valley Central High School in Pennington, New Jersey for 19 years, and AP Psychology as well for the past three.  He has also taught courses in statistics and financial mathematics at Princeton University and the College of New Jersey for the past two decades.  He has presented joint AP Statistics/AP U.S. Government projects at the AP Annual forum, and has worked closely with AdvanceKentucky mentoring teachers and leading their annual mock AP Statistics exam scoring.  He is a long time AP Statistics Reader, Table Leader, and Question Leader – writing and refining the rubrics for select AP exam questions.  He was also the AP Stats Reading’s Social Director.


One phrase has been repeated to me again and again – in various forms - over 20 years of teaching AP Statistics and attending associated workshops, and 25 years as an adjunct college instructor, as well as throughout my Statistics education as an undergrad and graduate student: Statistics is a Science in the Service of Other Sciences.


A Science in Service of Other Sciences


As a high school teacher with a challenging and intense curriculum to get through, I often have to remind myself of this. The reason our students get such a kick out of AP Statistics is just that: our discipline is applied. We rarely walk into class and spend 40-60 minutes solving for x, or calculating a slope & a y-intercept, or resolving an integral. We might however spend nearly a week on interpreting that slope and that y-intercept across many different contexts. That’s damn cool! That’s ultimately both the hook and the genuine value of our course.


To truly broaden the reach of the course, we should look to other AP disciplines that require statistical insight. Many AP subjects leverage data analysis among their core skills. Often, their teachers get anxious, or perhaps even intimidated by this (such as when one of my students corrects the AP Biology teacher on an interpretation of a p-value: “That’s not how Mr. Shrager says it!”). Now, our school’s AP Biology teacher is a genuinely smart and passionate educator – whose students perform at the highest levels on the AP Biology exam and go on to many careers leveraging this content – it’s simply not her fault that her interpretation of a p-value may not meet the nuanced interpretation that I require in my classroom – and that of course, I literally develop over months in my classroom in the time leading up to the AP exam.


While AP Statistics teachers often look towards AP Biology – which heavily features Statistics content in the course and on the exam, there are other AP disciplines that feature questions that sound like they come from our AP Statistics Course and Exam Description (aka “the CED”).  AP Psychology, AP United States Government, and AP Environmental Science are three other disciplines that have required “data analysis” components – and feature concepts that are remarkably similar to content that an AP Statistics student should be comfortable applying. “Statistics is a Science in the Service of Other Sciences,” whether it’s Social Science, Psychology, Biology, or Environmental Science – have we considered working across the aisle with these teachers and questioning how we can add value to their classrooms? While there is never enough time to extensively and genuinely collaborate with our colleagues – simply learning what is covered in those disciplines can have a huge impact on what we do in our classrooms, as well as giving us the unique opportunity to work collaboratively and inter-collegially with our colleagues from other departments.  In truth – isn’t this the essence of higher-level learning?


Let’s very briefly explore the data analysis content on AP exams other than AP Statistics:  


AP Psychology: 


Descriptive Statistics, Correlation, and the basics of Statistical Inference are all featured in AP Psychology.  Interestingly, there is some slightly different vocabulary utilized in the course for statistics concepts that should be familiar to any AP Statistics student, but using terms specific to the study of Psychology – which leads to great class discussion (Did you know that Psychologists call a confounding variable the “third variable problem?” Now you do! Correctly describing how “lurking” variables, or “third variables,” or “confounding variables” impact experimental design on an AP Statistics FRQ is among the most difficult tasks for AP Statistics students. It is just as challenging for AP Psychology students!).


The AP Psychology exam has 100 multiple choice questions, and 2 Free Response Questions (FRQ). Not only are data analysis questions scattered throughout the Multiple Choice content (specifically 10-14% of the questions are focused on experimental design, research methods, data analysis, and ethics. AP Statistics emphasizes all of those topics except the ethical considerations in experimentation), but also of the 2 AP Psychology FRQ, one of them is uniquely focused on statistical content.  


In 2023, an FRQ asked AP Psychology students to interpret standard deviations from two different samples and compare them in context, then to interpret a (low) p-value that resulted from comparing the two independent means. In 2022, they interpreted a scatterplot displaying an obvious negative correlation, and critiqued a researcher’s conclusions about the scatterplot. Out of seven possible points, the mean score on this 2022 Statistics-themed AP Psychology FRQ was 2.45 (it was 3.06 on the other non statistics-based Psychology FRQ). Bluntly, a solid AP Statistics student should have been able to score a 4 or 5 on this FRQ, never having spent a day in an AP Psychology class – simply with a solid knowledge ofi correlation, regression, and “third variables,” and the willingness to write answers in context. In truth, it has been said over and over again by AP Psychology students, that those that have taken AP Statistics simply have an unfair advantage on the exam!


AP United States Government & Politics: 


Other than Psychology, which is often taught out of a high school’s social studies department (though some schools house it in the science department), we rarely think of other high school “social studies” courses as having broad statistical content. Yet, AP United States Government and Politics (aka “AP Gov’t”) has 4 FRQ, and question #2 is always “the Quantitative Analysis question”. AP Gov’t students are asked to analyze graphical displays of data (often voting data) and then relate their analysis to a question from the AP Gov’t curriculum. A 2021 four-part AP Gov’t FRQ used pie-charts and histograms to ask students to analyze voting trends before and after gerrymandering in Ohio, then culminated the question by asking how these interpretations of data could pose a challenge to representative democracy.  Simply, it was a beautiful example of Statistics in the Service of Other Sciences, in this case, Political Science!


AP Biology:


With confidence intervals and Chi-Square showing up frequently, the stats content throughout the AP Biology course is unmatched among other AP disciplines. Students have had to run entire chi-square tests (filling out tables showing observed and expected values) and interpret p-values and confidence intervals in context. With mandatory labs completed by all AP Biology students, the requirement to interpret data is consistent and wide-ranging. The AP Biology contains 8 FRQ, two “long” questions and 6 “short” questions. One of the two long questions is designated as the data analysis question – and will almost always feature some flavor of statistical inference.


One of the “go-to” statistics questions for teachers of AP Biology is Question #1 from the 2013 operational exam.   In this question, students had to answer questions about an experimental design, then run (with no more than a scientific calculator) an entire chi-square goodness of fit test (they posed a null hypothesis, then filled data into boxes into a pre-labeled table, and calculated the test statistics), finally interpreting their results.   Interestingly, after the new 2020 AP Biology CED was released, AP Biology students can now use graphing calculators on the exam.   While not all AP Biology teachers may be familiar with the extensive statistics functionality on most graphing calculators, our students sure are!


Finally, teaching in the Northeast, we commonly assign summer work in AP classes (we don’t meet our students until sometimes a week after Labor Day – Summer work is simply necessary if we hope to complete the AP curriculum by early May). Last May, I worked with this wonderful AP Biology teacher to rework her summer assignment to give her students a good onramp for some of the basic statistics content they would be facing this year. The material?  I used AP Stats resources, of course!


AP Environmental Science:


While the material covered is not as statistically intense or sophisticated as AP Biology, AP Environmental Science (“APES”) is broken down into nine units broadly covering environment content topics, but all framed by a series of “Science Practices,” which includes “Visual Representations, Scientific Experiments, Data Analysis, and Mathematical Routines,” among others. APES has threaded data analysis throughout the course, and students have been asked to calculate and project energy resources & consumption and rates of aquatic and terrestrial pollution. APES students with a Statistics background consistently find themselves at a significant advantage in approaching these complicated problems.  Each APES exam has three FRQ, and question #1 is (you guessed it!) always the data analysis and experimental design question.


On one of the 2023 APES exams (there are two sets of operational questions), students had to identify elements of an experimental design (control group, hypothesis being tested, et al) then considering the output on a two-way table (two categorical variables), describe the apparent difference between variables and whether this difference supports the hypothesis.  While the APES students are not running a formal inference procedure (like their cousins in AP Biology), they are still drawing conclusions from observed differences in data.  On the other 2023 APES exam, students considered a bar chart comparing different restoration methods of plant life in forests.  The students needed to interpret the chart well enough to calculate an appropriate measure of center, describe an apparent relationship observed over time in the graphical display, and then use the data to make a claim that either supports or refutes a presented claim about “plant and animal restoration.”  While the subject matter may not be familiar to one who has not taken the class (and I certainly can’t claim any expertise in this particular branch of science), the skill-sets required is one that I would expect every one of my AP Statistics students to have mastered.    

 

Other AP Subjects:


While this post only briefly considers these four AP Subjects that significantly leverage Statistics and Data Analysis in their content areas, there are others:  AP Microeconomics and Macroeconomics, AP Research & AP Seminar, and AP Comparative Government all include some required facets of Data Analysis among their content.


Remember, specific AP FRQ (exam questions) and other subject’s CEDs, are all freely available on AP Central ( https://apcentral.collegeboard.org/ ). I have had a lot of fun looking particularly at old AP Psychology FRQ questions, and of course, AP Biology is a goldmine of Statistics content. Additionally, calculator policies (which changed for some subjects in their relatively recent updated CED update, including Biology and Environmental Science, which now allows use of the graphing calculator throughout) are easily accessible and worthwhile for the AP Statistics teacher to be made aware of.   Many AP teachers outside of our discipline are not comfortable with statistics functionality on the graphing calculator – yet if their students have been in your class – then THEY certainly know what they are doing!    (https://apstudents.collegeboard.org/exam-policies-guidelines/calculator-policies)


I hope you are motivated to see what is going on statistically among other disciplines – contribute to their classes, and work collaboratively with your colleagues. It took years to get there, but it is now part of the culture in our school among these classes. I hope you can make some headway in this direction as well – and while challenging, make your Statistics class one that is robust and dynamic, and can also function in the service of others.   


Spreadsheet of AP Exam FRQs with Stats Content


 

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