# Resource Library

#### Statistical Topic

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• ### Cartoon: Brass Ring

A cartoon that can be used to discuss the multiple testing issue and the concept of p-hacking. The cartoon was used in the June 2021 CAUSE cartoon caption contest and the winning caption was written by Jim Alloway from EMSQ Associates. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

• ### Cartoon: Fruit Stand

A cartoon that can be used to discuss the importance of using a paired analysis to reduce the variability in the response for a heterogeneous population. The cartoon was used in the February 2021 CAUSE cartoon caption contest and the winning caption was written by Jeremy Case from Taylor University.. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

• ### Poem: Type Two

A poem about type II errors in diagnostic testing using a diabetes test context.  The poem was written by Lawrence Lesser from The University of Texas at El Paso and received an honorable mention in the non-song category of the 2023 A-mu-sing Competition.  The author also provided the following outline for a lesson plan:

Some sample questions (one per stanza) students can explore or discuss
as a practical application of statistics to a prevalent disease
that likely affects (or will) a friend or relative of almost everyone.

First stanza: Look up history of diabetes prevalence to explore questions such as: Is “1 in 10” roughly accurate for the United States and how does that compare to other countries? Was the 2003 lowering of the threshold for a prediabetes diagnosis based on updated medical understanding of the disease or more of a policy decision to give an “earlier warning”?

Second stanza: How does a hypothesis testing framework apply to an oral glucose tolerance test (OGTT)? It’s warned that a false positive is possible if the patient did not eat at least 150g of carbohydrates for each of the 3 days before the test. (This is likely what happened to the poet, whose diagnosis was overturned just 2 months later by an endocrinologist.)

Third stanza: Given the usual trend that the null hypothesis usually means no effect, no difference, nothing special, explain whether it seems consistent that a normality test such as Anderson-Darling would let normality be the null. When might it make sense for a doctor to view having a particular disease as the null hypothesis (and what would be the Type I and Type II errors?)?

Fourth stanza: Explain how having only a few individual values each day from a blood glucose meter (BGM) risks missing dangerously high variability of glucose (students can Google how high variability can be a risk factor for hypoglycemia and diabetes complications). Discuss how output from a Continuous Glucose Monitor (CGM) that records values every 5 minutes can be used to check, for example, that the coefficient of variation is sufficiently low (e.g., < 36%) and that “time in range” (e.g., 70-180 or 70-140 mg/dL) is sufficiently high. Example output is on page S86 of https://diabetesjournals.org/care/issue/45/Supplement_1.

Fifth stanza: Have students look up current FDA guidelines on how accurate over-the-counter BGM readings need to be (e.g., https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7753858/) and have them connect this to margin of error, confidence intervals, etc.

Sixth stanza: Find online the diabetes “plate method” of taking a circular plate (9” in diameter) for a meal where half of the plate would have non-starchy vegetables, a quarter having lean protein, and a quarter with carbohydrate foods such as whole grains. How do this breakdown and total quantity compare to a pie chart of a typical meal that you (or typical college undergraduates) eat?

• ### Poem: Significance

This limerick was written in April 2021 by Larry Lesser of The University of Texas at El Paso to be used as a vehicle for​ discussing the issues and pitfalls of using .05 as a bright-line threshold for declaring statistical significance, in light of ASA recommendations.  The poe was also published in the June 2021 AmStat News.

• ### Song: Point-oh-five

A song to aid in the discussion of the meaning and interpretation of p-values and type I errors. The song's lyrics were written in 2017 by Lawrence Lesser from The University of Texas at El Paso and may be sung to the tune of the 1977 Bee Gees Grammy winning hit "Stayin' Alive." The audio recording was produced by Nicolas Acedo with vocals by Erika Araujo, both students in the Commercial Music Program at The University of Texas at El Paso.

• ### Song: When I'm Point Oh-Four

A song satirizing the use of fixed significance level hypothesis testing.  The song was written by Dennis K Pearl from Penn State University.  Lyrics may be sung to the tune of the Beatles 1967 hit "When I'm Sixty-Four." (Paul McCartney wrote the song in 1958).  The audio recording was produced by Nicolas Acedo with vocals by Alejandra Nunez Vargas, both students in the Commercial Music Program at The University of Texas at El Paso.

• ### Song: Simulation!

A song to introduce the basic idea of using simulation to calculate a P-value for a randomization test (by simulating lots of group assignments and seeing what proportion of them give more extreme test statistics than observed with the actual group assignments).  The lyrics were written in November 2018 by Larry Lesser from The University of Texas at El Paso and Dennis Pearl from Penn State University. May be sung to the tune of the 1980 number #1 song “Celebration” by Kool and the Gang. Audio of the parody was produced and sung by students in the commercial music program of The University of Teas at El Paso.

• ### Using Statistics Effectively in Mathematics Education Research

Funded by the National Science Foundation, workshops were held over a three-year period, each with about twenty participants nearly equally divided between mathematics educators and statisticians. In these exchanges the mathematics educators presented honest assessments of the status of mathematics education research (both its strengths and its weaknesses), and the statisticians provided insights into modern statistical methods that could be more widely used in such research. The discussions led to an outline of guidelines for evaluating and reporting mathematics education research, which were molded into the current report. The purpose of the reporting guidelines is to foster the development of a stronger foundation of research in mathematics education, one that will be scientific, cumulative, interconnected, and intertwined with teaching practice. The guidelines are built around a model involving five key components of a high-quality research program: generating ideas, framing those ideas in a research setting, examining the research questions in small studies, generalizing the results in larger and more refined studies, and extending the results over time and location. Any single research project may have only one or two of these components, but such projects should link to others so that a viable research program that will be interconnected and cumulative can be identified and used to effect improvements in both teaching practice and future research. The guidelines provide details that are essential for these linkages to occur. Three appendices provide background material dealing with (a) a model for research in mathematics education in light of a medical model for clinical trials; (b) technical issues of measurement, unit of randomization, experiments vs. observations, and gain scores as they relate to scientifically based research; and (c) critical areas for cooperation between statistics and mathematics education research, including qualitative vs. quantitative research, educating graduate students and keeping mathematics education faculty current in education research, statistics practices and methodologies, and building partnerships and collaboratives.

• ### Song: Every Assumption You Make

A song about the different assumptions needed for parametric statistical methods and the importance of checking how well they hold and what effect they may have on the results and conclusions. The lyrics were written in 2017 by Dennis K. Pearl from Penn State University and may be sung to the tune of "Every Breath You Take" written by Sting and made popular by The Police on their 1983 album "Synchronicity." Audio of the parody was produced and sung by students in the commercial music program of The University of Teas at El Paso.

• ### Poem: Hypothesis Testing

This limerick was written by Dr. Nyaradzo Mvududu of the Seattle Pacific University School of Education. The poem was given an honorable mention in the 2007 A-Mu-sing competition.