Statistical Inference & Techniques

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?

A song presenting common hypothesis tests and the steps in doing them with lyrics by Jamie Tan Xin Yee, Joelyn Chong, Deston Tang, Christine Sia, Nellie Lee, Josiah Tan, and Lee Yi Yuan who were all students at Singapore Management University taught by Rosie Ching Ju Mae.  May be sung to the tune of "LOVE" by Bert Kaempfert and Milt Gabler and recorded by Nat King Cole in 1965.  The vocals and guitar soundtrack on the audio were done by Joelyn. Editing of the soundtrack was done by the entire student team.The song placed tied for second in the 2023 A-mu-sing competition (see associated publicity).

A song to discuss how a confidence interval made for a population parameter will be biased if the sample is biased (e.g. starting with a random sample of n=100 but then having individuals drop out one at a time based on a non-ignorable reason).  The song was written IN MARCH 2019 by Lawrence Lesser, The University of Texas at El Paso, and Dennis Pearl, Penn State University, using the mid-20th century recursive folk song "99 Bottles of Beer." The idea for the song came from an article by Donald Byrd of University of Indiana in the September 2010 issue of Math Horizons where he suggested using the song for various learning objectives in Mathematics Education.

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.