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Odds are Huskers will be selected for multiple COVID tests
Amy Goodburn was among a handful of Huskers who bucked the odds in spring 2021.
Through the first three weeks of the University of Nebraska–Lincoln’s random COVID-19 testing a year ago, Goodburn was one of 239 students, instructors and staff who were selected thrice. Goodburn’s “luck” was the talk of Zoom meetings and had the senior associate vice chancellor and dean of undergraduate education pondering other odds-shattering opportunities.
“I tweeted that I’m going to have to buy a lottery ticket,” said Goodburn, who co-led the committees that shaped the university’s COVID-19 response. “It’s a little weird receiving the (need to test) emails that I helped draft. But, truthfully, I don’t mind.
“I’m happy to continue doing my part to support the health and safety of our Husker community.”
The university has returned to a random mitigation testing model for the spring 2022 semester. The testing begins the week of Jan. 31 and Huskers were notified about their participation via email on Jan. 27. Moving forward, selection emails will be delivered every Thursday the week before testing should be completed.
As it turns out, any statistician, mathematician or researcher would (odds are) shrug at Goodburn’s three-time selection. They also weren’t entirely shocked if it extended for another week — maybe two.
“The university’s testing program uses a basic random sample, with the same pools and equal probability of an individual being selected each week,” said Judy Walker, associate vice chancellor and professor of mathematics. “When you work out the math, we would expect a certain number of repeat selections through at least the first few weeks.”
The weekly random COVID-19 testing selects 20% (one in five) from two pools — students and faculty/staff. That translates into a weekly random testing of some 5,000 Huskers. And, each of those individuals are returned to their respective pools before a random selection is made in each subsequent week.
As the probability of weekly selection remains steady at 20%, factoring the odds shifts to a (relatively) simple exponent formula of 0.20^(number of weeks). Odds of being selected in all of the first four weeks would be:
- Weeks 1-2: 0.20 x 0.20 = 0.04, or 4%, or 1 in 25;
- Weeks 1-3: 0.20 x 0.20 x 0.20 = 0.008, or 0.8%, or 1 in 125; and
- Weeks 1-4: 0.20 x 0.20 x 0.20 x 0.20 = 0.0016, or 0.16%, or 1 in 625.
When compared to the pool sizes, those odds translate into repeat selections of:
- Weeks 1-2: 800 students and 200 faculty/staff;
- Weeks 1-3: 160 students and 40 faculty/staff; and
- Weeks 1-4: 32 students and 8 faculty/staff.
“We could also expect one or two faculty and staff, and six or seven students selected through the first five weeks,” Walker said. “And, there will likely be one student who is selected the first six weeks in a row.”
The probability of being selected six consecutive weeks is .000064, or .0064%, or 1 in 15,625.
Overall, the probability that Huskers will be selected multiple times (but not consecutively) throughout the spring semester are high and should be expected.
