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# A 4-Step Guide to Teaching Statistics to Science Majors

### William Gilliland, PhD

Associate Professor of Genetics, DePaul University in Chicago, IL

PhD in Population Biology, MS in Population Biology, BS in Biochemistry

For William Gilliland, PhD, it is as if teaching statistics to science students was always in the cards. “I didn’t take the subject until I was in grad school, but it was something I really enjoyed because I played a lot of Texas Hold ’Em,” he says. “Statistics helped me better understand how to calculate the odds.”

Today, as an associate professor at DePaul University’s College of Science and Health, Gilliland has found that the odds are not always in favor of students in his General Biology class taking to the subject quite so quickly. In fact, he noticed that many of the 120 incoming freshmen (all non-math majors) each quarter were only going through the motions of applying statistical reasoning. They did not really understand why they were following certain steps—or what the outcomes meant.

For example, Gilliland recalls asking students why they had chosen a particular test, and they answered that it was because the p-value was smaller. “They had no idea what a p-value meant,” he says. (It illustrates the likelihood of getting a certain result if your hypothesis is true.) “That’s a terrible reason to choose a statistical test, and it just belies a complete misunderstanding of the subject,” Gilliland says.

After considering what worked for him, Gilliland sought to put statistics into a context that would be more comprehensible for his students, in any of his classes. The result is a four-step approach based on analogies and familiar items (dice, coins, thermometers, and, of course, playing cards) that has resulted in immeasurable success.

## Context

“Much of the early work in statistics was done to address questions being raised for the first time by the new science of genetics, and many individuals (such as Sir Ronald Fisher) are known for their influences on both disciplines.”

— William Gilliland, PhD

Course: BIO 260 Genetics

Course description: Transmission of heritable traits, nature of genetic material, manner of its expression, its mutability, and its significance with respect to organismal and species variation.

## A four-step guide for teaching statistics to science majors

To help his science majors grasp statistical methods, Gilliland has created a process that takes students through four key steps to gradually build their understanding to a point at which they can apply their learnings. This approach begins with a theoretical explanation of randomness and genetics, moves on to the demonstration of odds using hands-on activities, makes statistical tables comprehensible with a simple analogy and then invites students to put everything to use in the lab. Here is what it looks like.

##### 1. Reinforce the connection to genetics

Gilliland lays the groundwork for statistical analysis by introducing (or reintroducing) Gregor Mendel, the scientist and Austrian monk best known for discovering the basic principles of heredity. Mendel’s training in mathematics and physics allowed him to make a second major contribution to science: He was one of the first people to recognize the importance of randomness.

“Genetics is the first science to talk about randomness, and Mendel was one of the first people to bring the idea of randomness to biology,” says Gilliland. “The science of statistics was developed in response to questions that geneticists were asking. And that combination of Mendelian genetics and Darwinian natural selection was a big moment.”

##### 2. Introduce physical examples of probability

Students’ first experience with a statistical test begins with Gilliland defining what “odds” are and using items from games (cards, dice, and coins) to show how to calculate odds for multiple events. (This is a simple way to start because, with things like a coin toss, the probabilities have been measured many times before, so the outcomes are predictable.)

“I try to do that mechanistically, and that’s why flipping coins is valuable,” says Gilliland. During his lectures, he passes out pennies and has students flip them, tracking their landing (heads or tails) in real time by using an iClicker. If a student gets heads, they press A. If they get tails, they press B.

“If we keep doing it, we start getting a bell curve,” he says. “Students get a chance to play around with this and see these numbers fall out when they apply the randomness over a large number of events. It’s amazing how good of a match you get, and it’s very impactful for students.”

Gilliland then connects the results of this activity to the randomization of genetics. “It’s what sets up the process for what we see in progeny,” he says. Essentially, organisms carry two copies of most genes—they received one copy each from their mother and father when they were conceived. When organisms reproduce, each gamete (eggs or sperm) get only one of those two copies. Because the chromosomes carrying the genes assort in a random mechanical fashion, “it’s the exact same randomness as with flipping a coin.”

##### 3. Make statistical tables comprehensible

Statistical tables can be difficult for non-math majors to comprehend, as they squeeze an enormous amount of information into a small amount of space. “Students look at the table and have no idea what they are doing,” Gilliland says.

However, students do understand what a thermometer is: It relates the temperature of its immediate surroundings to the height of liquid in a tube. “A thermometer is a standard curve relating the height of a liquid to temperature. A statistical table is the same,” says Gilliland. “It is a standard curve that relates the value of a calculation (the statistic) to the probability (the p-value) of having that calculation arise by chance.”

This is usually the aha! moment for students. “It puts numbers in a visual context by relating them to something else, and it gets students familiar with standard curves,” says Gilliland.

And, of course, a statistical test is asking a question—and different questions require different methods to answer them. “Often statistical tests are presented like magic spells you have to recite. I try and explain why you would do different tests. A chi-square test compares one data set to the outcomes predicted by your hypothesis. A t-test, on the other hand, compares two sets of data to each other, and asks if they have the same mean. Knowing what a tool does helps you reach for the correct one.”

##### 4. Connect it to work in the lab

“In the lab, students will get the data that we’re going to use with the statistics test,” says Gilliland, who notes that although students have had an opportunity to see these tests in action (during the exercises above), they still get guidance and feedback at the lab. “This is their chance to practice,” he says.

Of course, the lab experiments do not always work out perfectly: Some students will make mistakes (the same errors tend to crop up each quarter), perhaps choosing a chi-squared test over a t-test, but the study guide is there to help them get their heads around these concepts. “I want to help them see why they would do this test and not the other one,” he says.

“Statistics is important for practically every STEM field, and the skills students develop in my classes can be transferred to other subjects besides biology—or even just to let you do better at your weekly card game.”

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