# Zebra Hat

### Research on Student Learning about Random

#### Did you know....?

Before a statistics course, the definitions for *random* given most often by undergraduate students are:

- An occurrence that has no definite aim or purpose, unplanned, haphazard, spontaneous, different
- Selecting without prior knowledge, criteria or agenda, or choosing blindly with not particular method

Students write sentences such as,

- What a random time for it to rain
- His question was random and had nothing to do with the topic.

After a statistics class, when students are asked to provide the statistical meaning for *random* the most common definitions given are:

- When things are chosen without order, reason and/or pattern
- A process that creates a sample that is unbiased or representative of the population

Students rarely mention probability explicitly, though about 8% write that everyone had an equal chance of being selected for the sample and the same number indicate that a random sample was one selected by chance.

### Zebra and Hat Images

Use the images to contrast the colloquial and statistical meanings of the word *random*.

Random Zebras on a street in Shanghai |
Random Hat for drawing samples |

### Slides to enact a Hat vs Zebra Activity

### Possible Assessments

- Ask students to write a definition of the meaning of random as it is used in statistics.
- Ask students to describe a method of taking a random sample. For example, "How would you select a random sample of gas stations in our county?" or "How would take a random sample of all athletes who started college at our university?"

### Results from Classroom Testing

More than 10% of students exposed to the zebra vs. hat mnemonic image mentioned probability explicitly when defining *random* at the end of the semester. These students were also 5 times more likely than other students to say that everyone had an equally likely chance of being chosen in a random sample and twice as likely to say a random selection is one done by chance. More than 30% of the students mentioned a chance agent, such as a hat or dice, in their writing about randomness.

The percent of students who gave a valid statistical response to the question, "Describe how to take a random sample of 100 athletes who started college at our university in the last 40 years" went from 43% in a class that did not experience the zebra vs hat mnemonic image to 78% in a class that did.

### Further Reading

- Lecoutre M.-P., Rovira K., Lecoutre, B., & Poitevineau J. (2006). People’s intuitions about randomness and probability: an empirical study. Statistics Education Research Journal, 5(1), 20–35.
- Falk, R. (1991). Randomness – an ill-defined but much needed concept.
*Journal of Behavioral Decision Making*,*4*(3), 215–218. - Kaplan, J.J., Rogness, N. & Fisher, D. (2014). Exploiting Lexical Ambiguity to Help Students Understand the Meaning of
*Random*.*Statistics Education Research Journal, 22*(1)*.* - Wagenaar, W. (1991). Randomness and randomizers: Maybe the problem is not so big.
*Journal of Behavioral Decision Making*,*4*(3), 220-222.