# 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

### Possible Assessments

1. Ask students to write a definition of the meaning of random as it is used in statistics.
2. 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.