← Back to course
Data and Society 9-12 / Week 10 / Thursday
4/6
Week 10 · Models and Simulations

Thursday

Test and refine
// Can a simple model predict what will happen next?
⏱ about 20 min

Thursday: Test and Refine

Comet's tally sheet from Count Lab shows 11 arrivals. Wren's log still says 18.

"Maybe I rolled wrong," Comet says. "Let's roll again."

Wren taps the log. "What do you notice? Every run of our rule lands near 12, and the trial bench got 18."

"So the dice are fine," Comet says slowly. "The rule is what is off."

Nova hovers between the sheet and the log. "Would you like a hint?" she asks. "Turn your rule into a hypothesis. Then test it, the way a scientist would."

Comet pulls the pencil from behind her ear. "Data analyst, help me write the hypothesis."

Hypothesis, test, refine

A hypothesis is an idea you can test. The first rule's hypothesis is: about one slot in three has an arrival.

Simulations help people form hypotheses and refine them.

Wren's log is the test. It shows 18 arrivals in 36 slots, which is one slot in two.

When a prediction and a test disagree, you refine the model and test it again.

Model version (made-up runs from the Commons Count story)Faces that mean an arrivalExpected in 36 slotsThe crew's runWren's log
First rule1 or 2 (two faces of six)about 121118
Refined rule1, 2 or 3 (three faces of six)about 181718
REFINE THE RULE
  • Read the question.
  • Tap your answer.
In Wren's log, what fraction of the 36 slots had an arrival?
Which faces mean an arrival in the refined rule?
About how many arrivals does the refined rule expect in 36 slots?
The crew's refined run gave 17. How far is that from the log?

More and better data

The amount, quality and variety of data affect how good a model is.

Wren's log covers one Saturday at one trial bench. A model built on one day may not fit a quiet weekday morning.

Logging more days, at different times, would give the model more data, and more varied data, to test against.

StatementTrue or false?
A model is checked by testing its predictions.?
If one test disagrees, you should throw the whole model away.?
Data from more days could make the model better.?
A log from one Saturday is enough to predict every weekday morning.?
WHY THIS EXERCISETesting and refining is how a rough model becomes a useful one.
THE TEST AND REFINE CYCLE
  • ?State a hypothesis.
  • ?Make a prediction from the model.
  • ?Compare the prediction with the observed log.
  • ?Change the rule if they disagree.
  • ?Run the model again and compare.
WHY THIS EXERCISEThis cycle is how models and simulations help test and refine hypotheses.
An idea you can test is called a ____.
Changing a model after a test, to make it better, is called ____ it.
Try it
Run the refined rule for one hour: roll 6 times, and count each 1, 2 or 3 as an arrival.
The refined rule expects about 3 arrivals in 6 slots. How close did you get?
On paper, draw three bars side by side: the first rule's 12, the refined rule's 18 and Wren's log of 18. Start at 0.

Excellent scientific thinking. Tomorrow is Impact Friday: models that decide things about people.

← Wednesday