Module 6 Worksheet: Probability, Randomness, and Variation
Scenario
A short run of unusual results has prompted someone to conclude that something has changed.
Data
Dataset: repeated-trials-summary.csv
| trial_block | attempts | successes | observed_rate |
|---|---|---|---|
| B01 | 10 | 7 | 0.70 |
| B02 | 10 | 3 | 0.30 |
| B03 | 10 | 6 | 0.60 |
| B04 | 10 | 5 | 0.50 |
| B05 | 10 | 4 | 0.40 |
| B06 | 50 | 27 | 0.54 |
Your Task
Compare the 10-attempt blocks with the 100- and 200-attempt blocks.
Questions
- What rate would you expect over this many observations?
- How far from expectation is what actually happened?
- Could this have occurred with no change at all?
- What would make the claim more convincing?
- How many more observations would you want?
- What can be said now?
- What should not be said yet?
Write Your Conclusion
State what the run is consistent with, in both directions, and what you would do next.
Self-Check
- Did I work out the expected value first?
- Did I consider that ordinary variation explains this?
- Did I say what evidence would change my mind?
- Did I avoid declaring a change prematurely?