When a gap is too big to be chance
- The idea
- Predict
- See it
- Why
- Check
The idea
“My results are off, but that's probably just chance or measurement error.”
Chance really does nudge results, and real crosses rarely hit their predicted ratio exactly. So blaming chance for odd data feels careful.
The short version
The mistake: My results are off, but that's probably just chance or measurement error.
What's actually true: Chance explains only small gaps, smaller as samples grow. A big gap in a big sample, or in every repeat, is almost surely real.
- Results scatter around the expected value, depending on which offspring you happen to count. That scatter is sampling error.
- It's biggest in small samples and shrinks as you count more. Count 4 times as many and it halves.
- Chance and random error push results up one time and down the next. A gap that points the same way in every repeat has a cause.
- A chi-square test checks a gap against chance at that sample size. For 260 purple of 400, chi-square is 36, far above the 3.84 cutoff, so you reject chance.
On the exam: Before you blame chance, check the sample size and whether the gap points the same way every time.