Chi-Square Visual Lab (AP Bio)
Enter observed counts and an expected ratio. The chart and table show where χ² comes from.
Inputs
Total N = 100
Categories
Chi-square critical values (right-tail)
| df | α = 0.10 | α = 0.05 | α = 0.01 |
|---|---|---|---|
| 1 | 2.706 | 3.841 | 6.635 |
| 2 | 4.605 | 5.991 | 9.210 |
| 3 | 6.251 | 7.815 | 11.345 |
| 4 | 7.779 | 9.488 | 13.277 |
| 5 | 9.236 | 11.070 | 15.086 |
| 6 | 10.645 | 12.592 | 16.812 |
AP tip: df = (# categories − 1). A small χ² means observed is close to expected.
Observed vs Expected
χ² Breakdown
χ² = 0.480
df = 1
p ≈ 0.488
Decision: Not enough evidence to conclude the result is different from chance (p = 0.488 ≥ α = 0.05).
Because the p-value (0.488) is greater than or equal to α (0.05), we cannot reject the null hypothesis — the result is consistent with chance.
| Category | Observed (O) | Expected (E) | (O−E)²/E |
|---|---|---|---|
| Purple | 72 | 75.00 | 0.120 |
| White | 28 | 25.00 | 0.360 |
Interpretation: Each category contributes a piece of χ². Big contributions show where your deviation is coming from.