Observed counts and association
Source: Simulated teaching data (draw 941). This analysis uses 160 of 160 rows; Excluded rows: 0 (unselected groups or missing/invalid selected values).
Inspect input rows
First 12 rows (before exclusions)
| group | event |
|---|---|
| Control | 0 |
| Control | 0 |
| Control | 0 |
| Control | 1 |
| Control | 0 |
| Control | 1 |
| Control | 0 |
| Control | 0 |
| Control | 0 |
| Control | 0 |
| Control | 0 |
| Control | 1 |
χ²(1, N = 160) = 9.14, p = .002.
Observed counts
| Group | 1 | 0 | Total |
|---|---|---|---|
| Control | 26 | 54 | 80 |
| Intervention | 45 | 35 | 80 |
Inspect expected counts under independence
Expected counts
| Group | 1 | 0 |
|---|---|---|
| Control | 35.50 | 44.50 |
| Intervention | 35.50 | 44.50 |
Group A is Control; group B is Intervention. The event is “1”. Effects compare B with A. Risk and odds estimates use the observed counts.
95% intervals for event risks and effects
| Quantity | Estimate | Lower | Upper |
|---|---|---|---|
| Risk: Control | 0.33 | 0.23 | 0.43 |
| Risk: Intervention | 0.56 | 0.45 | 0.67 |
| Risk difference (B − A) | 0.24 | 0.08 | 0.38 |
| Risk ratio (B / A) | 1.73 | 1.20 | 2.51 |
| Odds ratio (B / A) | 2.67 | 1.40 | 5.08 |
Risk intervals use Wilson’s method; the difference uses Newcombe’s method. Ratio intervals use an approximate log-normal method. A zero cell may make a ratio unavailable. An odds ratio is not a risk ratio.
Horizontal: 1 = Control; 2 = Intervention. Vertical: Event probability.
- Control
- Intervention
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Try this: Reverse the event category. Which probabilities and ratios change?
Explain what happens
Each event probability becomes its complement. The odds ratio becomes its reciprocal. The independence tests remain the same because relabeling does not change the association.
Assumptions and method
Observations must be independent, categories mutually exclusive, and counts actual observations. These calculations do not handle paired binary data, clustered observations, survey weights, or time-to-event data.
Read the method reference