12-02 · Scientific interpretation: recap
Say what you want to compare
In the invented cress study, researchers choose pulse or mist watering for trays and count sprouts on day 10. Our question compares mist minus pulse in the chance that a seed sprouts. We give each of six sowing batches equal weight and set the tray difference to zero. These choices describe the quantity we want to estimate.
For another study, name the animals or groups researchers treated or followed, the outcome and units, the comparison direction, the time, and what you hold fixed or average over. A coefficient in a model table may describe a different comparison.
| Comparison | Cress example | Value if methods are equal |
|---|---|---|
| Difference | Mist chance minus pulse chance | 0 |
| Ratio | Mist chance divided by pulse chance | 1 |
| Percentage-point difference | Probability difference multiplied by 100 | 0 |
| Odds ratio | Ratio of the two methods’ odds; odds are chance of sprouting divided by chance of not sprouting | 1 |
For illustrative chances of 0.40 with pulse and 0.55 with mist, the difference is 15 percentage points, the ratio is 1.375, and the relative increase is 37.5%. These illustrative numbers are separate from the fitted lesson results.
Why the model has a tray term
Researchers count sprouts out of 25 seeds in each tray. All seeds in a tray share its watering and growing conditions. The binomial model describes a count out of a known number; the shared tray difference allows the chance of sprouting to vary among trays after allowing for watering and batch. This is called a tray random intercept. There is one count for each tray.
To answer our chosen question, set that tray difference to zero, predict the probability for each batch, and average those six probabilities equally. That is different from averaging over trays whose differences vary, and from averaging model log-odds before converting to probabilities. The model and target are teaching choices for this study, not defaults for your project.
Distinguish uncertainty from seed variation
A seed either sprouts or does not. An interval for its expected chance of sprouting describes uncertainty in that chance; it does not contain 95% of individual seeds. A future tray count also varies with tray conditions and the seed outcomes.
A narrow interval cannot repair biased measurements, related observations treated as unrelated, or an unfair treatment comparison. An interval crossing zero does not prove the two methods are equal. An interval excluding zero does not establish that a change is useful. Compare its size and uncertainty with a worthwhile change chosen before seeing the results. Our 15-percentage-point classroom threshold is hypothetical.
A 95% confidence procedure has its stated coverage over repeated studies under its assumptions. It does not assign a 95% probability to a fixed unknown effect inside this particular observed interval.
Write for a reader who has not seen your code
In the figure and caption, identify the comparison, units, day, interval, trays receiving each watering method, and invented data. In the paragraph, explain what researchers did, the model and estimate, practical meaning and one limitation. For your project, explain your own study before choosing a model and comparison.