# Confidence and sample size

AI answers vary between runs. Ask the same question twice and you can get two different
sets of brands. Every number Shruwd shows is therefore an estimate from a sample, and it
is shown with the range that sample supports.

## Reading the range

A result reads `32% (24–41%)`. That range is a 95% confidence interval.

The point estimate is the best single guess. The range is how much the sample constrains
it. Two results with the same middle can carry completely different weight:

| Result | What it supports |
|---|---|
| `32% (29–35%)` | A solid number. Act on it. |
| `32% (10–60%)` | Barely more than "somewhere in the middle". Wait for more data. |

Intervals narrow as responses accumulate. A prompt set measured for three months has
much tighter ranges than one measured for two weeks, with no change in your visibility.

## Why a number is sometimes withheld

Shruwd never displays a metric computed from fewer than **ten responses**. You get
**insufficient data** and a count of how many more runs are needed.

This is not an error, not a loading state, and not zero. It means the sample cannot
support a number yet, and printing one anyway would invite a decision the data does not
justify.

Where you will meet it:

- **Individual prompts** hit it often. Each prompt is asked three times per cycle, so a
  single prompt needs several weeks of cycles to clear ten responses.
- **Your whole prompt set** clears it immediately, because every prompt contributes.
- **Narrow filters** — one prompt, one engine, a short date range — can drop back below
  the floor. Widen the range or the selection.

## How the ranges are calculated

You do not need this to use the product, but it is here so the numbers can be checked.

**Rates** — mention rate, citation share, self-citation rate and the coverage rates — use
a **Wilson score interval**. These are proportions that sit near 0% or 100% more often
than not, exactly where the textbook normal approximation produces nonsense like a lower
bound below zero.

**Share of voice** uses a **percentile bootstrap** over 1,000 resamples instead. It is a
ratio where the same response feeds both the numerator and the denominator, so it is not
a simple proportion and a Wilson interval would misstate it.

The bootstrap's randomness is seeded per brand, entity, engine and day, so recomputing a
past day returns exactly the same interval. An interval that shifted every time the page
loaded would be worth nothing.

## Next steps

- [Methodology](https://shruwd.io/methodology) — why Shruwd works this way, on one page
- [When a number has moved](https://shruwd.io/docs/metrics/when-a-number-has-moved.md) — comparing two periods
- [Metric definitions](https://shruwd.io/docs/metrics/metric-definitions.md) — what each number counts