# `PtcRunner.Metrics.Statistics`
[🔗](https://github.com/andreasronge/ptc_runner/blob/main/lib/ptc_runner/metrics/statistics.ex#L1)

Statistical comparison functions for benchmark results.

Pure math — no external dependencies.

# `fisher_exact_p`

```elixir
@spec fisher_exact_p(
  non_neg_integer(),
  non_neg_integer(),
  non_neg_integer(),
  non_neg_integer()
) ::
  float()
```

Fisher exact test p-value for 2x2 contingency table (two-tailed).

Compares pass/fail counts between two variants.
Uses log-factorials to avoid overflow.

## Examples

    iex> p = PtcRunner.Metrics.Statistics.fisher_exact_p(5, 5, 5, 5)
    iex> p == 1.0
    true

# `sample_size_for_two_proportions`

```elixir
@spec sample_size_for_two_proportions(float(), float(), float(), float()) ::
  pos_integer()
```

Sample size per group for comparing two proportions.

Uses the standard formula for desired power and significance level.
Returns the number of observations needed per group.

## Examples

    iex> n = PtcRunner.Metrics.Statistics.sample_size_for_two_proportions(0.5, 0.6)
    iex> n
    388

# `wilson_interval`

```elixir
@spec wilson_interval(non_neg_integer(), pos_integer(), float()) :: {float(), float()}
```

Wilson score confidence interval for a proportion.

Returns `{lower, upper}` bounds. Uses z=1.96 for 95% confidence (default).

## Examples

    iex> {lower, upper} = PtcRunner.Metrics.Statistics.wilson_interval(7, 10)
    iex> is_float(lower) and is_float(upper)
    true

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*Consult [api-reference.md](api-reference.md) for complete listing*