# Personal baseline choice: methods and claim sheet

## Evidence label

Reproducible methods note with one constructed six-session example and an
exact calculation under a stated normal, independent, no-change model. This is
not participant research, a population simulation, an Altamens telemetry
analysis or evidence that any training changes cognition.

## Worked sequence

The six constructed session scores are `85, 102, 98, 101, 99, 105`. Session 6
is compared with the first session, the mean of sessions 1–3 and the mean of
sessions 1–5. The resulting apparent changes are +20, +10 and +8 points.
The sequence was chosen for transparent arithmetic, not to imitate a person.

## No-change model

Let every comparable session score be independent and normally distributed
around the same fixed level with standard deviation sigma = 10 points. For a
baseline that averages n sessions and one independent future score, the
standard deviation of the difference is:

`sigma_change = sigma * sqrt(1 + 1/n)`

The one-sided probability of an apparent gain at least t is:

`0.5 * erfc(t / (sigma_change * sqrt(2)))`

The published table reports t = 10 and 15 points for n = 1, 3 and 5. These are
model outputs, not false-positive rates for an Altamens game. Real sessions
can be correlated, heteroscedastic, non-normal and affected by task familiarity,
strategy, fatigue, item mix, device or version changes.

## Reproduction

Requires Python 3.10+ and only the standard library:

```bash
python3 calculate.py
```

The script asserts every displayed value and rewrites `examples.csv`.

## Claim boundaries

- Averaging more independent baseline sessions reduces baseline sampling noise
  under the model; it does not remove uncertainty from the future score.
- A longer baseline can mix early practice effects with later performance. More
  sessions are not automatically more valid.
- A descriptive change score does not identify learning, retention, transfer,
  impairment or a meaningful individual change threshold.
- No customer, account, analytics, device or game telemetry was accessed.
- Literature search, drafting, calculations and publication preparation used
  an OpenAI automated assistant. There was no independent human methods review
  and no journal peer review.