estimation op• Data kinds: signal × signal → table
• Call: import fullseye as fs; fs.ledger.stat_ttest_paired(x, y) -> 'dict' (to call the implementation directly, import mathestimation; mathestimation.stat_ttest_paired(x, y) -> 'dict'; from the registry, opsmath.get("stat_ttest_paired"))
> This operator's description has not been translated yet. The original text follows as it is.
対応のある t 検定: 同じ対象を 2 回測った差 d = x − y の平均が 0 か。
t = mean(d) / (sd(d)/√n)、自由度 n−1、両側の p 値。返り値 `{"t", "df", "p", "mean_diff"}`。
Every mathops op validates its input before computing (nothing slips through silently):
• **complex input raises ValueError** — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• **masked arrays with masked elements raise ValueError** — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• **NaN/Inf raises ValueError on every input** (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• (none yet)
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
estimation)assign_hungarian · hist_distance · stat_ttest_welch · stat_ks_test · stat_chi2_gof · crlb_gaussian · kalman_smooth · mat_expm
*Provenance: mathestimation.py — MATH operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.