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ThearchyHelios
180 lines
12 KiB
Python
180 lines
12 KiB
Python
"""差异检验（app/analysis/differ.py，细案 01 §5）：比率小样本走 Fisher、均值 Welch、Holm、rows 敏感性翻转。每个用例都顺带核对
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复算和运行逐字段相同。"""
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from __future__ import annotations
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import math
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from fractions import Fraction
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import pytest
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from app.analysis import stats
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from tests.analysis_samples import analyze, call_error, snap
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RATE_SQL = "SELECT region, SUM(refund_flag) AS refunds, COUNT(*) AS orders FROM orders GROUP BY region"
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def rates(rows):
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return snap("Q1", RATE_SQL, ["region", "refunds", "orders"], rows)
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async def rate(rows, **params):
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params = {"query": "Q1", "by": "region", "numerator": "refunds", "denominator": "orders", "label": "退款率", **params}
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return await analyze("differ", "rate", snaps=[rates(rows)], **params)
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async def test_small_samples_use_fisher_and_say_it_may_be_noise():
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result = await rate([["西南", 2, 40], ["华东", 5, 230]])
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assert result["method"] == "differ.rate@1"
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assert result["verdict"] == {"code": "no_evidence", "subjects": [["西南"], ["华东"]], "direction": None}
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assert result["values"]["test"] == "fisher" and result["values"]["n_a"] == "40" and result["values"]["n_b"] == "230"
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assert Fraction(result["values"]["p"]) == pytest.approx(stats.fisher_exact(2, 38, 5, 225), rel=1e-9)
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assert result["phrase"] == ("西南和华东的退款率差异可能只是样本波动（样本量 40、230）；样本少（有格子的期望频数不到 5），"
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"用了精确检验")
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assert "p 值" not in result["phrase"] and "显著" not in result["phrase"]
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assert result["settings"] == {"differ_alpha": 0.05, "min_expected": 5}
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async def test_large_samples_use_the_pooled_z_test():
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result = await rate([["西南", 80, 1000], ["华东", 40, 1000]])
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assert result["verdict"] == {"code": "differs", "subjects": [["西南"], ["华东"]], "direction": "up"}
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z, p = stats.pooled_z(80, 1000, 40, 1000)
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assert Fraction(result["values"]["p"]) == pytest.approx(p, rel=1e-9) and result["values"]["test"] == "z"
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low, high = stats.newcombe(80, 1000, 40, 1000)
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assert Fraction(result["values"]["ci_lo"]) == pytest.approx(low, rel=1e-9)
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assert result["values"]["a"] == "0.08" and result["values"]["diff"] == "0.04"
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assert result["phrase"] == "西南的退款率（8.0%）高于华东（4.0%），差异站得住"
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lower = await rate([["西南", 80, 1000], ["华东", 40, 1000]], pairs=[["华东", "西南"]])
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assert lower["verdict"]["direction"] == "down" and lower["phrase"].startswith("华东的退款率（4.0%）低于西南（8.0%）")
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async def test_several_groups_each_against_the_rest_with_holm():
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rows = [["西南", 80, 1000], ["华东", 40, 1000], ["华南", 42, 1000], ["华北", 38, 1000]]
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result = await rate(rows)
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table = result["table"]
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assert [r[0] for r in table["rows"]] == ["西南", "华东", "华南", "华北"]
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assert table["rows"][0][1] == "其余各地区"
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# 对照组那一列有「其余各地区」这样的叫法：写 text；没记类型的分组列（组那一列）不写
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assert table["column_types"]["b"] == "text" and "a" not in table["column_types"]
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assert table["column_types"]["p"] == "number" and table["column_types"]["test"] == "text"
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raw = [Fraction(r[10]) for r in table["rows"]]
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adjusted = [Fraction(r[11]) for r in table["rows"]]
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assert all(a >= p for a, p in zip(adjusted, raw))
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assert adjusted == pytest.approx(stats.holm([float(p) for p in raw]), rel=1e-9)
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assert result["verdict"]["code"] == "differs" and result["verdict"]["subjects"] == [["西南"], ["其余各地区"]]
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assert any(c["code"] == "multiple_comparisons" and c["text"] == "比了 4 对，已按次数校正" for c in result["caveats"])
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assert result["phrase"] == "比了 4 对，1 对差异站得住：西南的退款率（8.0%）高于其余各地区（4.0%）"
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ref = await rate(rows, reference="华东")
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assert [r[0] for r in ref["table"]["rows"]] == ["西南", "华南", "华北"] and ref["params"]["reference"] == "华东"
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async def test_rate_call_errors():
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assert (await call_error("differ", "rate", snaps=[rates([["西南", 5, 4], ["华东", 1, 9]])], query="Q1", by="region",
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numerator="refunds", denominator="orders")).code == "not_count"
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assert (await call_error("differ", "rate", snaps=[rates([["西南", 1.5, 4], ["华东", 1, 9]])], query="Q1",
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by="region", numerator="refunds", denominator="orders")).code == "not_count"
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unknown = await call_error("differ", "rate", snaps=[rates([["西南", 1, 4], ["华东", 1, 9]])], query="Q1",
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by="region", numerator="refunds", denominator="orders", pairs=[["西南", "东北"]])
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assert unknown.code == "unknown_group" and "西南、华东" in unknown.message
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dup = await call_error("differ", "rate", snaps=[rates([["西南", 1, 4], ["西南", 1, 9]])], query="Q1", by="region",
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numerator="refunds", denominator="orders")
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assert dup.code == "duplicate_rows"
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async def test_means_from_sums_and_squares_use_welch():
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sql = "SELECT channel, SUM(amount) AS s, SUM(amount * amount) AS ss, COUNT(*) AS n FROM orders GROUP BY channel"
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rows = [["线上", 5000, 300000, 100], ["线下", 4000, 200000, 100]]
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result = await analyze("differ", "mean", snaps=[snap("Q1", sql, ["channel", "s", "ss", "n"], rows)], query="Q1",
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by="channel", sum="s", sumsq="ss", n="n", label="客单价")
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va = (300000 - 5000 ** 2 / 100) / 99
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vb = (200000 - 4000 ** 2 / 100) / 99
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expected = stats.welch(50, va, 100, 40, vb, 100)
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assert Fraction(result["values"]["p"]) == pytest.approx(expected.p, rel=1e-9)
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assert result["verdict"]["code"] == "differs" and result["values"]["test"] == "welch"
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assert result["phrase"] == "线上的客单价（50）高于线下（40），差异站得住"
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assert result["method"] == "differ.welch@1" and result["settings"] == {"differ_alpha": 0.05, "min_n": 30}
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async def test_means_from_mean_sd_and_n_and_small_samples():
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sql = "SELECT channel, avg_amount, sd_amount, n FROM channel_stats"
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rows = [["线上", 52, 12, 12], ["线下", 50, 11, 400]]
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result = await analyze("differ", "mean", snaps=[snap("Q1", sql, ["channel", "avg_amount", "sd_amount", "n"], rows)],
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query="Q1", by="channel", mean="avg_amount", sd="sd_amount", n="n", label="客单价")
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assert result["verdict"]["code"] == "no_evidence"
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note = next(c for c in result["caveats"] if c["code"] == "small_sample")
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assert note["text"] == "有一组的样本数不到 30（线上 12），结论不稳"
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assert result["phrase"].startswith("线上和线下的客单价差异可能只是样本波动（样本量 12、400）")
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async def test_rows_mode_flags_a_single_value_that_flips_the_verdict():
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base = [["线下", v] for v in [40, 60] * 200]
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online = [["线上", f"{v:.1f}"] for v in [41.3, 61.3] * 200]
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online[-1] = ["线上", "231.3"]
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s = snap("Q1", "SELECT channel, amount FROM orders", ["channel", "amount"], online + base)
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result = await analyze("differ", "rows", snaps=[s], query="Q1", by="channel", value="amount", label="客单价")
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assert result["method"] == "differ.welch_rows@1"
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assert result["verdict"]["code"] == "differs"
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note = next(c for c in result["caveats"] if c["code"] == "outlier_sensitive")
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assert note["text"] == "去掉最大的一笔后，差异不再站得住"
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assert note["text"] in result["phrase"]
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hidden = [["线上", 50 + (i % 7)] for i in range(30)] + [["线下", 48 + (i % 5)] for i in range(30)] + [["线上", 400]]
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s = snap("Q1", "SELECT channel, amount FROM orders", ["channel", "amount"], hidden)
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flipped = await analyze("differ", "rows", snaps=[s], query="Q1", by="channel", value="amount", label="客单价")
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assert flipped["verdict"]["code"] == "no_evidence"
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assert any(c["text"] == "去掉最大的一笔后，差异变得站得住" for c in flipped["caveats"])
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async def test_two_periods_of_the_same_group():
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sql = "SELECT week, SUM(refund_flag) AS refunds, COUNT(*) AS orders FROM orders WHERE region = '西南' GROUP BY week"
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s = snap("Q1", sql, ["week", "refunds", "orders"], [["W41", 30, 1000], ["W42", 60, 1000], ["W40", 31, 1000]])
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result = await analyze("differ", "rate", snaps=[s], query="Q1", period="week", base="W41", target="W42",
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numerator="refunds", denominator="orders", label="退款率")
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assert result["verdict"] == {"code": "differs", "subjects": [["W42"], ["W41"]], "direction": "up"}
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assert result["inputs"][0]["rows"] == [0, 1]
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assert result["phrase"] == "W42 的退款率（6.0%）高于 W41（3.0%），差异站得住"
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async def test_a_group_with_one_value_cannot_be_tested():
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s = snap("Q1", "SELECT channel, amount FROM orders", ["channel", "amount"], [["线上", 5], ["线下", 4], ["线下", 6]])
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result = await analyze("differ", "rows", snaps=[s], query="Q1", by="channel", value="amount")
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assert result["status"] == "refused" and result["reason_code"] == "untestable"
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assert result["reason"] == "线上只有 1 个样本，算不了差异"
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assert result["phrase"] == "差异检验没有做成：线上只有 1 个样本，算不了差异"
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async def test_no_pair_with_a_p_value_is_refused_not_said_to_be_noise():
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sql = "SELECT region, AVG(amount) AS m, 0 AS sd, COUNT(*) AS n FROM orders GROUP BY 1"
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means = snap("Q1", sql, ["region", "m", "sd", "n"], [["华东", 120, 0, 1], ["华南", 80, 0, 1]])
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mean = await analyze("differ", "mean", snaps=[means], query="Q1", by="region", mean="m", sd="sd", n="n",
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label="客单价")
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assert mean["reason_code"] == "untestable" and mean["reason"] == "华东只有 1 个样本、华南只有 1 个样本，算不了差异"
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assert mean["verdict"] is None and mean["settings"] == {"differ_alpha": 0.05, "min_n": 30}
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rows = snap("Q2", "SELECT region, amount FROM orders", ["region", "amount"], [["华东", 120], ["华南", 80]])
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one = await analyze("differ", "rows", snaps=[rows], query="Q2", by="region", value="amount")
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assert one["reason"] == "华东只有 1 个样本、华南只有 1 个样本，算不了差异"
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zero = await rate([["华东", 0, 0], ["华南", 3, 10]])
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assert zero["reason_code"] == "untestable" and zero["reason"] == "华东的样本量为 0，算不了差异"
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async def test_pairs_without_a_p_value_are_named_and_not_counted():
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result = await rate([["西南", 80, 1000], ["华东", 40, 1000], ["华北", 0, 0]])
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rows = {r[0]: r for r in result["table"]["rows"]}
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assert rows["华北"][-1] == "华北的样本量为 0，算不了" and rows["华北"][10] is None
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note = next(c for c in result["caveats"] if c["code"] == "untested")
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assert note["text"] == "另有 1 对算不了（华北的样本量为 0）"
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# 华北一单都没有：西南的其余合计就是华东，两对都站得住；华北那一对不算进「比了几对」
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assert result["phrase"] == ("比了 2 对，2 对差异站得住：西南的退款率（8.0%）高于其余各地区（4.0%）；华东的退款率（4.0%）"
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"低于其余各地区（8.0%）；另有 1 对算不了（华北的样本量为 0）")
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assert {"code": "multiple_comparisons", "text": "比了 2 对，已按次数校正"} in result["caveats"]
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async def test_the_outlier_is_looked_for_in_the_real_groups_not_in_the_pooled_rest():
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# 三组各和其余合计比：最远的那一笔在第二组（华南）。只在真实的各组里找、由各组重建「其余」合计，去掉它以后华南高出来就站得住
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base = [10, 11, 9, 10, 12, 8, 10, 11, 10, 9, 11, 10]
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rows = ([["华东", v] for v in base] + [["华南", v + 2] for v in base[:-1]] + [["华南", 100]]
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+ [["华北", v] for v in base])
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s = snap("Q1", "SELECT region, amount FROM orders", ["region", "amount"], rows)
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result = await analyze("differ", "rows", snaps=[s], query="Q1", by="region", value="amount", label="客单价")
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assert result["verdict"]["code"] == "no_evidence"
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assert {"code": "outlier_sensitive", "text": "去掉最大的一笔后，差异变得站得住"} in result["caveats"]
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assert math.isfinite(float(result["values"]["diff"]))
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