数据分布与变异分析

Summary of distribution and variability

Conversion rate (approximately normal as provided)

• Central tendency: A = 3.1%, B = 3.4% (absolute lift = +0.30 percentage points; relative lift ≈ +9.7%).
• Dispersion (using provided variances): VarA = 0.00020, VarB = 0.00025 → SDA ≈ 1.41 pp, SDB ≈ 1.58 pp. B shows about 25% higher variance than A.
• Signal vs. noise: The observed lift (0.30 pp) is small relative to the stated SDs; standardized difference ≈ 0.20 SD (small).
• Important note on variance scale: With nA = 12,000 and nB = 11,800, a binomial model would imply much smaller SEs (~0.16–0.17 pp). Please confirm whether the reported variances are for the estimator (sampling variance), per-bucket/day variability, or another definition; inference about precision depends on this.

Session duration (right-skewed)

• Central tendency: A = 210s, B = 218s (∆ = +8s; ≈ +3.8%).
• Shape: Right-skew implies a long upper tail; the mean is sensitive to outliers and can be pulled upward. The median is expected to be below the mean.
• Variability characterization: For skewed time metrics, dispersion is better summarized with robust statistics (median, IQR, 90th/95th percentiles). For parametric modeling or comparing means, log-transformation (or modeling on a Gamma/lognormal scale) stabilizes variance and reduces tail influence.

Failure rate (rare events; binomial/Poisson-like)

• Central tendency: A = 0.12%, B = 0.13% (≈ 14–15 failures at the stated samples; relative lift ≈ +8.3%, absolute +0.01 pp).
• Dispersion: For rare events, the sampling distribution is right-skewed; normal approximations can be fragile at these counts. Approximate SE of the proportion: A ≈ 0.0316 pp, B ≈ 0.0333 pp; relative SE ≈ 25–26%, indicating high relative uncertainty. The observed difference is tiny versus this noise.

Implications and next steps for measurement

• Confirm the definition of the conversion-rate variances; if they represent sampling variance, they are unusually large given n and will materially change conclusions.
• Report dispersion with methods matched to each metric’s distribution:
  • Conversion: SEs and 95% CIs (logit-scale CIs are variance-stabilized).
  • Session duration: median, IQR, upper-tail percentiles; compare log-mean or use robust estimators.
  • Failure rate: exact/binomial or Poisson CIs (not normal), and monitor for overdispersion.
• Interpret differences relative to variability: on Day 3, conversion and failure-rate gaps are small compared to their respective noise; the session-duration increase occurs on a skewed distribution where robust summaries are preferred.

以下为近14日转化数据的分布与变异性要点，聚焦可执行结论：

总体结论

• 人群层面：女性25-34的均值高于男性25-34，但两者差异在统计上不显著；男性波动更大。
• 时段层面：晚间20-22均值高于上午10-12，提升约10.9%；晚间分布明显右偏，均值易被促销拉高。
• 单品层面：SKU-107与SKU-311转化率显著高于整体区间均值，合计贡献21%，呈现头部集中。

人群分布与变异性（14日）

• 女性25-34：均值4.2%，方差0.00040（标准差≈2.0个百分点），变异系数≈47.6%。均值95%置信区间约[3.15%，5.25%]。
• 男性25-34：均值3.5%，方差0.00050（标准差≈2.24个百分点），变异系数≈63.9%。均值95%置信区间约[2.33%，4.67%]。
• 组间差异检验（近似Welch t，n=14天/组）：均值差0.7个百分点，t≈0.87，p≈0.39；差异的95%区间约[-0.87，+2.27]个百分点。结论：在当前样本与波动水平下，性别组均值差异缺乏统计显著性；男性波动更大（更不稳定）。

时段分布与偏态

• 上午10-12：均值4.6%。
• 晚上20-22：均值5.1%，相对上午提升约+10.9%（+0.5个百分点）。
• 分布形态：晚间数据右偏（促销驱动长尾），均值对极值敏感。推断晚间中位数可能低于均值，实际「典型水平」可能被均值高估。建议并行观察中位数、截尾/温莎化均值，以及将“是否促销”纳入分层或回归调整，以剥离促销的拉升效应。

单品贡献与集中度

• SKU-107转化6.8%，SKU-311转化5.9%，均高于各人群与时段均值区间，表现属头部。
• 两SKU合计贡献21%，显示明显的集中效应（近似帕累托特征）。短期配置资源向头部SKU倾斜具有放大产出潜力，但需监测其日波动与促销依赖度，防止收益集中且不稳。

方法与假设说明

• 方差、标准差基于日转化率（比例）；置信区间与显著性检验假设日度近似独立且满足正态近似。若存在强促销日或自相关，建议采用稳健方法（如Newey-West或分层模型）复核结论。

可执行要点

• 监控男性25-34的波动来源，优先做日度稳定性优化（如频控、素材与落地页一致性）。
• 晚间20-22与促销强关联，评估在非促销日的真实基线表现；报告中增加中位数/稳健均值。
• 放大SKU-107/311投放与陈列，但并行跟踪其贡献的日度方差与边际效应，避免过度集中导致整体波动上升。