统计术语专业解释

Definition: The Minimum Detectable Effect (MDE), also called the Minimum Detectable Effect Size (MDES), is the smallest true effect (difference or change) that a study is designed to detect with a specified statistical power (1−β) at a given Type I error rate (α), given the study design and assumed variability. Formally, it is the smallest δ such that P(reject H0 | true effect = δ) ≥ 1−β.

Key properties
- It is a design-time quantity determined by α, power, sample size/allocation, variance, test sidedness, and analysis method.
- It is expressed in the natural units of the metric (absolute MDE); a relative MDE is the absolute MDE divided by a baseline level.
- It reflects detectability, not the observed effect or practical importance.

General formula
- For many common tests, an accurate approximation is:
  MDE ≈ (z1−α/2 + z1−β) × SE(Δ̂)
  where SE(Δ̂) is the standard error of the estimator of the effect (Δ̂), computed under assumed values. For one-sided tests use z1−α instead of z1−α/2.

Common cases
- Difference in means (two independent groups):
  SE(Δ̂) = sqrt(σ1^2/n1 + σ2^2/n2).
  If σ1 = σ2 = σ and n1 = n2 = n: MDE ≈ (z1−α/2 + z1−β) × σ × sqrt(2/n).
- Difference in proportions (two independent groups):
  A practical planning approximation uses a baseline rate p (or a pooled estimate):
  SE(Δ̂) ≈ sqrt(p(1−p) × (1/n1 + 1/n2)),
  so MDE ≈ (z1−α/2 + z1−β) × sqrt(p(1−p) × (1/n1 + 1/n2)).
  More exact calculations use variance under both H0 and H1 and may require iteration if p under treatment is p+δ.

Related considerations
- Allocation ratio r = nt/nc, total N: SE scales as sqrt(1/nt + 1/nc); equal allocation (r = 1) minimizes MDE for fixed N.
- Multiple comparisons or sequential looks require α-adjustments (e.g., Bonferroni, group-sequential), which increase the MDE.
- Clustered or correlated data inflate SE via a design effect: DE = 1 + (m−1)×ICC; multiply SE by sqrt(DE).
- Standardized MDES (e.g., Cohen’s d) equals the MDE divided by the assumed standard deviation.

Interpretation
- If a study’s MDE is δ, the design has the specified power to detect effects of size ≥ δ; smaller true effects are likely to go undetected.
- Reporting MDE alongside null results clarifies which effect sizes can be ruled out by the study.

队列分析（Cohort Analysis）是一种纵向数据分析方法，将对象（如用户、客户、设备等）按某个共同特征或起始事件（通常是首次发生时间，如首访、注册、首购）划分为“队列”，并在相对时间维度上跟踪各队列的行为与指标变化，以比较不同队列的表现、识别时间与事件驱动的效应、分离样本“年龄”影响与整体环境变化。

关键要点：
- 队列定义：基于共同特征或锚点事件进行分组，常见为获取队列（按首次接触时间）、行为队列（按首购/首用事件）、属性队列（按渠道、地区等）。
- 时间轴：采用相对时间（如第1周、第2月）跟踪同一队列在不同“龄期”的指标，避免横截面平均掩盖差异。
- 核心指标：留存率、流失率、活跃度、转化率、复购率、ARPU/LTV等，按队列规模标准化以便比较。
- 典型输出：队列热力矩阵（队列×期数）、留存/生存曲线、累计收入或复购曲线。
- 主要用途：评估产品迭代或营销活动对不同批次用户的影响；比较渠道质量；识别生命周期规律与结构性变化。

与横截面分析的区别在于，队列分析在相对时间上追踪同源群体的演化，能有效控制混合样本导致的平均偏差和季节性/宏观环境干扰。