统计学基础|先把问题问对:数据分析的六大类型

先问清楚问题:数据分析的六种类型

Ask the Right Question First: Six Types of Data Analysis

导读:Leek & Peng, "What is the question?", Science, 2015 | 中英双语

一、为什么问题类型如此重要

Why the type of question matters

近年来,"可重复性"(reproducibility)成为科学界关注的焦点:同样的数据和代码,能否得到同样的结果?约翰斯·霍普金斯大学的两位生物统计学家 Jeffery Leek 与 Roger Peng 指出,可重复只是最低要求。一项分析完全可以被他人精确重复,却依然是错的。

Reproducibility has become a central concern in science: can the same data and code produce the same results? Biostatisticians Jeffery Leek and Roger Peng of Johns Hopkins University argue that reproducibility is only a minimum standard. An analysis can be perfectly reproducible and still be wrong.

他们认为,分析可重复之后,真正需要回答的问题是"这个分析对不对"。而在他们看来,最常见的错误不是公式或软件用错,而是把一种问题当成了另一种问题。文章的副标题直接点明了这一点:

Being able to rerun an analysis says nothing about whether its conclusions are right. In their view, the most frequent failure is not a wrong formula or a software bug, but confusing one kind of question with another. The article's subtitle puts it plainly:

"Mistaking the type of question being considered is the most common error in data analysis."

误判所要回答的问题类型,是数据分析中最常见的错误。

二、六种数据分析类型

The six types of data analysis

作者把数据分析分为六类,从易到难依次为:描述、探索、推断、预测、因果、机制。下面逐一介绍,例子为本文所加。

The authors classify data analyses into six types, from least to most demanding: descriptive, exploratory, inferential, predictive, causal, and mechanistic. Each is introduced below; the examples are our own.

图 1 数据分析的六种类型及其各自回答的问题

Figure 1. The six types of data analysis and the question each one answers (Source: Leek & Peng, "What is the question?", Science, 2015)

1 描述性分析 Descriptive

概括一组数据的基本情况(计数、平均数、分布等),不对数据之外作任何结论。

Describes what a data set contains, such as counts, averages and distributions, without drawing conclusions beyond it.

例 统计某市各区的常住人口和年龄结构。

Example: reporting the population and age structure of each district in a city.

✔ 能说明:这组数据是什么样的。

✘ 不能说明:数据为什么是这样,或在其他数据中是否成立。

2 探索性分析 Exploratory

在数据中寻找可能值得研究的关系与趋势,其产物是假设,而不是结论。

Looks for relationships and trends that may be worth studying; it produces hypotheses rather than conclusions.

例 浏览学生数据时发现,每周学习时长越长的学生,考试成绩往往越高。

Example: while browsing student records, noticing that students who study more hours per week tend to score higher.

✔ 能说明:哪些现象值得进一步研究。

✘ 不能说明:这些发现是否真实存在,需要用新数据确认。

3 推断性分析 Inferential

评估样本中看到的规律在更大的总体中是否真实存在,以及这一判断有多大不确定性。已发表的研究中,这类分析最为常见。

Asks whether a pattern seen in a sample is likely to be real in the wider population, and how uncertain that judgment is. It is the type most often found in published research.

例 用全校学生的随机样本,检验学习时长与成绩的相关在全校范围内是否显著。

Example: using a random sample to test whether the association between study time and scores holds across the whole school.

✔ 能说明:两个变量之间的关系在总体中是否存在。

✘ 不能说明:在非随机化研究中,这种关系的成因或机制。

4 预测性分析 Predictive

利用已知信息,为某个具体个体估计其尚未观测到的结果。

Builds a rule that estimates an unknown outcome for a particular person or unit from information already known about them.

例 根据一名学生的出勤率和作业成绩,预测他期末考试能否及格。

Example: predicting whether a student will pass the final exam from attendance and homework scores.

✔ 能说明:一个变量能否用来准确预测另一个变量。

✘ 不能说明:为什么能够预测,也不说明改变特征会改变结果。

5 因果分析 Causal

研究如果人为改变某个变量,另一个变量平均会发生多大、什么方向的变化。

Asks how much, and in which direction, an outcome would change on average if we intervened on another variable.

例 将学生随机分为两组,一组接受课后辅导,比较两组平均成绩的差异。

Example: randomly assigning students to receive tutoring or not, and comparing average scores between the groups.

✔ 能说明:干预对总体的平均效应。

✘ 不能说明:干预对每一个个体都一定有效。因果效应是平均意义上的。

6 机制分析 Mechanistic

确定一个变量作用于另一个变量的确切过程,使改变的结果完全确定、不含随机成分。

Establishes the exact process by which one variable acts on another, so that the result of a change is fully determined, with no randomness left.

例 在工程中,精确确定改变零件尺寸会如何改变其承受的应力。

Example: in engineering, establishing exactly how changing a component's dimensions changes the stress it bears.

✔ 能说明:变量之间确定的作用过程。

✘ 局限:除工程等领域外,极具挑战,很少能够实现。

三、如何判断自己在做哪一类分析

How to identify your type of analysis

原文用一张流程图(上图1)帮助读者判断分析类型。按照其思路,可以依次问自己以下几个问题:

The article offers a flowchart for this. Following its logic, you can ask yourself the following questions in turn:

第 1 步 数据只是收集起来,还没有被汇总?→ 还谈不上数据分析。

Step 1: Data collected but never summarized? It is not yet an analysis.

第 2 步 只给出汇总结果,不加解读?→ 描述性分析。

Step 2: Summaries reported with no interpretation → descriptive.

第 3 步 有解读,但没有评估结论能否推广到新数据?→ 探索性分析。

Step 3: Interpreted, but with no check on whether the findings generalize → exploratory.

第 4 步 评估了推广性,但不涉及干预:

 目标是估计个体的结果 → 预测性分析;目标是总体中的关系 → 推断性分析。

Step 4: Generalization assessed, but no intervention in view:

 estimating individual outcomes → predictive; relationships in the population → inferential.

第 5 步 关心的是干预的效果:

 平均效应 → 因果分析;完全确定的效应 → 机制分析。

Step 5: Interested in the effect of an intervention:

 an average effect → causal; a fully determined effect → mechanistic.

四、常见错误:把一类问题当成另一类

Common mistakes: answering the wrong question

作者总结了几种最常见的混淆。它们如此普遍,以至于各自都有了约定俗成的说法:

The authors list the most frequent confusions, which are so common that each has its own well-known phrase:

|------------------|-------------------|------------------------------------------------|-------------------------------|
| 实际类型 Actual type | 被误当成 Mistaken for | 常用说法 Phrase | 含义 What goes wrong |
| 推断 Inferential | 因果 Causal | 相关不等于因果 Correlation does not imply causation | 把总体中存在的关联解释为因果效应 |
| 探索 Exploratory | 推断 Inferential | 数据疏浚 Data dredging | 在数据中反复搜寻后找到的模式,未经新数据检验就当作确定结论 |
| 探索 Exploratory | 预测 Predictive | 过拟合 Overfitting | 在已有数据上表现良好的规律,被直接用于预测新数据 |
| 描述 Descriptive | 推断 Inferential | 单一样本分析 n of 1 analysis | 把对单一数据集的描述推广到总体 |

作者还举了两个现实中的例子:关于手机使用与脑癌之间关联的推断性分析,被解读成了因果结论;利用谷歌搜索词追踪流感疫情的探索性分析,被当作了预测性分析。

The authors cite two real cases: an inferential analysis of the association between cellphone use and brain cancer was interpreted as causal, and an exploratory analysis of Google search terms related to flu outbreaks was treated as predictive.

因果蔓延(causal creep):当同一研究或同一数据集中包含多项分析时,问题更加复杂。例如一项随机对照试验,其主要分析可以推断因果,但在同一数据上做的次要分析并不具备随机化的保障,却常被赋予同样的分量。作者建议,分析中的每一步都应按其最初的目的标明类型。

Causal creep: things get harder when multiple analyses are performed in the same study or on the same data. In a randomized trial, for example, the primary analysis can support causal claims, but secondary analyses on the same data lack that protection, yet are often given the same weight. The authors recommend labeling every step of an analysis according to its original intent.

五、延伸:CDA 数据分析师认证与六类分析能力

Extension: the CDA certification and the six types of analysis

理解了六类分析之后,一个自然的问题是:如何系统地训练这些能力?在国内,CDA 数据分析师(Certified Data Analyst)认证体系提供了一个较为完整的参考框架。它由中国商业联合会数据分析专业委员会等机构推动,把数据分析能力划分为三个等级,与本文的六类分析可以形成对应关系。

Having understood the six types, a natural question follows: how can these skills be trained systematically? In China, the CDA (Certified Data Analyst) certification offers a fairly complete reference framework. Promoted by institutions such as the Data Analysis Committee of the China General Chamber of Commerce, it divides data analysis competence into three levels, which map onto the six types discussed above.

|-----------------|-------------------------------------|-----------------------------|
| 等级 Level | 主要能力 Core competence | 对应的分析类型 Corresponding types |
| Level Ⅰ 业务数据分析师 | 数据采集、清洗、描述统计、报表与可视化,能独立完成业务数据的整理与呈现 | 描述性、探索性 |
| Level Ⅱ 建模分析师 | 统计推断、假设检验、回归与分类建模、模型评估与调优 | 推断性、预测性 |
| Level Ⅲ 数据科学家 | 实验设计、因果推断、机器学习与复杂业务问题的端到端解决 | 因果性、机制性(部分) |

需要强调的是,认证等级并不等于分析能力的高低排序,而是问题类型的覆盖范围。一位只做描述性分析的 Level Ⅰ 分析师,如果清楚自己回答的是"数据是什么样的",其结论就是可靠的;反之,一位掌握复杂模型的 Level Ⅲ 分析师,若把预测模型的结果当作因果结论汇报,同样会犯本文所说的最常见错误。

It should be stressed that the levels are not a ranking of analytical ability but a coverage of question types. A Level Ⅰ analyst who only does descriptive work is reliable as long as they know they are answering "what does the data look like"; conversely, a Level Ⅲ analyst with sophisticated models can still commit the most common error described here by reporting predictive results as causal conclusions.

因此,准备 CDA 认证的过程,不妨与本文的判断流程结合起来:每学一种方法,先问它回答的是哪一类问题,能说明什么、不能说明什么。这样,证书背后才是真正可迁移的分析素养,而不只是工具操作。

When preparing for the CDA certification, it therefore helps to pair each method with the flowchart above: for every technique learned, first ask which type of question it answers, and what it can and cannot establish. Only then does the certificate stand for transferable analytical literacy rather than mere tool operation.

五、小结

Takeaways

  1. 可重复性是必要条件,但不能保证分析正确。

Reproducibility is necessary but does not guarantee correctness.

  1. 数据分析可分为描述、探索、推断、预测、因果、机制六类,难度依次增加。

Analyses fall into six types of increasing difficulty: descriptive, exploratory, inferential, predictive, causal, and mechanistic.

  1. 每类分析能得出的结论不同,最常见的错误是用一类分析的结果回答另一类问题。

Each type supports different conclusions; the most common error is using one type to answer another type of question.

  1. 作者认为,这种混淆是可重复性危机、新闻报道误读科学结论等问题的重要原因,解决之道在于数据分析教育。

The authors link this confusion to the replication crisis and to misleading press coverage, and argue that the remedy lies in data analysis education.

  1. 动手分析之前,先问清楚:我要回答的究竟是哪一类问题?

Before analyzing, ask: what type of question am I actually trying to answer?

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