数据分析

数据分析Data analysis是一个对数据进行检查、清洗、转换 transformation和建模的过程，其目的是收集有用的信息并得出结论，为决策作出信息支撑。数据分析涉及个方面并且有多种方法，涵盖了不同名称的技术，被用于商业、自然科学和社会科学等不同领域。在当今的商业世界，数据分析在帮助人们更科学地做出的决策和帮助企业更有效地运营方面发挥着重要作用。^[1]

数据挖掘 Data mining是一种特殊的数据分析技术，侧重于统计建模和探索未来知识前景（而不仅仅是的描述行为目的）。同时，现代智能商业严重依赖于聚合的数据分析，尤其是在商业信息方面。在统计应用中，数据分析可以分为描述性统计学descriptive statistics、探索性数据分析exploratory data analysis (EDA)和实证性数据分析 confirmatory data analysis (CDA)。EDA 侧重于发现数据中的新特征，而 CDA 侧重于确认或证伪现有的假设。预测分析Predictive analytics的重点是应用统计模型进行预测或分类，而文本分析text analytics则应用统计学、语言学和结构化技术从文本源中提取和分类信息（文本是一种非结构化数据）。以上就是各种各样的数据分析。

数据整合 Data integration是数据分析的先驱，数据分析与数据可视化data visualization同数据传播data dissemination密切相关。

数据分析的流程

Data science process flowchart from Doing Data Science, by Schutt & O'Neil (2013)

Data science process flowchart from Doing Data Science, by Schutt & O'Neil (2013)

数据科学处理流程图，来自《数据科学实战 Doing Data Science》，Schutt & o’ neil (2013)

分析是指将一个整体分解成独立的部分来进行个别检查。数据分析是获取原始数据并将其转化为用户决策有用信息的过程。通过收集和分析数据来回答问题、检验假设或推翻理论。

统计学家 John Tukey 在1961年将数据分析定义为“分析数据并解释这些过程所产生结果的技术，同时规划数据收集以使数据分析过程更容易、更精确或更准确的方法，以及所有适用于数据分析的（数学）统计的机制和结果。”^[2]

数据分析可以分为以下几个步骤，如下所述。这些阶段是迭代的iterative，因为后期阶段的反馈可能会导致重复额外的与前期阶段相同的工作。用于数据挖掘的 CRISP 框架有类似的步骤。

数据要求

有用以分析的输入数据是必须的，因为分析是基于数据来指导分析的人或客户的需求（这些人将使用分析的最终产品）而规定的。收集数据的一般实体类型称为实验单元experimental unit (例如，一个人或一群人)。关于总体 population的具体变量（例如，年龄和收入）可以被指定和获得。数据可以是数值变量的或分类变量的(也就是数字的文本标签)。^[3]

数据收集

数据可以通过各种来源收集。需求可以由分析人员传达给数据保管人，例如组织内的信息技术人员。这些数据可以从环境中的传感器，如交通摄像机、卫星、记录设备等接收，也可以通过访谈、从网上资源下载或阅读文档而获得。^[3]

数据处理

The phases of the intelligence cycle used to convert raw information into actionable intelligence or knowledge are conceptually similar to the phases in data analysis.

[通过知识循环intelligence cycle将原始信息转化为可操作智慧或知识，这在概念上类似于数据分析中的阶段]

一开始获得的数据必须经过处理整合以便进行分析。以电子表格或统计软件为例，这可能涉及到将数据以表格格式放置到行和列中（即结构化数据 structured data）以便后续分析。^[3]

数据筛选

Once processed and organised, the data may be incomplete, contain duplicates, or contain errors. The need for data cleaning will arise from problems in the way that data are entered and stored. Data cleaning is the process of preventing and correcting these errors. Common tasks include record matching, identifying inaccuracy of data, overall quality of existing data, deduplication, and column segmentation.^[4] Such data problems can also be identified through a variety of analytical techniques. For example, with financial information, the totals for particular variables may be compared against separately published numbers believed to be reliable.^[5] Unusual amounts above or below pre-determined thresholds may also be reviewed. There are several types of data cleaning that depend on the type of data such as phone numbers, email addresses, employers etc. Quantitative data methods for outlier detection can be used to get rid of likely incorrectly entered data. Textual data spell checkers can be used to lessen the amount of mistyped words, but it is harder to tell if the words themselves are correct.^[6]

Once processed and organised, the data may be incomplete, contain duplicates, or contain errors. The need for data cleaning will arise from problems in the way that data are entered and stored. Data cleaning is the process of preventing and correcting these errors. Common tasks include record matching, identifying inaccuracy of data, overall quality of existing data, deduplication, and column segmentation. Such data problems can also be identified through a variety of analytical techniques. For example, with financial information, the totals for particular variables may be compared against separately published numbers believed to be reliable. Unusual amounts above or below pre-determined thresholds may also be reviewed. There are several types of data cleaning that depend on the type of data such as phone numbers, email addresses, employers etc. Quantitative data methods for outlier detection can be used to get rid of likely incorrectly entered data. Textual data spell checkers can be used to lessen the amount of mistyped words, but it is harder to tell if the words themselves are correct.

一旦经过处理和组织，就会发现数据可能不完整、重复或含有错误。

 --嘉树（讨论） 根据语义增加“就会发现”如何如何

由于输入和存储数据的方式的问题，因此我们需要进行数据清理。数据筛选是预防和纠正这些错误的过程。常见的任务包括匹配记录、识别不准确的数据、监控现有数据的整体质量、处理数据重复和分割列等。这样的数据问题也可以通过很多种分析技术来识别。例如，利用财务信息，可以将特定变量的与被所有数据认为可靠的单独公布的数字进行比较。高于或低于预先确定的阈值的异常数额可能会被核查。有几种类型的数据清理依赖于数据的类型，如电话号码，电子邮件地址，雇主等。异常值检查outlier detection的定量方法可以用来去除可能的输入错误的数据。文本数据拼写检查器Textual data spell checkers可以用来减少拼写错误单词的数量，但是很难判断这些单词本身是否正确。

探索性数据分析

数据被筛选之后就可以进行分析。分析者可能会运用各种被称为探索性数据分析的技术着手理解数据中包含的信息。^[7]^[8] 发现的过程可能导致额外的数据清洗或数据请求，因此这些活动可能具有迭代性质。在描述统计学量，例如平均值或中位数时，就可以用来帮助理解数据。数据可视化还可以被用于检查图形格式的数据，以获得关于数据中的信息的额外的洞察力。^[3]

建模和算法

数学公式或被称为算法的模型可用于在数据中识别变量之间的关系，如相关性或因果关系。一般来说，模型可以根据以下规则建立：根据数据中的其他变量来评估数据中的某一特定变量，并用基于模型的准确性设置残差（即数据 = 模型 + 误差）。^[9]

统计推断 Inferential statistics包括测量特定变量之间关系的技术。例如，回归分析可以用来建立广告的变化的模型，可以知道广告的变化（独立变量 [math]\displaystyle{ x }[/math]）是否可以解释销售的变化（因变量 [math]\displaystyle{ y }[/math]）。用数学术语来说，[math]\displaystyle{ y }[/math]（销售）是 [math]\displaystyle{ x }[/math] （广告）的函数。它可以被描述为[math]\displaystyle{ Y = aX + b + error }[/math]，其中模型的设计使得 [math]\displaystyle{ a }[/math] 和 [math]\displaystyle{ b }[/math] 在模型某预测给定范围 [math]\displaystyle{ x }[/math] 的 [math]\displaystyle{ y }[/math] 时具有最小的误差。分析人员可能会尝试建立描述数据的模型，以简化分析和表示结果。^[9]

数据产品

数据产品是一种计算机应用程序，它接收数据输入并产生输出，将它们反馈回到环境中。它可能基于一个模型或算法。一个例子是一种可以分析客户购买历史并推荐客户可能喜欢的其他物品的应用程序。^[3]

Communication 交流

Data visualization to understand the results of a data analysis.^[10]

Data visualization to understand the results of a data analysis.

[用于了解数据分析结果的数据可视化]

Once the data are analyzed, it may be reported in many formats to the users of the analysis to support their requirements. The users may have feedback, which results in additional analysis. As such, much of the analytical cycle is iterative.^[3]

Once the data are analyzed, it may be reported in many formats to the users of the analysis to support their requirements. The users may have feedback, which results in additional analysis. As such, much of the analytical cycle is iterative.

数据被分析后可以用多种格式报告给分析的用户，以支持他们的需求。这些用户可能会有一些反馈，从而需要进行额外的分析。因此，大部分的分析周期是迭代的。

When determining how to communicate the results, the analyst may consider data visualization techniques to help clearly and efficiently communicate the message to the audience. Data visualization uses information displays (such as tables and charts) to help communicate key messages contained in the data. Tables are helpful to a user who might look up specific numbers, while charts (e.g., bar charts or line charts) may help explain the quantitative messages contained in the data.

在决定如何传达结果的时候，分析师可能会考虑数据可视化技术来帮助清晰有效地向听众传达信息。数据可视化使用信息显示（如表格和图表）来帮助传递数据中的关键信息。表格对查找特定数字的用户很有帮助，而图表（例如柱状图或折线图）可以帮助解释数据中的定量信息。

Quantitative messages 定量数据

A time series illustrated with a line chart demonstrating trends in U.S. federal spending and revenue over time.

随时间变化的美国联邦政府收支变化趋势时间序列折线图

A scatterplot illustrating correlation between two variables (inflation and unemployment) measured at points in time.

两个变量（通货膨胀和失业）在时间点上的相关性散点图

Stephen Few described eight types of quantitative messages that users may attempt to understand or communicate from a set of data and the associated graphs used to help communicate the message. Customers specifying requirements and analysts performing the data analysis may consider these messages during the course of the process.

Stephen Few 描述了用户可能试图从一组数据以及用于帮助传达信息的相关图表中理解或传达的八种定量信息。指定需求的客户和执行数据分析的分析人员可以在分析过程中考虑这些消息。

Time-series: A single variable is captured over a period of time, such as the unemployment rate over a 10-year period. A line chart may be used to demonstrate the trend.

Time-series: A single variable is captured over a period of time, such as the unemployment rate over a 10-year period. A line chart may be used to demonstrate the trend.

时间序列: 在一段时间内捕捉单一变量，如10年间的失业率。可以用折线图来说明趋势。

Ranking: Categorical subdivisions are ranked in ascending or descending order, such as a ranking of sales performance (the measure) by sales persons (the category, with each sales person a categorical subdivision) during a single period. A bar chart may be used to show the comparison across the sales persons.

Ranking: Categorical subdivisions are ranked in ascending or descending order, such as a ranking of sales performance (the measure) by sales persons (the category, with each sales person a categorical subdivision) during a single period. A bar chart may be used to show the comparison across the sales persons.

排名: 按升序或降序对分类子类目进行排名，例如按销售人员（即类别，每个销售人员都有一个分类子类目）对一个时期内的销售业绩（即测量）进行排名。条形图可以用来在销售人员之间比较。

Part-to-whole: Categorical subdivisions are measured as a ratio to the whole (i.e., a percentage out of 100%). A pie chart or bar chart can show the comparison of ratios, such as the market share represented by competitors in a market.

Part-to-whole: Categorical subdivisions are measured as a ratio to the whole (i.e., a percentage out of 100%). A pie chart or bar chart can show the comparison of ratios, such as the market share represented by competitors in a market.

部分对整体: 分类子类目是以部分占整体的比例来衡量的（即占100% 的百分比）。饼图或条形图可以用来显示比率的比较，例如市场中竞争对手所占的市场份额。

Deviation: Categorical subdivisions are compared against a reference, such as a comparison of actual vs. budget expenses for several departments of a business for a given time period. A bar chart can show comparison of the actual versus the reference amount.

Deviation: Categorical subdivisions are compared against a reference, such as a comparison of actual vs. budget expenses for several departments of a business for a given time period. A bar chart can show comparison of the actual versus the reference amount.

偏差: 将分类子类目与参考数据进行比较，例如对一个企业的几个部门在给定时间内实际支出与预算支出进行比较。条形图可以比较实际金额与参考金额的差异。

Frequency distribution: Shows the number of observations of a particular variable for given interval, such as the number of years in which the stock market return is between intervals such as 0–10%, 11–20%, etc. A histogram, a type of bar chart, may be used for this analysis.

Frequency distribution: Shows the number of observations of a particular variable for given interval, such as the number of years in which the stock market return is between intervals such as 0–10%, 11–20%, etc. A histogram, a type of bar chart, may be used for this analysis.

频率分布: 显示特定变量在给定时间间隔内的观测数量，例如股票市场回报率stock market return在0-10% 、11-20% 等时间间隔内的年数。直方图作为一种条形图可以用来进行这种分析。

Correlation: Comparison between observations represented by two variables (X,Y) to determine if they tend to move in the same or opposite directions. For example, plotting unemployment (X) and inflation (Y) for a sample of months. A scatter plot is typically used for this message.

Correlation: Comparison between observations represented by two variables (X,Y) to determine if they tend to move in the same or opposite directions. For example, plotting unemployment (X) and inflation (Y) for a sample of months. A scatter plot is typically used for this message.

相关性: 用两个变量(x，y)表示的观测值之间的比较，以确定它们是否倾向于朝相同或相反的方向移动。例如，通常使用散点图绘制几个月的失业率x和通货膨胀率y之间的关系。

Nominal comparison: Comparing categorical subdivisions in no particular order, such as the sales volume by product code. A bar chart may be used for this comparison.

Nominal comparison: Comparing categorical subdivisions in no particular order, such as the sales volume by product code. A bar chart may be used for this comparison.

称名变量的比较: 比较分类子类目而没有特定的顺序，例如按产品代码标注的销售量。条形图可能被用于作这种比较。

Geographic or geospatial: Comparison of a variable across a map or layout, such as the unemployment rate by state or the number of persons on the various floors of a building. A cartogram is a typical graphic used.^[11]^[12]

Geographic or geospatial: Comparison of a variable across a map or layout, such as the unemployment rate by state or the number of persons on the various floors of a building. A cartogram is a typical graphic used.

地理图或地理空间: 在地图或布局中对一个变量的比较，例如州的失业率或建筑物各层的人数。地图是一种典型的图形。

Techniques for analyzing quantitative data 分析定性数据的技术

Author Jonathan Koomey has recommended a series of best practices for understanding quantitative data. These include:

作者Jonathan Koomey推荐了一系列理解定量数据的最佳方法。其中包括:

Check raw data for anomalies prior to performing an analysis;

在实施数据分析之前检查原始数据中的异常值；

Re-perform important calculations, such as verifying columns of data that are formula driven;

重新执行重要的计算，例如验证公式驱动formula driven的数据列；

Confirm main totals are the sum of subtotals;

确认总计是小计的和；

Check relationships between numbers that should be related in a predictable way, such as ratios over time;

检查那些可以通过一些方法预测的数字之间的关系，例如随时间变化的比例；

Normalize numbers to make comparisons easier, such as analyzing amounts per person or relative to GDP or as an index value relative to a base year;
使数字正态化以便于比较，例如分析每个人的数量，或相对于GDP 的数量，或相对于基准年的数量指数；

Break problems into component parts by analyzing factors that led to the results, such as DuPont analysis of return on equity.^[5]
通过分析导致结果的因素将问题整体分解为几个部分，如净资产收益率return on equity的杜邦分析DuPont analysis^[5]。

For the variables under examination, analysts typically obtain descriptive statistics for them, such as the mean (average), median, and standard deviation. They may also analyze the distribution of the key variables to see how the individual values cluster around the mean.

对于被调查的变量，分析师通常会得到它们的描述统计学变量，比如平均数、中位数和标准差。他们还可以分析关键变量的分布情况，来看各个值是如何围绕平均数聚集的。

An illustration of the MECE principle used for data analysis.

The consultants at McKinsey and Company named a technique for breaking a quantitative problem down into its component parts called the MECE principle. Each layer can be broken down into its components; each of the sub-components must be mutually exclusive of each other and collectively add up to the layer above them. The relationship is referred to as "Mutually Exclusive and Collectively Exhaustive" or MECE. For example, profit by definition can be broken down into total revenue and total cost. In turn, total revenue can be analyzed by its components, such as revenue of divisions A, B, and C (which are mutually exclusive of each other) and should add to the total revenue (collectively exhaustive).

An illustration of the MECE principle used for data analysis. The consultants at McKinsey and Company named a technique for breaking a quantitative problem down into its component parts called the MECE principle. Each layer can be broken down into its components; each of the sub-components must be mutually exclusive of each other and collectively add up to the layer above them. The relationship is referred to as "Mutually Exclusive and Collectively Exhaustive" or MECE. For example, profit by definition can be broken down into total revenue and total cost. In turn, total revenue can be analyzed by its components, such as revenue of divisions A, B, and C (which are mutually exclusive of each other) and should add to the total revenue (collectively exhaustive).

一个用于数据分析的MECE 原理MECE principle的说明。麦肯锡咨询公司的顾问们提出了一种将定量问题分解为其组成部分的技术，称为 MECE 原理。每一层都可以分解成它的组成部分；每一个子组成部分必须相互排斥，共同构成它们上一级的层次。这种关系被称为“相互排斥且集体穷尽Mutually Exclusive and Collectively Exhaustive”或 MECE。例如，根据定义，利润可以分为总收入和总成本。反过来，总收入可以通过其组成部分进行分析，如部门 A、 B 和 C 的收入（它们相互排斥），并且它们的总和应该是总收入（总体上穷尽）。

Analysts may use robust statistical measurements to solve certain analytical problems. Hypothesis testing is used when a particular hypothesis about the true state of affairs is made by the analyst and data is gathered to determine whether that state of affairs is true or false. For example, the hypothesis might be that "Unemployment has no effect on inflation", which relates to an economics concept called the Phillips Curve. Hypothesis testing involves considering the likelihood of Type I and type II errors, which relate to whether the data supports accepting or rejecting the hypothesis.

分析师可能会使用稳健的统计测量来解决特定的分析问题。当分析师对事件的真实状态做出特定假设，并收集数据以确定事件的真实状态时，就使用假设检验Hypothesis testing。例如，一个假设可能是“失业对通货膨胀没有影响” ，这个假设与一个叫做菲利普斯曲线Phillips Curve的经济学概念有关。假设检验包括考虑第一类和第二类错误的可能性，这些错误与数据是否支持接受或拒绝假设有关。

Regression analysis may be used when the analyst is trying to determine the extent to which independent variable X affects dependent variable Y (e.g., "To what extent do changes in the unemployment rate (X) affect the inflation rate (Y)?"). This is an attempt to model or fit an equation line or curve to the data, such that Y is a function of X.

当分析师试图确定自变量 X 对因变量 Y 的影响程度时，可以使用回归分析Regression analysisD的方法（例如，“失业率(X)的变化对通货膨胀率(Y)的影响程度如何？”）。这是一种建模或拟合一个方程直线（或曲线）数据的尝试，使得 Y 是 X 的一个函数。

Necessary condition analysis (NCA) may be used when the analyst is trying to determine the extent to which independent variable X allows variable Y (e.g., "To what extent is a certain unemployment rate (X) necessary for a certain inflation rate (Y)?"). Whereas (multiple) regression analysis uses additive logic where each X-variable can produce the outcome and the X's can compensate for each other (they are sufficient but not necessary), necessary condition analysis (NCA) uses necessity logic, where one or more X-variables allow the outcome to exist, but may not produce it (they are necessary but not sufficient). Each single necessary condition must be present and compensation is not possible.

当分析师试图确定自变量 X 在多大程度上允许变量 Y 的出现时，可以使用 https://www.erim.eur.nl/centres/Necessary-condition-analysis/ 必要条件分析Necessary condition analysis(NCA)（例如，“某个失业率(X)在多大程度上对某个通货膨胀率(Y)是必要的? ”）。（多重）回归分析分析使用加法逻辑additive logic，其中每个 X 变量可以产生结果，X 之间可以相互补偿（这些X都是充分的，但不是必要的），然而必要条件分析使用必要逻辑necessity logic，其中一个或多个 X 变量允许结果的存在，但也可能不产生这个结果（它们是必要不充分的关系）。每个单一的必要条件都必须存在，变量之间不允许补偿。

Analytical activities of data users 数据用户的分析活动

Users may have particular data points of interest within a data set, as opposed to general messaging outlined above. Such low-level user analytic activities are presented in the following table. The taxonomy can also be organized by three poles of activities: retrieving values, finding data points, and arranging data points.^[13]^[14]^[15]^[16]

Users may have particular data points of interest within a data set, as opposed to general messaging outlined above. Such low-level user analytic activities are presented in the following table. The taxonomy can also be organized by three poles of activities: retrieving values, finding data points, and arranging data points.

与上面概述的一般的消息传递不同，用户可能对数据集当中的特定数据点感兴趣。下表介绍了这种低层次的用户分析活动。分类可以由活动的三个极来组织: 检索值retrieving values、查找数据点finding data points和排列数据点arranging data points。

{ | 类“ wikitable”边框“1” - What comedies have won awards? - What comedies have won awards? - “哪些喜剧获了奖？” - Which funds underperformed the SP-500? - Which funds underperformed the SP-500? “-哪些基金的表现不如 SP-500？”

#	Task	General Description	Pro Forma Abstract	Examples	#	Task	General Description	Pro Forma Abstract	Examples	#	Task	General Description	Pro Forma Abstract	Examples
1	1	1	Retrieve Value	Retrieve Value	检索值Retrieve Value	Given a set of specific cases, find attributes of those cases.	Given a set of specific cases, find attributes of those cases.	给定特定的一组案例，找出这些案例的属性。	What are the values of attributes {X, Y, Z, ...} in the data cases {A, B, C, ...}?	What are the values of attributes {X, Y, Z, ...} in the data cases {A, B, C, ...}?	数据案例{A, B, C, ... }中属性{ X, Y, Z, ... }的值是什么？	- What is the mileage per gallon of the Ford Mondeo?	- What is the mileage per gallon of the Ford Mondeo?	“-每加仑汽油在福特Mondeo车上的行驶里程是多少？” - How long is the movie Gone with the Wind? - How long is the movie Gone with the Wind? “-电影《乱世佳人》有多长？”
2	2	2	Filter	Filter	过滤Filter	Given some concrete conditions on attribute values, find data cases satisfying those conditions.	Given some concrete conditions on attribute values, find data cases satisfying those conditions.	给定属性值的一些具体条件，找出满足这些条件的数据案例。	Which data cases satisfy conditions {A, B, C...}?	Which data cases satisfy conditions {A, B, C...}?	哪些数据案例满足条件{A, B, C... } ？	- What Kellogg's cereals have high fiber?	- What Kellogg's cereals have high fiber?
3	3	3	Compute Derived Value	Compute Derived Value	计算派生值Compute Derived Value	Given a set of data cases, compute an aggregate numeric representation of those data cases.	Given a set of data cases, compute an aggregate numeric representation of those data cases.	给定一组数据案例，计算这些数据案例以聚合形式表示的数值。	What is the value of aggregation function F over a given set S of data cases?	What is the value of aggregation function F over a given set S of data cases?	聚合函数aggregation function F 在给定数据集 S 上的值是多少？	- What is the average calorie content of Post cereals?	- What is the average calorie content of Post cereals?	“-波斯特谷物Post cereals的平均热量是多少？” - What is the gross income of all stores combined? - What is the gross income of all stores combined? “-所有商店的总收入是多少？” - How many manufacturers of cars are there? - How many manufacturers of cars are there? “-有多少汽车制造商？”
4	4	4	Find Extremum	Find Extremum	寻找极值Find Extremum	Find data cases possessing an extreme value of an attribute over its range within the data set.	Find data cases possessing an extreme value of an attribute over its range within the data set.	查找数据集中在某属性的某范围内具有极端取值的数据案例。	What are the top/bottom N data cases with respect to attribute A?	What are the top/bottom N data cases with respect to attribute A?	属性 A 的顶部或底部的 N 个数据案例是什么？	- What is the car with the highest MPG?	- What is the car with the highest MPG?	“- 有最高 MPG 的汽车是什么？” - What director/film has won the most awards? - What director/film has won the most awards? “- 哪个导演/哪部电影获奖最多？” - What Marvel Studios film has the most recent release date? - What Marvel Studios film has the most recent release date? “- 哪部漫威电影公司的电影具有最近上映的日期？”
5	5	5	Sort	Sort	排序Sort	Given a set of data cases, rank them according to some ordinal metric.	Given a set of data cases, rank them according to some ordinal metric.	给定一组数据案例，根据某种顺序度量对它们进行排序。	What is the sorted order of a set S of data cases according to their value of attribute A?	What is the sorted order of a set S of data cases according to their value of attribute A?	根据属性 A 的值，一组数据案例 S 怎样排序？	- Order the cars by weight.	- Order the cars by weight.	“-按重量给汽车排序。” - Rank the cereals by calories. - Rank the cereals by calories. “- 按卡路里排列谷物。”
6	6	6	Determine Range	Determine Range	确定范围Determine Range	Given a set of data cases and an attribute of interest, find the span of values within the set.	Given a set of data cases and an attribute of interest, find the span of values within the set.	给定一组数据案例和一个感兴趣的属性，查找该组中的值的范围。	What is the range of values of attribute A in a set S of data cases?	What is the range of values of attribute A in a set S of data cases?	在一组数据案例 S 中，属性 A 的值范围是多少？	- What is the range of film lengths?	- What is the range of film lengths?	“-胶卷的长度范围是多少？” - What is the range of car horsepowers? - What is the range of car horsepowers? “-汽车的马力范围是多少？” - What actresses are in the data set? - What actresses are in the data set? “-数据库里有哪些女演员？”
7	7	7	Characterize Distribution	Characterize Distribution	特征分布Characterize Distribution	Given a set of data cases and a quantitative attribute of interest, characterize the distribution of that attribute's values over the set.	Given a set of data cases and a quantitative attribute of interest, characterize the distribution of that attribute's values over the set.	给定一组数据案例和一个感兴趣的定量属性，刻画该属性值在该集上的分布情况。	What is the distribution of values of attribute A in a set S of data cases?	What is the distribution of values of attribute A in a set S of data cases?	属性 A 的值在一组数据案例 S 中的分布情况如何？	- What is the distribution of carbohydrates in cereals?	- What is the distribution of carbohydrates in cereals?	“-谷物中碳水化合物的分布情况如何？” - What is the age distribution of shoppers? - What is the age distribution of shoppers? “-购物者的年龄分布情况如何？”
8	8	8	Find Anomalies	Find Anomalies	寻找异常值Find Anomalies	Identify any anomalies within a given set of data cases with respect to a given relationship or expectation, e.g. statistical outliers.	Identify any anomalies within a given set of data cases with respect to a given relationship or expectation, e.g. statistical outliers.	识别给定数据集中与给定关系或期望有关的任何异常值，例如统计异常值。	Which data cases in a set S of data cases have unexpected/exceptional values?	Which data cases in a set S of data cases have unexpected/exceptional values?	在一组数据案例中，哪些数据案例具有意外的或异常的取值？	- Are there exceptions to the relationship between horsepower and acceleration?	- Are there exceptions to the relationship between horsepower and acceleration?	“-马力和加速度之间的关系有例外吗？” - Are there any outliers in protein? - Are there any outliers in protein? “-蛋白质是否有异常值？”
9	9	9	Cluster	Cluster	Cluster 集群	Given a set of data cases, find clusters of similar attribute values.	Given a set of data cases, find clusters of similar attribute values.	给定一组数据案例，找出相似属性值的集群。	Which data cases in a set S of data cases are similar in value for attributes {X, Y, Z, ...}?	Which data cases in a set S of data cases are similar in value for attributes {X, Y, Z, ...}?	一组数据案例中的哪些数据案例在属性{ X, Y, Z, ... }的值上相似？	- Are there groups of cereals w/ similar fat/calories/sugar?	- Are there groups of cereals w/ similar fat/calories/sugar?	“-有没有含脂肪 / 卡路里 / 糖类似的谷类食物？” - Is there a cluster of typical film lengths? - Is there a cluster of typical film lengths? “-是否有一组典型的电影长度？”
10	10	10	Correlate	Correlate	相关Correlate	Given a set of data cases and two attributes, determine useful relationships between the values of those attributes.	Given a set of data cases and two attributes, determine useful relationships between the values of those attributes.	给定一组数据案例和两个属性，确定这些属性值之间的有用关系。	What is the correlation between attributes X and Y over a given set S of data cases?	What is the correlation between attributes X and Y over a given set S of data cases?	在给定的数据案例集 S 中，属性 X 和 Y 之间的相关性是什么？	- Is there a correlation between carbohydrates and fat?	- Is there a correlation between carbohydrates and fat?	“-碳水化合物和脂肪之间有关系吗？” - Is there a correlation between country of origin and MPG? - Is there a correlation between country of origin and MPG? “-起源国和 MPG 之间有联系吗？” - Do different genders have a preferred payment method? - Do different genders have a preferred payment method? “- 不同性别是否倾向不同的付款方式？” - Is there a trend of increasing film length over the years? - Is there a trend of increasing film length over the years? “- 电影长度是否有逐年增加的趋势？”
11	11	11	Contextualization^[16]	Contextualization	语境化Contextualization	Given a set of data cases, find contextual relevancy of the data to the users.	Given a set of data cases, find contextual relevancy of the data to the users.	给定一组数据案例，找出数据与用户语境化的相关性。	Which data cases in a set S of data cases are relevant to the current users' context?	Which data cases in a set S of data cases are relevant to the current users' context?	一组数据案例中的哪些数据案例与当前用户的语境相关？	- Are there groups of restaurants that have foods based on my current caloric intake?	- Are there groups of restaurants that have foods based on my current caloric intake?	“-是否有几组餐馆根据我目前摄入的热量来提供食物？”

|}

Barriers to effective analysis 有效分析的障碍

Barriers to effective analysis may exist among the analysts performing the data analysis or among the audience. Distinguishing fact from opinion, cognitive biases, and innumeracy are all challenges to sound data analysis.

数据的分析人员之间或分析结果的受众之间可能存在有效分析的障碍。区分事实fact与观点opinion 、认知偏差cognitive biases 和数学盲innumeracy都是对一个好的数据分析的挑战。

Confusing fact and opinion 混淆事实和观点

模板:Quote box

Effective analysis requires obtaining relevant facts to answer questions, support a conclusion or formal opinion, or test hypotheses. Facts by definition are irrefutable, meaning that any person involved in the analysis should be able to agree upon them. For example, in August 2010, the Congressional Budget Office (CBO) estimated that extending the Bush tax cuts of 2001 and 2003 for the 2011–2020 time period would add approximately $3.3 trillion to the national debt.^[17] Everyone should be able to agree that indeed this is what CBO reported; they can all examine the report. This makes it a fact. Whether persons agree or disagree with the CBO is their own opinion.

Effective analysis requires obtaining relevant facts to answer questions, support a conclusion or formal opinion, or test hypotheses. Facts by definition are irrefutable, meaning that any person involved in the analysis should be able to agree upon them. For example, in August 2010, the Congressional Budget Office (CBO) estimated that extending the Bush tax cuts of 2001 and 2003 for the 2011–2020 time period would add approximately $3.3 trillion to the national debt. Everyone should be able to agree that indeed this is what CBO reported; they can all examine the report. This makes it a fact. Whether persons agree or disagree with the CBO is their own opinion.

有效的分析需要获得相关的事实来回答问题、支持结论、支持正式的观点，或者检验假设。事实的定义是不可辩驳的，这意味着任何参与分析的人都应该能够同意它们。例如，2010年8月，美国国会预算办公室Congressional Budget Office(CBO)估计，延长布什2001年和2003年的2011-2020年减税政策将使国家债务增加约3.3万亿美元。每个人都应该能够同意这确实是国会预算办公室报告的；他们都可以检查报告。这使该报告的内容成为一个事实。人们可以选择自己观点：是否同意国会预算办公室的报告。

As another example, the auditor of a public company must arrive at a formal opinion on whether financial statements of publicly traded corporations are "fairly stated, in all material respects." This requires extensive analysis of factual data and evidence to support their opinion. When making the leap from facts to opinions, there is always the possibility that the opinion is erroneous.

另一个例子是，上市公司的审计师必须就上市公司的财务报表是否“在所有重大方面得到公允陈述”达成正式意见，这需要对事实数据和证据进行广泛的分析，以支持他们的观点。在从事实到观点的飞跃中，总是存在着观点错误的可能性。

Cognitive biases 认知偏差

There are a variety of cognitive biases that can adversely affect analysis. For example, confirmation bias is the tendency to search for or interpret information in a way that confirms one's preconceptions. In addition, individuals may discredit information that does not support their views.

各种各样的认知偏差cognitive biases会对分析产生不利影响。例如，证实偏见confirmation bias是指人们倾向于以确认自己先入之见的方式来寻找或解释信息。此外，人们都可能会质疑那些与他们观点不相符的信息。

Analysts may be trained specifically to be aware of these biases and how to overcome them. In his book Psychology of Intelligence Analysis, retired CIA analyst Richards Heuer wrote that analysts should clearly delineate their assumptions and chains of inference and specify the degree and source of the uncertainty involved in the conclusions. He emphasized procedures to help surface and debate alternative points of view.^[18]

Analysts may be trained specifically to be aware of these biases and how to overcome them. In his book Psychology of Intelligence Analysis, retired CIA analyst Richards Heuer wrote that analysts should clearly delineate their assumptions and chains of inference and specify the degree and source of the uncertainty involved in the conclusions. He emphasized procedures to help surface and debate alternative points of view.

为了了解和克服这些偏见，分析师可能会接受专门培训。退休的美国中情局分析师Richards Heuer在他的《情报分析心理学Psychology of Intelligence Analysis》一书中写道，分析师应该清楚地描述他们的预设和推断链，明确结论中包含的不确定性的程度和来源。他强调有助于提出和辩论不同观点的程序。

Innumeracy 数学盲

Effective analysts are generally adept with a variety of numerical techniques. However, audiences may not have such literacy with numbers or numeracy; they are said to be innumerate. Persons communicating the data may also be attempting to mislead or misinform, deliberately using bad numerical techniques.^[19]

Effective analysts are generally adept with a variety of numerical techniques. However, audiences may not have such literacy with numbers or numeracy; they are said to be innumerate. Persons communicating the data may also be attempting to mislead or misinform, deliberately using bad numerical techniques.

高效的分析师通常善于使用各种数字的技术。然而，受众可能没有这样的数字和算术读写能力；他们被认为是数学盲Innumeracy。传递数据的人也可能试图误导mislead或误报misinform，故意使用糟糕的数字技术。

For example, whether a number is rising or falling may not be the key factor. More important may be the number relative to another number, such as the size of government revenue or spending relative to the size of the economy (GDP) or the amount of cost relative to revenue in corporate financial statements. This numerical technique is referred to as normalization^[5] or common-sizing. There are many such techniques employed by analysts, whether adjusting for inflation (i.e., comparing real vs. nominal data) or considering population increases, demographics, etc. Analysts apply a variety of techniques to address the various quantitative messages described in the section above.

For example, whether a number is rising or falling may not be the key factor. More important may be the number relative to another number, such as the size of government revenue or spending relative to the size of the economy (GDP) or the amount of cost relative to revenue in corporate financial statements. This numerical technique is referred to as normalization or common-sizing. There are many such techniques employed by analysts, whether adjusting for inflation (i.e., comparing real vs. nominal data) or considering population increases, demographics, etc. Analysts apply a variety of techniques to address the various quantitative messages described in the section above.

例如，一个数是上升还是下降可能不是关键因素。更重要的可能是相对于另一个数的数，例如相对于经济规模（国内生产总值）的政府收入或支出，或者公司财务报表中相对于收入的成本金额。这种数的技术称为归一化normalization或共同比common-sizing。分析师们使用了许多这样的技术，无论是对通货膨胀进行调整（如，比较实际数据与名义上的数据），还是考虑人口增长、人口统计学信息等。分析人员应用各种技术来处理上面一节中描述的各种定量信息。

Analysts may also analyze data under different assumptions or scenarios. For example, when analysts perform financial statement analysis, they will often recast the financial statements under different assumptions to help arrive at an estimate of future cash flow, which they then discount to present value based on some interest rate, to determine the valuation of the company or its stock. Similarly, the CBO analyzes the effects of various policy options on the government's revenue, outlays and deficits, creating alternative future scenarios for key measures.

分析师也可能在不同的假设或情景下分析数据。例如，当分析师进行财务报表分析时，他们通常会根据不同的假设重新编制财务报表，以得出对未来现金流的估计，然后根据一定的利率贴现到现在的价值，以确定公司或其股票的估价。同样，国会预算办公室分析了各种政策选择对政府收入、支出和赤字的影响，为关键措施创造了可供选择的未来情景。

Practitioner notes 从业者注意事项

This section contains rather technical explanations that may assist practitioners but are beyond the typical scope of a Wikipedia article.

这个部分包含了一些技术性的解释，它们可能对从业者有所帮助，但是超出了维基百科文章的典型范围。

Initial data analysis 初始数据分析

The most important distinction between the initial data analysis phase and the main analysis phase, is that during initial data analysis one refrains from any analysis that is aimed at answering the original research question. The initial data analysis phase is guided by the following four questions:模板:Sfn

The most important distinction between the initial data analysis phase and the main analysis phase, is that during initial data analysis one refrains from any analysis that is aimed at answering the original research question. The initial data analysis phase is guided by the following four questions:

在初始数据分析阶段和主要分析阶段之间最重要的区别是，在初始数据分析阶段，人们不进行任何旨在回答原始研究问题的分析。初始数据分析阶段由下列四个问题指导:

Quality of data 数据质量

The quality of the data should be checked as early as possible. Data quality can be assessed in several ways, using different types of analysis: frequency counts, descriptive statistics (mean, standard deviation, median), normality (skewness, kurtosis, frequency histograms), n: variables are compared with coding schemes of variables external to the data set, and possibly corrected if coding schemes are not comparable.

应尽早检查数据的质量。数据质量可以通过几种方式，使用不同类型的分析进行评估: 频数、描述统计学量（平均值、标准差、中位数）、正态性（偏态、峰度、频率直方图）、 n: 变量与数据集外部变量的编码方案进行比较，如果和编码方案不具有可比性，则可能对数据进行修正。

Test for common-method variance.

检验共同方法变异common-method variance

The choice of analyses to assess the data quality during the initial data analysis phase depends on the analyses that will be conducted in the main analysis phase.模板:Sfn

The choice of analyses to assess the data quality during the initial data analysis phase depends on the analyses that will be conducted in the main analysis phase.

在初始数据分析阶段，评估数据质量的分析方法的选择取决于将在主要分析阶段进行的分析。

Quality of measurements 测量的质量

The quality of the measurement instruments should only be checked during the initial data analysis phase when this is not the focus or research question of the study. One should check whether structure of measurement instruments corresponds to structure reported in the literature.

当测量仪器的质量不是研究的重点或研究问题的时候，它只能在初始数据分析阶段进行检验。从业者应该检查测量仪器的结构是否符合文献报告的结构。

There are two ways to assess measurement: [NOTE: only one way seems to be listed]

有两种方法来评估测量: [注意: 似乎只列出了一种方法]

Analysis of homogeneity (internal consistency), which gives an indication of the reliability of a measurement instrument. During this analysis, one inspects the variances of the items and the scales, the Cronbach's α of the scales, and the change in the Cronbach's alpha when an item would be deleted from a scale模板:Sfn

同质性检验（内部一致性internal consistency）用来表示测量仪器的可靠性Reliability。在这个分析过程中，我们会检查各个项目的变异和量尺刻度，量尺的克隆巴赫α系数 Cronbach’s alpha ，以及当一个项目从量尺上被删除时克隆巴赫α系数的变化。

Initial transformations初始的转换

After assessing the quality of the data and of the measurements, one might decide to impute missing data, or to perform initial transformations of one or more variables, although this can also be done during the main analysis phase.模板:Sfn

After assessing the quality of the data and of the measurements, one might decide to impute missing data, or to perform initial transformations of one or more variables, although this can also be done during the main analysis phase.

在对数据和测量的质量进行评估之后，从业者可能会决定填补缺失的数据，或者对一个或多个变量进行初始的转换initial transformations，尽管这也可以在主要分析阶段进行。

Possible transformations of variables are:^[22]

Possible transformations of variables are:

变量可能的转换如下:

Square root transformation (if the distribution differs moderately from normal)
平方根转换（如果数据分布与正态分布略有不同）

Log-transformation (if the distribution differs substantially from normal)
对数转换（如果数据分布与正态分布大不相同）

Inverse transformation (if the distribution differs severely from normal)
倒数转换（如果分布与正态分布严重不同）

Make categorical (ordinal / dichotomous) (if the distribution differs severely from normal, and no transformations help)
分类变量处理（顺序或二元变量）（如果分布与正态分布严重不同，且没有转换方法可以补救）

Did the implementation of the study fulfill the intentions of the research design? 研究的实施是否完成了研究设计的目的？

One should check the success of the randomization procedure, for instance by checking whether background and substantive variables are equally distributed within and across groups.

从业者应该检查随机化程序是否成功，例如通过检查背景变量background variables和实质变量substantive variables是否在组内和组间均匀分布。

If the study did not need or use a randomization procedure, one should check the success of the non-random sampling, for instance by checking whether all subgroups of the population of interest are represented in sample.

如果研究不需要或不使用随机化程序，则应检查非随机抽样是否成功，例如检查样本是否代表了相关总体的所有分组。

Other possible data distortions that should be checked are:

其他应该检查的可能的数据扭曲有:

dropout (this should be identified during the initial data analysis phase)

Item nonresponse (whether this is random or not should be assessed during the initial data analysis phase)

Treatment quality (using manipulation checks).模板:Sfn

数据遗失Dropout（这应该在初始数据分析阶段进行识别）

项目回收率Response rate（是否随机，应在初始数据分析阶段进行评估）

操纵质量Treatment quality （使用操纵检验manipulation check）模板:Sfn

Characteristics of data sample数据样本的特征

In any report or article, the structure of the sample must be accurately described. It is especially important to exactly determine the structure of the sample (and specifically the size of the subgroups) when subgroup analyses will be performed during the main analysis phase.

在任何报告或文章中，样本的结构必须被准确描述。在主要分析阶段进行子群subgroups分析时，准确确定样本的结构（特别是子群的大小）尤为重要。

The characteristics of the data sample can be assessed by looking at:

数据样本的特征可以通过以下几个方面进行评估:

Basic statistics of important variables
重要变量的基本统计学特征

Scatter plots
散点图

Correlations and associations
相关和联系

Cross-tabulations模板:Sfn
交叉表Cross-tabulations

Final stage of the initial data analysis 初始数据分析的最后阶段

During the final stage, the findings of the initial data analysis are documented, and necessary, preferable, and possible corrective actions are taken.

在最后阶段，从业者需要记录初始数据分析的结果，并采取必要的、可取的和可能的纠正措施。

Also, the original plan for the main data analyses can and should be specified in more detail or rewritten.
In order to do this, several decisions about the main data analyses can and should be made:

此外，主要数据分析的原始计划可以而且应该更详细地说明或重写。为了做到这一点，可以而且应该对主要数据分析作出以下几个决定:

In the case of non-normals: should one transform variables; make variables categorical (ordinal/dichotomous); adapt the analysis method?
在非正态分布的情况下，是否应该：有数据转换变量；使变量分类化（序列化/二分类）；改进分析方法？

In the case of missing data: should one neglect or impute the missing data; which imputation technique should be used?
在有缺失数据的情况下：是否应该忽视或插补缺失数据？应该使用哪种插补方法？

In the case of outliers: should one use robust analysis techniques?
在有异常值的情况下：是否应该使用稳健的分析技术？

In case items do not fit the scale: should one adapt the measurement instrument by omitting items, or rather ensure comparability with other (uses of the) measurement instrument(s)?
在项目和测量量尺不匹配的情况下：是否应省略项目以对测量仪器进行调整，还是应确保与其他（用途的）测量仪器具有可比性？

In the case of (too) small subgroups: should one drop the hypothesis about inter-group differences, or use small sample techniques, like exact tests or bootstrapping?
在具有（太）小的子群的情况下：是否应该放弃群体间差异的假设，或者使用小样本技术，比如精确检验exact tests或者bootstrapping？

In case the randomization procedure seems to be defective: can and should one calculate propensity scores and include them as covariates in the main analyses?模板:Sfn

在随机化程序似乎有缺陷的情况下：能够而且应该计算倾向分数propensity scores并将其作为协变量包括在主要分析中吗？

Analysis 分析

Several analyses can be used during the initial data analysis phase:模板:Sfn

Several analyses can be used during the initial data analysis phase:

在初始数据分析阶段可以使用以下几种分析:

Univariate statistics (single variable)
单变量统计学（单变量）

Bivariate associations (correlations)
双变量关联（相关）

Graphical techniques (scatter plots)
图表技术（散点图）

It is important to take the measurement levels of the variables into account for the analyses, as special statistical techniques are available for each level:模板:Sfn

It is important to take the measurement levels of the variables into account for the analyses, as special statistical techniques are available for each level:

在进行分析时必须考虑到变量的测量水平，因为每个水平都有专门的统计技术:

Nominal and ordinal variables
称名和顺序变量

- Frequency counts (numbers and percentages)
- 频数（数和百分比）

- Associations
- 相关

- - circumambulations (crosstabulations)
  - circumambulations （交叉表crosstabulations）

- - hierarchical loglinear analysis (restricted to a maximum of 8 variables)
  - 层次对数线性分析hierarchical loglinear analysis（最多只能有8个变量）

- - loglinear analysis (to identify relevant/important variables and possible confounders)
  - 对数线性分析 loglinear analysis（确定相关/重要的变量及可能的混淆因素）

- Exact tests or bootstrapping (in case subgroups are small)
- 精确检验exact tests或者bootstrapping（当子群很小时）

- Computation of new variables
- 计算新变量

Continuous variables
连续变量

- Distribution
- 分布

- - Statistics (M, SD, variance, skewness, kurtosis)
  - 统计学量（均值M，标准差SD，方差，偏度，峰度）

- - Stem-and-leaf displays
  - 茎叶图Stem-and-leaf displays

- - Box plots
  - 箱图Box plots

Nonlinear analysis非线性分析

Nonlinear analysis is often necessary when the data is recorded from a nonlinear system. Nonlinear systems can exhibit complex dynamic effects including bifurcations, chaos, harmonics and subharmonics that cannot be analyzed using simple linear methods. Nonlinear data analysis is closely related to nonlinear system identification.^[23]

Nonlinear analysis is often necessary when the data is recorded from a nonlinear system. Nonlinear systems can exhibit complex dynamic effects including bifurcations, chaos, harmonics and subharmonics that cannot be analyzed using simple linear methods. Nonlinear data analysis is closely related to nonlinear system identification.

非线性分析Nonlinear analysis通常在数据是从非线性系统中获取的时候是必要的。非线性系统可以表现出复杂的动力学效应，包括分岔bifurcations、混沌chaos、谐波harmonics和次谐波subharmonics，这些效应不能用简单的线性方法进行分析。非线性数据分析与非线性系统辨识密切相关。

Main data analysis 主要数据分析

In the main analysis phase analyses aimed at answering the research question are performed as well as any other relevant analysis needed to write the first draft of the research report.模板:Sfn

In the main analysis phase analyses aimed at answering the research question are performed as well as any other relevant analysis needed to write the first draft of the research report.

主要分析阶段进行旨在回答研究问题的分析，以及撰写研究报告初稿所需的其他相关分析。

Exploratory and confirmatory approaches探索性和验证性方法

In the main analysis phase either an exploratory or confirmatory approach can be adopted. Usually the approach is decided before data is collected. In an exploratory analysis no clear hypothesis is stated before analysing the data, and the data is searched for models that describe the data well. In a confirmatory analysis clear hypotheses about the data are tested.

在主要的分析阶段，可以采用探索性或验证性的方法。通常方法是在收集数据之前决定的。探索性分析中，分析数据之前没有明确的假设，分析人员搜索能够很好地描述数据的模型。验证性分析对数据进行明确的假设检验。

Exploratory data analysis should be interpreted carefully. When testing multiple models at once there is a high chance on finding at least one of them to be significant, but this can be due to a type 1 error. It is important to always adjust the significance level when testing multiple models with, for example, a Bonferroni correction. Also, one should not follow up an exploratory analysis with a confirmatory analysis in the same dataset. An exploratory analysis is used to find ideas for a theory, but not to test that theory as well. When a model is found exploratory in a dataset, then following up that analysis with a confirmatory analysis in the same dataset could simply mean that the results of the confirmatory analysis are due to the same type 1 error that resulted in the exploratory model in the first place. The confirmatory analysis therefore will not be more informative than the original exploratory analysis.模板:Sfn

Exploratory data analysis should be interpreted carefully. When testing multiple models at once there is a high chance on finding at least one of them to be significant, but this can be due to a type 1 error. It is important to always adjust the significance level when testing multiple models with, for example, a Bonferroni correction. Also, one should not follow up an exploratory analysis with a confirmatory analysis in the same dataset. An exploratory analysis is used to find ideas for a theory, but not to test that theory as well. When a model is found exploratory in a dataset, then following up that analysis with a confirmatory analysis in the same dataset could simply mean that the results of the confirmatory analysis are due to the same type 1 error that resulted in the exploratory model in the first place. The confirmatory analysis therefore will not be more informative than the original exploratory analysis.

对探索性数据分析的解释应该非常谨慎。当同时测试多个模型时，发现其中至少一个模型具有统计学意义显著的几率很高，但这可能是由于 Ⅰ 类错误。在测试多个模型时，总是调整显著性水平很重要，例如，使用Bonferroni校正。另外，不应该在同一数据集中进行探索性分析后进行验证性分析。one should not follow up an exploratory analysis with a confirmatory analysis in the same dataset. 探索性分析是用来为一个理论寻找想法，但不是用来检验这个理论的。当一个数据集中使用探索性分析发现了一个模型，然后在同一个数据集中进行验证性分析，这可能仅仅意味着验证性分析的结果首先是由于和探索性分析中同样的 Ⅰ 类错误而导致的。因此，验证性分析不会比最初的探索性分析更有用。

Stability of results 结果的稳定性

It is important to obtain some indication about how generalizable the results are.模板:Sfn While this is often difficult to check, one can look at the stability of the results. Are the results reliable and reproducible? There are two main ways of doing that.

It is important to obtain some indication about how generalizable the results are. While this is often difficult to check, one can look at the stability of the results. Are the results reliable and reproducible? There are two main ways of doing that.

得到一些说明这些结果有多么普遍的指标是重要的。虽然普遍性通常很难检验，但可以表示结果的稳定性的一些信息。有两种主要的方法来保证结果的可靠和可重复性。

Cross-validation. By splitting the data into multiple parts, we can check if an analysis (like a fitted model) based on one part of the data generalizes to another part of the data as well. Cross-validation is generally inappropriate, though, if there are correlations within the data, e.g. with panel data. Hence other methods of validation sometimes need to be used. For more on this topic, see statistical model validation.
交叉验证Cross-validation。通过将数据分成多个部分，我们可以检查基于一部分数据的分析（如拟合模型）是否也可以推广到另一部分数据。不过如果数据内部（例如与面板数据panel data）存在相关性，那么交叉验证通常是不适当的。因此，有时需要使用其他验证方法。有关此主题的更多信息，请参阅统计模型验证statistical model validation。

Sensitivity analysis. A procedure to study the behavior of a system or model when global parameters are (systematically) varied. One way to do that is via bootstrapping.
敏感度分析Sensitivity analysis。一种在全局变量（系统地）变化时研究系统或模型的行为的程序。一种方法是通过 Bootstrapping 方法。

Free software for data analysis数据分析的免费软件

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Notable free software for data analysis include:

著名的数据分析免费软件包括:

DevInfo – a database system endorsed by the United Nations Development Group for monitoring and analyzing human development.

ELKI – data mining framework in Java with data mining oriented visualization functions.

KNIME – the Konstanz Information Miner, a user friendly and comprehensive data analytics framework.

Orange – A visual programming tool featuring interactive data visualization and methods for statistical data analysis, data mining, and machine learning.

Pandas – Python library for data analysis

PAW – FORTRAN/C data analysis framework developed at CERN

R – a programming language and software environment for statistical computing and graphics.

ROOT – C++ data analysis framework developed at CERN

SciPy – Python library for data analysis

Data.Analysis – A .NET library for data analysis and transformation

DevInfo -联合国发展集团United Nations Development Group认可的用于监测和分析人类发展的数据库系统。

ELKI -面向数据挖掘的可视化功能的 Java 数据挖掘框架。

KNIME -Konstanz Information Miner，一个用户友好和综合的数据分析框架。

Orange -可视化编程工具，具有交互式数据可视化interactive data visualization、数据可视化data visualization和统计数据分析方法、数据挖掘data mining和机器学习 machine learning的特点。

pandas-用于数据分析的 Python 库

物理学分析工作站Physics Analysis Workstation(PAW)- CERN 开发的 FORTRAN/C 数据分析框架。

R -用于统计计算和图形处理的编程语言和软件环境。

ROOT - CERN ]开发的 C++ 数据分析框架

SciPy -用于数据分析的 Python 库

International data analysis contests国际性的数据分析比赛

Different companies or organizations hold a data analysis contests to encourage researchers utilize their data or to solve a particular question using data analysis. A few examples of well-known international data analysis contests are as follows.

不同的公司或组织纷纷举办数据分析竞赛，以鼓励研究人员利用他们的数据，或利用其数据分析技能解决特定的问题。以下是一些著名的国际数据分析比赛的例子。

Kaggle competition held by Kaggle^[24]

由 Kaggle 举办的Kaggle 竞赛。

LTPP data analysis contest held by FHWA and ASCE.^[25]^[26]

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由 FHWA 和 ASCE 举办的 LTPP 国际数据分析竞赛。

References 参考文献

Citations 引用

↑ Xia, B. S., & Gong, P. (2015). Review of business intelligence through data analysis. Benchmarking, 21(2), 300-311. doi:10.1108/BIJ-08-2012-0050
↑ John Tukey-The Future of Data Analysis-July 1961
↑ ^3.0 ^3.1 ^3.2 ^3.3 ^3.4 ^3.5 引用错误：无效<ref>标签；未给name属性为Schutt & O'Neil的引用提供文字
↑ "Data Cleaning". Microsoft Research. Retrieved 26 October 2013.
↑ ^5.0 ^5.1 ^5.2 ^5.3 Perceptual Edge-Jonathan Koomey-Best practices for understanding quantitative data-February 14, 2006
↑ Hellerstein, Joseph (27 February 2008). "Quantitative Data Cleaning for Large Databases" (PDF). EECS Computer Science Division: 3. Retrieved 26 October 2013.
↑ Stephen Few-Perceptual Edge-Selecting the Right Graph For Your Message-September 2004
↑ Behrens-Principles and Procedures of Exploratory Data Analysis-American Psychological Association-1997
↑ ^9.0 ^9.1 引用错误：无效<ref>标签；未给name属性为Judd and McClelland 1989的引用提供文字
↑ Grandjean, Martin (2014). "La connaissance est un réseau" (PDF). Les Cahiers du Numérique. 10 (3): 37–54. doi:10.3166/lcn.10.3.37-54.
↑ Stephen Few-Perceptual Edge-Selecting the Right Graph for Your Message-2004
↑ Stephen Few-Perceptual Edge-Graph Selection Matrix
↑ Robert Amar, James Eagan, and John Stasko (2005) "Low-Level Components of Analytic Activity in Information Visualization"
↑ William Newman (1994) "A Preliminary Analysis of the Products of HCI Research, Using Pro Forma Abstracts"
↑ Mary Shaw (2002) "What Makes Good Research in Software Engineering?"
↑ ^16.0 ^16.1 "ConTaaS: An Approach to Internet-Scale Contextualisation for Developing Efficient Internet of Things Applications". ScholarSpace. HICSS50. Retrieved May 24, 2017.
↑ "Congressional Budget Office-The Budget and Economic Outlook-August 2010-Table 1.7 on Page 24" (PDF). Retrieved 2011-03-31.
↑ "Introduction". cia.gov.
↑ Bloomberg-Barry Ritholz-Bad Math that Passes for Insight-October 28, 2014
↑ Aarons, D. (2009). Report finds states on course to build pupil-data systems. Education Week, 29(13), 6.
↑ Rankin, J. (2013, March 28). How data Systems & reports can either fight or propagate the data analysis error epidemic, and how educator leaders can help. Presentation conducted from Technology Information Center for Administrative Leadership (TICAL) School Leadership Summit.
↑ Tabachnick & Fidell, 2007, p. 87-88.
↑ Billings S.A. "Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains". Wiley, 2013
↑ "The machine learning community takes on the Higgs". Symmetry Magazine. July 15, 2014. Retrieved 14 January 2015.
↑ Nehme, Jean (September 29, 2016). "LTPP International Data Analysis Contest". Federal Highway Administration. Retrieved October 22, 2017.
↑ "Data.Gov:Long-Term Pavement Performance (LTPP)". May 26, 2016. Retrieved November 10, 2017.

Bibliography 自传

Adèr, Herman J. (2008a). "Chapter 14: Phases and initial steps in data analysis". Advising on research methods : a consultant's companion. Huizen, Netherlands: Johannes van Kessel Pub. pp. 333–356. ISBN 9789079418015. OCLC 905799857.

Adèr, Herman J. (2008b). "Chapter 15: The main analysis phase". Advising on research methods : a consultant's companion. Huizen, Netherlands: Johannes van Kessel Pub. pp. 357–386. ISBN 9789079418015. OCLC 905799857.

Tabachnick, B.G. & Fidell, L.S. (2007). Chapter 4: Cleaning up your act. Screening data prior to analysis. In B.G. Tabachnick & L.S. Fidell (Eds.), Using Multivariate Statistics, Fifth Edition (pp. 60–116). Boston: Pearson Education, Inc. / Allyn and Bacon.