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Data analysis is a process of inspecting, cleansing, transforming, and
modelling In general, a model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. ...
data Data (; ) are individual facts A fact is something that is truth, true. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to experience. Standard reference works are often used ...

data
with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, and is used in different business, science, and social science domains. In today's business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively.
Data mining Data mining is a process of extracting and discovering patterns in large data set A data set (or dataset) is a collection of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...
is a particular data analysis technique that focuses on statistical modelling and knowledge discovery for predictive rather than purely descriptive purposes, while
business intelligence Business intelligence (BI) comprises the strategies and technologies used by enterprises for the data analysis Data analysis is a process of inspecting, cleansing, transforming, and modelling In general, a model is an informative representat ...
covers data analysis that relies heavily on aggregation, focusing mainly on business information. In statistical applications, data analysis can be divided into
descriptive statistics A descriptive statistic (in the count noun In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The trad ...
,
exploratory data analysis In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a mor ...
(EDA), and
confirmatory data analysis A statistical hypothesis is a hypothesis that is testable on the basis of Observable variable, observed data statistical model, modelled as the realised values taken by a collection of random variables. A set of data is modelled as being realised ...
(CDA). EDA focuses on discovering new features in the data while CDA focuses on confirming or falsifying existing
hypotheses A hypothesis (plural hypotheses) is a proposed explanation An explanation is a set of statements Statement or statements may refer to: Common uses *Statement (computer science)In computer programming Computer programming is the proce ...

hypotheses
.
Predictive analytics Predictive analytics encompasses a variety of statistics, statistical techniques from data mining, predictive modelling, and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events. ...
focuses on the application of statistical models for predictive forecasting or classification, while
text analytics Text mining, also referred to as ''text data mining'', similar to text analytics, is the process of deriving high-quality information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity i ...
applies statistical, linguistic, and structural techniques to extract and classify information from textual sources, a species of
unstructured data Unstructured data (or unstructured information) is information that either does not have a pre-defined data model A data model (or datamodel) is an abstract model that organizes elements of data and standardizes how they relate to one another and ...
. All of the above are varieties of data analysis.
Data integration Data integration involves combining data Data (; ) are individual facts A fact is something that is truth, true. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to experienc ...

Data integration
is a precursor to data analysis, and data analysis is closely linked to
data visualization Data visualization (often abbreviated data viz) is an interdisciplinary field that deals with the Graphics, graphic Representation (arts), representation of data. It is a particularly efficient way of communicating when the data is numerous as ...
and data dissemination.


The process of data analysis

''Analysis'', refers to dividing a whole into its separate components for individual examination. ''Data analysis'', is a
process A process is a series or set of activities that interact to produce a result; it may occur once-only or be recurrent or periodic. Things called a process include: Business and management *Business process A business process, business method ...
for obtaining
raw data Raw data, also known as primary data, are ''data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sense, data are a set of values of qualitative property, qualitative or quantity, qua ...
, and subsequently converting it into information useful for decision-making by users. ''Data'', is collected and analyzed to answer questions, test hypotheses, or disprove theories. Statistician
John Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ...
, defined data analysis in 1961, as:
"Procedures for analyzing data, techniques for interpreting the results of such procedures, ways of planning the gathering of data to make its analysis easier, more precise or more accurate, and all the machinery and results of (mathematical) statistics which apply to analyzing data."
There are several phases that can be distinguished, described below. The phases are
iterative Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...
, in that feedback from later phases may result in additional work in earlier phases. The CRISP framework, used in
data mining Data mining is a process of extracting and discovering patterns in large data set A data set (or dataset) is a collection of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...
, has similar steps.


Data requirements

The data is necessary as inputs to the analysis, which is specified based upon the requirements of those directing the analysis (or customers, who will use the finished product of the analysis). The general type of entity upon which the data will be collected is referred to as an
experimental unit In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with ...
(e.g., a person or population of people). Specific variables regarding a population (e.g., age and income) may be specified and obtained. Data may be numerical or categorical (i.e., a text label for numbers).


Data collection

Data is collected from a variety of sources. The requirements may be communicated by analysts to custodians of the data; such as, Information Technology personnel within an organization. The data may also be collected from sensors in the environment, including traffic cameras, satellites, recording devices, etc. It may also be obtained through interviews, downloads from online sources, or reading documentation.


Data processing

Data, when initially obtained, must be processed or organized for analysis. For instance, these may involve placing data into rows and columns in a table format (''known as''
structured data A data model (or datamodel) is an abstract model that organizes elements of data and standardizes how they relate to one another and to the properties of real-world entities. For instance, a data model may specify that the data element representing ...

structured data
) for further analysis, often through the use of spreadsheet or statistical software.


Data cleaning

Once processed and organized, the data may be incomplete, contain duplicates, or contain errors. The need for ''data cleaning'' will arise from problems in the way that the datum 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 that are believed to be reliable.Perceptual Edge-Jonathan Koomey-Best practices for understanding quantitative data-February 14, 2006
/ref> Unusual amounts, above or below predetermined thresholds, may also be reviewed. There are several types of data cleaning, that are dependent upon the type of data in the set; this could be phone numbers, email addresses, employers, or other values. Quantitative data methods for outlier detection, can be used to get rid of data that appears to have a higher likelihood of being input incorrectly. Textual data spell checkers can be used to lessen the amount of mis-typed words. However, it is harder to tell if the words themselves are correct.


Exploratory data analysis

Once the datasets are cleaned, they can then be analyzed. Analysts may apply a variety of techniques, referred to as
exploratory data analysis In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a mor ...
, to begin understanding the messages contained within the obtained data. The process of data exploration may result in additional data cleaning or additional requests for data; thus, the initialization of the ''iterative phases'' mentioned in the lead paragraph of this section.
Descriptive statistics A descriptive statistic (in the count noun In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The trad ...
, such as, the average or median, can be generated to aid in understanding the data.
Data visualization Data visualization (often abbreviated data viz) is an interdisciplinary field that deals with the Graphics, graphic Representation (arts), representation of data. It is a particularly efficient way of communicating when the data is numerous as ...
is also a technique used, in which the analyst is able to examine the data in a graphical format in order to obtain additional insights, regarding the messages within the data.


Modelling and algorithms

Mathematical formulas or models (known as
algorithms In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ...
), may be applied to the data in order to identify relationships among the variables; for example, using
correlation In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a m ...
or causation. In general terms, models may be developed to evaluate a specific variable based on other variable(s) contained within the dataset, with some '' residual error'' depending on the implemented model's accuracy (''e.g.'', Data = Model + Error).
Inferential statistics Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution, distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical ...
, includes utilizing techniques that measure the relationships between particular variables. For example,
regression analysis In statistical model A statistical model is a mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a u ...
may be used to model whether a change in advertising (''independent variable X''), provides an explanation for the variation in sales (''dependent variable Y''). In mathematical terms, ''Y'' (sales) is a function of ''X'' (advertising). It may be described as (''Y'' = ''aX'' + ''b'' + error), where the model is designed such that (''a'') and (''b'') minimize the error when the model predicts ''Y'' for a given range of values of ''X''. Analysts may also attempt to build models that are descriptive of the data, in an aim to simplify analysis and communicate results.


Data product

A data product is a computer application that takes ''data inputs'' and generates ''outputs'', feeding them back into the environment. It may be based on a model or algorithm. For instance, an application that analyzes data about customer purchase history, and uses the results to recommend other purchases the customer might enjoy.


Communication

Once data is 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. When determining how to communicate the results, the analyst may consider implementing a variety of data visualization techniques to help communicate the message more clearly and efficiently to the audience. Data visualization uses information displays (graphics such as, tables and charts) to help communicate key messages contained in the data.
Tables Table may refer to: * Table (information) A table is an arrangement of information or data, typically in rows and columns, or possibly in a more complex structure. Tables are widely used in communication, research, and data analysis. Tables ap ...
are a valuable tool by enabling the ability of a user to query and focus on specific numbers; while charts (e.g., bar charts or line charts), may help explain the quantitative messages contained in the data.


Quantitative messages

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. #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 A line chart or line plot or line graph or curve chart is a type of chart A chart is a graphical representation Graphic communication as the name suggests is communication using graphic elements. These elements include symbols such as glyp ...

line chart
may be used to demonstrate the trend. #Ranking: Categorical subdivisions are ranked in ascending or descending order, such as a ranking of sales performance (the ''measure'') by salespersons (the ''category'', with each salesperson a ''categorical subdivision'') during a single period. A
bar chart A bar chart or bar graph is a chart or graph that presents Categorical variable, categorical data with Rectangle, rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizo ...

bar chart
may be used to show the comparison across the salespersons. #Part-to-whole: Categorical subdivisions are measured as a ratio to the whole (i.e., a percentage out of 100%). A
pie chart A pie chart (or a circle chart) is a circular Statistical graphics, statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area ...

pie chart
or bar chart can show the comparison of ratios, such as the market share represented by competitors in a market. #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 the comparison of the actual versus the reference amount. #Frequency distribution: Shows the number of observations of a particular variable for a 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 histogram is an approximate representation of the distributionDistribution may refer to: Mathematics *Distribution (mathematics) Distributions, also known as Schwartz distributions or generalized functions, are objects that generaliz ...

histogram
, a type of bar chart, may be used for this analysis. #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 A scatter plot (also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram) is a type of plot Plot or Plotting may refer to: Art, media and entertainment * Plot (narrative), the story of a piece of fiction Mus ...

scatter plot
is typically used for this message. #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. #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 A cartogram (also called a value-area map or an anamorphic map, the latter common among German-speakers) is a thematic map upright=1.15, Isarithmic map of minimum temperature used as plant hardiness zones. A thematic map is a type of map that ...
is a typical graphic used.


Techniques for analyzing quantitative data

Author Jonathan Koomey has recommended a series of best practices for understanding quantitative data. These include: *Check raw data for anomalies prior to performing an analysis; *Re-perform important calculations, such as verifying columns of data that are formula driven; *Confirm main totals are the sum of subtotals; *Check relationships between numbers that should be related in a predictable way, such as ratios over time; *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; *Break problems into component parts by analyzing factors that led to the results, such as
DuPont analysis 400px, Graphical representation of DuPont analysis. DuPont analysis (also known as the DuPont identity, DuPont equation, DuPont framework, DuPont model or the DuPont method) is an expression which breaks ROE (return on equityThe return on equity (RO ...
of return on equity. For the variables under examination, analysts typically obtain
descriptive statistics A descriptive statistic (in the count noun In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The trad ...
for them, such as the mean (average),
median In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a m ...

median
, and
standard deviation In statistics, the standard deviation is a measure of the amount of variation or statistical dispersion, dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected v ...

standard deviation
. They may also analyze the
distributionDistribution may refer to: Mathematics *Distribution (mathematics) Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distr ...
of the key variables to see how the individual values cluster around the mean. The consultants at
McKinsey and Company McKinsey & Company is an American worldwide management consulting Management consulting is the practice of helping organization An organization, or organisation ( Commonwealth English; see spelling differences), is an entity – such a ...
named a technique for breaking a quantitative problem down into its component parts called the
MECE principle The MECE principle, (mutually exclusive and collectively exhaustive) pronounced by many as "ME-see", and pronounced by the author as "Meese" like Greece or niece, is a grouping principle for separating a set of items into subsets that are mutually e ...
. Each layer can be broken down into its components; each of the sub-components must be
mutually exclusive In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, ...
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 the revenue of divisions A, B, and C (which are mutually exclusive of each other) and should add to the total revenue (collectively exhaustive). Analysts may use robust statistical measurements to solve certain analytical problems.
Hypothesis testing A statistical hypothesis test is a method of statistical inference Statistical inference is the process of using data analysis Data analysis is a process of inspecting, Data cleansing, cleansing, Data transformation, transforming, and Data ...
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 The Phillips curve is a single-equation economic model, named after William Phillips (economist), William Phillips, hypothesizing an inverse relationship between rates of unemployment and corresponding rates of rises in wages that result within ...

Phillips Curve
. Hypothesis testing involves considering the likelihood of
Type I and type II errors In statistical hypothesis testing A statistical hypothesis test is a method of statistical inference used to determine a possible conclusion from two different, and likely conflicting, hypotheses. In a statistical hypothesis test, a null hypot ...
, which relate to whether the data supports accepting or rejecting the hypothesis.
Regression analysis In statistical model A statistical model is a mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a u ...
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.
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.


Analytical activities of data users

Users may have particular data points of interest within a data set, as opposed to the 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.


Barriers to effective analysis

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.


Confusing fact and opinion

Effective analysis requires obtaining relevant
fact A fact is something that is true True most commonly refers to truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things ...
s to answer questions, support a conclusion or formal
opinion An opinion is a judgement Judgement (or US spelling judgment) is also known as ''adjudication'' which means the evaluation of evidence to make a decision. Judgement is also the ability to make considered decisions. The term has four dist ...

opinion
, or test
hypotheses A hypothesis (plural hypotheses) is a proposed explanation An explanation is a set of statements Statement or statements may refer to: Common uses *Statement (computer science)In computer programming Computer programming is the proce ...

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 The Congressional Budget Office (CBO) is a federal agency within the legislative branch A legislature is a deliberative assembly A deliberative assembly is a gathering of members (of any kind of collective) who use parliamentary procedure ...

Congressional Budget Office
(CBO) estimated that extending the
Bush tax cuts The phrase Bush tax cuts refers to changes to the United States tax code passed originally during the presidency of George W. Bush George W. Bush's tenure as the List of presidents of the United States, 43rd president of the United States b ...
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. 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.


Cognitive biases

There are a variety of
cognitive bias A cognitive bias is a systematic pattern of deviation from norm (philosophy), norm or rationality in judgment. Individuals create their own "subjective reality" from their perception of the input. An individual's construction of reality, not the O ...
es that can adversely affect analysis. For example,
confirmation bias Confirmation bias is the tendency to search for, interpret, favor, and recall information in a way that confirms or supports one's prior belief A belief is an attitude Attitude may refer to: Philosophy and psychology * Attitude (psycholo ...
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. 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.


Innumeracy

Effective analysts are generally adept with a variety of numerical techniques. However, audiences may not have such literacy with numbers or
numeracy Numeracy is the ability to reason and to apply simple numerical concepts. Basic numeracy skills consist of comprehending fundamental arithmetical operations like addition, subtraction, multiplication, and division. For example, if one can unders ...
; they are said to be innumerate. Persons communicating the data may also be attempting to mislead or misinform, deliberately using bad numerical techniques. 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. Analysts may also analyze data under different assumptions or scenario. For example, when analysts perform
financial statement analysis Financial statement analysis (or financial analysis) is the process of reviewing and analyzing a company's financial statement Financial statements (or financial reports) are formal records of the financial activities and position of a business ...
, 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.


Other topics


Smart buildings

A data analytics approach can be used in order to predict energy consumption in buildings. The different steps of the data analysis process are carried out in order to realise smart buildings, where the building management and control operations including heating, ventilation, air conditioning, lighting and security are realised automatically by miming the needs of the building users and optimising resources like energy and time.


Analytics and business intelligence

Analytics is the "extensive use of data, statistical and quantitative analysis, explanatory and predictive models, and fact-based management to drive decisions and actions." It is a subset of
business intelligence Business intelligence (BI) comprises the strategies and technologies used by enterprises for the data analysis Data analysis is a process of inspecting, cleansing, transforming, and modelling In general, a model is an informative representat ...
, which is a set of technologies and processes that uses data to understand and analyze business performance to drive decision-making .


Education

In
education Education is the process of facilitating learning, or the acquisition of knowledge, skills, value (ethics), values, morals, beliefs, habits, and personal development. Educational methods include teaching, training, storytelling, discussion ...

education
, most educators have access to a
data system Data system is a term used to refer to an organized collection of symbols A symbol is a mark, sign, or word In linguistics, a word of a spoken language can be defined as the smallest sequence of phonemes that can be uttered in isolation with ...
for the purpose of analyzing student data. These data systems present data to educators in an over-the-counter data format (embedding labels, supplemental documentation, and a help system and making key package/display and content decisions) to improve the accuracy of educators’ data analyses.


Practitioner notes

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


Initial data analysis

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:


Quality of data

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), normal
imputationImputation can refer to: *Imputation (law) {{Other uses of, imputation, Imputation (disambiguation) In law, the principle of imputation or attribution underpins the concept that '' ignorantia juris non excusat''— ignorance of the law does not exc ...
is needed. *Analysis of : outlying observations in the data are analyzed to see if they seem to disturb the distribution. *Comparison and correction of differences in coding schemes: variables are compared with coding schemes of variables external to the data set, and possibly corrected if coding schemes are not comparable. *Test for 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.


Quality of measurements

The quality of the 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. There are two ways to assess measurement quality: *Confirmatory factor analysis *Analysis of homogeneity (
internal consistencyIn statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a ...
), which gives an indication of the
reliability Reliability, reliable, or unreliable may refer to: Science, technology, and mathematics Computing * Data reliability (disambiguation), Data reliability, a property of some disk arrays in computer storage * High availability * Reliability (computer ...
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


Initial transformations

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.
Possible transformations of variables are: *Square root transformation (if the distribution differs moderately from normal) *Log-transformation (if the distribution differs substantially from normal) *Inverse transformation (if the distribution differs severely from normal) *Make categorical (ordinal / dichotomous) (if the distribution differs severely from normal, and no transformations help)


Did the implementation of the study fulfill the intentions of the research design?

One should check the success of the
randomization Randomization is the process of making something random In common parlance, randomness is the apparent or actual lack of pattern A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of ...
procedure, for instance by checking whether background and substantive variables are equally distributed within and across groups.
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.
Other possible data distortions that should be checked are: * dropout (this should be identified during the initial data analysis phase) *Item non-response (whether this is random or not should be assessed during the initial data analysis phase) *Treatment quality (using manipulation checks).


Characteristics of data sample

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.
The characteristics of the data sample can be assessed by looking at: *Basic statistics of important variables *Scatter plots *Correlations and associations *Cross-tabulations


Final stage of the initial data analysis

During the final stage, the findings of the initial data analysis are documented, and necessary, preferable, and possible corrective actions are taken.
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: *In the case of non-s: should one
transform Transform may refer to: Arts and entertainment *Transform (Powerman 5000 album), ''Transform'' (Powerman 5000 album), 2003 *Transform (Rebecca St. James album), ''Transform'' (Rebecca St. James album), 2000 *Transform (scratch), a type of scratc ...
variables; make variables categorical (ordinal/dichotomous); adapt the analysis method? *In the case of
missing data In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more ...
: should one neglect or impute the missing data; which imputation technique should be used? *In the case of
outlier In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a ...

outlier
s: should one use robust analysis techniques? *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)? *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 In general, bootstrapping usually refers to a self-starting process that is supposed to continue or grow without external input. Etymology Tall boot A boot, plural boots, is a type of specific footwear Footwear refers to garments wor ...
? *In case the
randomization Randomization is the process of making something random In common parlance, randomness is the apparent or actual lack of pattern A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of ...
procedure seems to be defective: can and should one calculate propensity scores and include them as covariates in the main analyses?


Analysis

Several analyses can be used during the initial data analysis phase: *Univariate statistics (single variable) *Bivariate associations (correlations) *Graphical techniques (scatter plots) 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: *Nominal and ordinal variables **Frequency counts (numbers and percentages) **Associations ***circumambulations (crosstabulations) ***hierarchical loglinear analysis (restricted to a maximum of 8 variables) ***loglinear analysis (to identify relevant/important variables and possible confounders) **Exact tests or bootstrapping (in case subgroups are small) **Computation of new variables *Continuous variables **Distribution ***Statistics (M, SD, variance, skewness, kurtosis) ***Stem-and-leaf displays ***Box plots


Nonlinear analysis

Nonlinear analysis is often necessary when the data is recorded from a
nonlinear system In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...
. Nonlinear systems can exhibit complex dynamic effects including bifurcations,
chaos Chaos or CHAOS may refer to: Arts, entertainment and media Fictional elements * Chaos (Kinnikuman), Chaos (''Kinnikuman'') * Chaos (Sailor Moon), Chaos (''Sailor Moon'') * Chaos (Sesame Park), Chaos (''Sesame Park'') * Chaos (Warhammer), Chaos ('' ...
,
harmonics A harmonic is any member of the harmonic series Harmonic series may refer to either of two related concepts: *Harmonic series (mathematics) *Harmonic series (music) {{Disambig .... The term is employed in various disciplines, including music ...

harmonics
and
subharmonics In music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General include common elements such as (which governs and ), (and its associated con ...
that cannot be analyzed using simple linear methods. Nonlinear data analysis is closely related to
nonlinear system identification System identification The field of system identification uses statistical methods to build mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that ac ...
.Billings S.A. "Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains". Wiley, 2013


Main data analysis

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.


Exploratory and confirmatory approaches

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.
Exploratory data analysis In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a mor ...
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 Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * Typ ...

type 1 error
. It is important to always adjust the significance level when testing multiple models with, for example, a
Bonferroni correction In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with ...
. 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 Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * Typ ...

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.


Stability of results

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. * '' 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 In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more ...
. Hence other methods of validation sometimes need to be used. For more on this topic, see
statistical model validation In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more ...
. * ''
Sensitivity analysis Sensitivity analysis is the study of how the uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already ...
''. 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 In general, bootstrapping usually refers to a self-starting process that is supposed to continue or grow without external input. Etymology Tall boot A boot, plural boots, is a type of specific footwear Footwear refers to garments wor ...
.


Free software for data analysis

Notable free software for data analysis include: * DevInfo – A database system endorsed by the
United Nations Development Group The United Nations Sustainable Development Group (UNSDG), previously the United Nations Development Group (UNDG), is a consortium of 36 United Nations The United Nations (UN) is an intergovernmental organization that aims to maintain inte ...
for monitoring and analyzing human development. *
ELKI ELKI (for ''Environment for DeveLoping KDD-Applications Supported by Index-Structures'') is a data mining (KDD, knowledge discovery in databases) software framework In computer programming, a software framework is an abstraction (computer scien ...
– Data mining framework in Java with data mining oriented visualization functions. *
KNIME KNIME (), the Konstanz Information Miner, is a free and open-source Free and open-source software (FOSS) is software that is both free software and open-source software where anyone is free software license, freely licensed to use, copy, study ...

KNIME
– The Konstanz Information Miner, a user friendly and comprehensive data analytics framework. *
Orange Orange most often refers to: *Orange (colour), occurs between red and yellow in the visible spectrum *Orange (fruit), the fruit of the tree species '' Citrus'' × ''sinensis'' ** Orange blossom, its fragrant flower *Some other citrus or citrus-li ...
– A visual programming tool featuring
interactive data visualization Data visualization (often abbreviated ''data viz'') is an interdisciplinary field that deals with the graphic Graphics (from Greek ''graphikos'', "belonging to drawing") are visual images or designs on some surface, such as a wall, canvas, ...
and methods for statistical data analysis,
data mining Data mining is a process of extracting and discovering patterns in large data set A data set (or dataset) is a collection of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...
, and
machine learning Machine learning (ML) is the study of computer algorithms that can improve automatically through experience and by the use of data. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data ...

machine learning
. *
Pandas Pediatric autoimmune neuropsychiatric disorders associated with streptococcal infections (PANDAS) is a hypothesis that there exists a subset of children with rapid onset of obsessive-compulsive disorder (OCD) or tic disorders and these symptom ...
– Python library for data analysis. *
PAW A paw is the soft foot-like part of a mammal Mammals (from Latin language, Latin , 'breast') are a group of vertebrate animals constituting the class (biology), class Mammalia (), and characterized by the presence of mammary glands which i ...
– FORTRAN/C data analysis framework developed at
CERN The European Organization for Nuclear Research (french: Organisation européenne pour la recherche nucléaire), known as CERN (; ; derived from the name ), is a Europe Europe is a continent A continent is any of several large la ...
. * R – A programming language and software environment for statistical computing and graphics. *
ROOT In vascular plant Vascular plants (from Latin ''vasculum'': duct), also known as Tracheophyta (the tracheophytes , from Greek τραχεῖα ἀρτηρία ''trācheia artēria'' 'windpipe' + φυτά ''phutá'' 'plants'), form a large grou ...

ROOT
– C++ data analysis framework developed at
CERN The European Organization for Nuclear Research (french: Organisation européenne pour la recherche nucléaire), known as CERN (; ; derived from the name ), is a Europe Europe is a continent A continent is any of several large la ...
. *
SciPy SciPy (pronounced "sigh pie") is a free and open-source Free and open-source software (FOSS) is software Software is a collection of instructions Instruction or instructions may refer to: Computing * Instruction, one operation of a p ...
– Python library for data analysis. *
Julia Julia is usually a feminine given name. It is a Latinate feminine form of the name Julio (given name), Julio and Julius. (For further details on etymology, see wikt:Iulius#Latin, Wiktionary entry “Julius”.) The given name ''Julia'' had been ...
- A programming language well-suited for numerical analysis and computational science.


International data analysis contests

Different companies or organizations hold data analysis contests to encourage researchers to 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: * Kaggle competition, which is held by
Kaggle Kaggle, a subsidiary of Google LLC Google LLC is an American Multinational corporation, multinational technology company that specializes in Internet-related services and products, which include online advertising, online advertising ...
. * LTPP data analysis contest held by
FHWA The Federal Highway Administration (FHWA) is a division of the United States Department of Transportation The United States Department of Transportation (USDOT or DOT) is a federal Cabinet Cabinet or The Cabinet may refer to: Furniture ...
and
ASCE The American Society of Civil Engineers (ASCE) is a 501(c)(3), tax-exempt professional body founded in 1852 to represent members of the civil engineering profession worldwide. Headquartered in Reston, Virginia, it is the oldest national engine ...

ASCE
.


See also

*
Actuarial science Actuarial science is the discipline that applies mathematical Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which the ...
*
Analytics Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data Data (; ) are individual facts A fact is something that is truth, ...

Analytics
*
Big data Big data is a field that treats ways to analyze, systematically extract information from, or otherwise deal with data set A data set (or dataset) is a collection of data Data (; ) are individual facts, statistics, or items of informati ...

Big data
*
Business intelligence Business intelligence (BI) comprises the strategies and technologies used by enterprises for the data analysis Data analysis is a process of inspecting, cleansing, transforming, and modelling In general, a model is an informative representat ...
*
Censoring (statistics) In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with ...
*
Computational physics Computational physics is the study and implementation of numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathemat ...
*
Data acquisition Data acquisition is the process of sampling signals that measure real world physical conditions and converting the resulting samples into digital numeric values that can be manipulated by a computer. Data acquisition systems, abbreviated by the init ...
* Data blending *
Data governance Data governance is a term used on both a macro and a micro level. The former is a political concept and forms part of international relations and Internet governance Governance is all the processes of interactions be they through the laws ...
*
Data mining Data mining is a process of extracting and discovering patterns in large data set A data set (or dataset) is a collection of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...
*
Data Presentation Architecture Data visualization (often abbreviated ''data viz'') is an interdisciplinary field that deals with the graphic Graphics (from Greek ''graphikos'', "belonging to drawing") are visual images or designs on some surface, such as a wall, canvas, ...
*
Data science #REDIRECT Data science#REDIRECT Data science Data science is an Interdisciplinarity, interdisciplinary field that uses scientific methods, processes, algorithms and systems to extract knowledge and insights from structured and unstructured data ...

Data science
*
Digital signal processing Digital signal processing (DSP) is the use of digital processing Digital data, in information theory and information systems, is information represented as a string of discrete symbols each of which can take on one of only a finite number of ...
*
Dimension reduction Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally ...
* Early case assessment *
Exploratory data analysis In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a mor ...
*
Fourier analysis In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...
*
Machine learning Machine learning (ML) is the study of computer algorithms that can improve automatically through experience and by the use of data. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data ...

Machine learning
* Multilinear PCA *
Multilinear subspace learning Multilinear subspace learning is an approach to dimensionality reduction.M. A. O. Vasilescu, D. Terzopoulos (2003"Multilinear Subspace Analysis of Image Ensembles" "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVP ...
* Multiway data analysis *
Nearest neighbor searchNearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: ...
*
Nonlinear system identification System identification The field of system identification uses statistical methods to build mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that ac ...
*
Predictive analytics Predictive analytics encompasses a variety of statistics, statistical techniques from data mining, predictive modelling, and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events. ...
*
Principal component analysis The principal components of a collection of points in a real coordinate space are a sequence of p unit vectors, where the i-th vector is the direction of a line that best fits the data while being orthogonal to the first i-1 vectors. Here, a best ...
*
Qualitative research Qualitative research relies on data obtained by the researcher from first-hand observation, interviews, questionnaires (on which participants write descriptively), focus groups, participant-observation, recordings made in natural settings, docum ...
*
Scientific computing Computational science, also known as scientific computing or scientific computation (SC), is a field that uses advanced computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes ...
*
Structured data analysis (statistics) Structured data analysis is the statistics, statistical data analysis of structured data. This can arise either in the form of an ''a priori'' structure such as multiple-choice questionnaires or in situations with the need to search for structure t ...
*
System identification The field of system identification uses statistical methods to build mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set o ...
*
Test method A test method is a method Method ( grc, μέθοδος, methodos) literally means a pursuit of knowledge, investigation, mode of prosecuting such inquiry, or system. In recent centuries it more often means a prescribed process for completing a task ...
*
Text analytics Text mining, also referred to as ''text data mining'', similar to text analytics, is the process of deriving high-quality information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity i ...
*
Unstructured data Unstructured data (or unstructured information) is information that either does not have a pre-defined data model A data model (or datamodel) is an abstract model that organizes elements of data and standardizes how they relate to one another and ...
*
Wavelet A wavelet is a wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other wor ...

Wavelet
* List of big data companies


References


Citations


Bibliography

* * *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.


Further reading

* Adèr, H.J. & Gideon J. Mellenbergh, Mellenbergh, G.J. (with contributions by D.J. Hand) (2008). ''Advising on Research Methods: A Consultant's Companion''. Huizen, the Netherlands: Johannes van Kessel Publishing. * Chambers, John M.; Cleveland, William S.; Kleiner, Beat; Tukey, Paul A. (1983). ''Graphical Methods for Data Analysis'', Wadsworth/Duxbury Press. * Fandango, Armando (2017). ''Python Data Analysis, 2nd Edition''. Packt Publishers. * Juran, Joseph M.; Godfrey, A. Blanton (1999). ''Juran's Quality Handbook, 5th Edition.'' New York: McGraw Hill. * Lewis-Beck, Michael S. (1995). ''Data Analysis: an Introduction'', Sage Publications Inc, * NIST/SEMATECH (2008
''Handbook of Statistical Methods''
* Pyzdek, T, (2003). ''Quality Engineering Handbook'', * Richard Veryard (1984). ''Pragmatic Data Analysis''. Oxford : Blackwell Scientific Publications. * Tabachnick, B.G.; Fidell, L.S. (2007). ''Using Multivariate Statistics, 5th Edition''. Boston: Pearson Education, Inc. / Allyn and Bacon, {{Authority control Data analysis, Scientific method Computational fields of study Big data Data management