Data Analysis
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Data analysis is a process of inspecting, cleansing, transforming, and
modeling 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. Models c ...
data In the pursuit of knowledge, data (; ) is a collection of discrete Value_(semiotics), values that convey information, describing quantity, qualitative property, quality, fact, statistics, other basic units of meaning, or simply sequences of sy ...
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 is a particular data analysis technique that focuses on statistical modeling 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 and management of business information. Common functions of business intelligence technologies include reporting, online analytical p ...
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 sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and an ...
,
exploratory data analysis In statistics, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but pri ...
(EDA), and confirmatory data analysis (CDA). EDA focuses on discovering new features in the data while CDA focuses on confirming or falsifying existing hypotheses.
Predictive analytics Predictive analytics encompasses a variety of statistical techniques from data mining, predictive modeling, and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events. In busine ...
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 from text. It involves "the discovery by computer of new, previously unknown information, by automatically extra ...
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 or is not organized in a pre-defined manner. Unstructured information is typically text-heavy, but may contain data such as dates, num ...
. All of the above are varieties of data analysis.
Data integration Data integration involves combining data residing in different sources and providing users with a unified view of them. This process becomes significant in a variety of situations, which include both commercial (such as when two similar companies ...
is a precursor to data analysis, and data analysis is closely linked to data visualization 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, activities that produce a specific se ...
for obtaining
raw data Raw data, also known as primary data, are ''data'' (e.g., numbers, instrument readings, figures, etc.) collected from a source. In the context of examinations, the raw data might be described as a raw score (after test scores). If a scientist ...
, 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, 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, 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 analytics (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, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a " random variable". Common examples of a unit would be a single person, animal, plant, manufactured item, or countr ...
(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 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 a car be c ...
) 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, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but pri ...
, 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 sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and an ...
, such as, the average or median, can be generated to aid in understanding the data. Data visualization 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.


Modeling and algorithms

Mathematical formulas or models (also known as
algorithms In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
), may be applied to the data in order to identify relationships among the variables; for example, using correlation 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 distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers propertie ...
, includes utilizing techniques that measure the relationships between particular variables. For example,
regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...
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 (furniture), a piece of furniture with a flat surface and one or more legs * Table (landform), a flat area of land * Table (information), a data arrangement with rows and columns * Table (database), how the table d ...
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 graph or curve chart is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments. It is a basic type of chart common in many fields. It is similar to a ...
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 data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart i ...
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 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 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 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 of a set of features (countries, provinces, etc.), in which their geographic size is altered to be directly proportiona ...
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 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 equity) into three parts. The name comes from the DuPont company that began us ...
of return on equity. For the variables under examination, analysts typically obtain
descriptive statistics A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and an ...
for them, such as the mean (average), median, and standard deviation. They may also analyze the
distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations * Probability distribution, the probability of a particular value or value range of a vari ...
of the key variables to see how the individual values cluster around the mean. The consultants at
McKinsey and Company McKinsey & Company is a global management consulting firm founded in 1926 by University of Chicago professor James O. McKinsey, that offers professional services to corporations, governments, and other organizations. McKinsey is the oldest and ...
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 ...
. 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 A collective is a group of entities that share or are motivated by at least one common issue or interest, or work together to achieve a common objective. Collectives can differ from cooperatives in that they are not necessarily focused upon an ...
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 used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...
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 an economic model, named after William Phillips hypothesizing a correlation between reduction in unemployment and increased rates of wage rises within an economy. While Phillips himself did not state a linked relationship ...
. Hypothesis testing involves considering the likelihood of
Type I and type II errors In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the fa ...
, which relate to whether the data supports accepting or rejecting the hypothesis.
Regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...
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 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 The Congressional Budget Office (CBO) is a List of United States federal agencies, federal agency within the United States Congress, legislative branch of the United States government that provides budget and economic information to Congress. Ins ...
(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 and extended during the presidency of Barack Obama, through: * Economic Growth and Tax Relief Reconciliation Act o ...
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 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. 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 Richards "Dick" J. Heuer, Jr. was a CIA veteran of 45 years and most known for his work on analysis of competing hypotheses and his book, Psychology of Intelligence Analysis'' This is the Introduction to Heuer's book ''Psychology of Intelligence An ...
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; 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 just financial analysis) is the process of reviewing and analyzing a company's financial statements to make better economic decisions to earn income in future. These statements include the income statement, balanc ...
, 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 and management of business information. Common functions of business intelligence technologies include reporting, online analytical p ...
, 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 a purposeful activity directed at achieving certain aims, such as transmitting knowledge or fostering skills and character traits. These aims may include the development of understanding, rationality, kindness, and honesty ...
, most educators have access to a
data system Data system is a term used to refer to an organized collection of symbols and processes that may be used to operate on such symbols. Any organised collection of symbols and symbol-manipulating operations can be considered a data system. Hence, huma ...
for the purpose of analyzing student data. These data systems present data to educators in an
over-the-counter data Over-the-counter data (OTCD) is a design approach used in data systems, particularly educational technology data systems, in order to increase the accuracy of users' data analyses by better reporting data. The approach involves adhering to stand ...
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 imputation is needed. *Analysis of extreme observations: 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 In applied statistics, (e.g., applied to the social sciences and psychometrics), common-method variance (CMV) is the spurious "variance that is attributable to the measurement method rather than to the construct (philosophy of science), constructs ...
. 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
measurement instruments A measuring instrument is a device to measure a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Esta ...
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 consistency In statistics and research, internal consistency is typically a measure based on the correlations between different items on the same test (or the same subscale on a larger test). It measures whether several items that propose to measure the same g ...
), which gives an indication of the
reliability Reliability, reliable, or unreliable may refer to: Science, technology, and mathematics Computing * Data reliability (disambiguation), a property of some disk arrays in computer storage * High availability * Reliability (computer networking), a ...
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. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution d ...
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 check Manipulation check is a term in experimental research in the social sciences which refers to certain kinds of secondary evaluations of an experiment. Overview Manipulation checks are measured variables that show what the manipulated variables co ...
s).


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-
normal Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Norma ...
s: should one
transform Transform may refer to: Arts and entertainment * Transform (scratch), a type of scratch used by turntablists * ''Transform'' (Alva Noto album), 2001 * ''Transform'' (Howard Jones album) or the title song, 2019 * ''Transform'' (Powerman 5000 album ...
variables; make variables categorical (ordinal/dichotomous); adapt the analysis method? *In the case of
missing data In statistics, missing data, or missing values, occur when no data value is stored for the variable in an observation. Missing data are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data. Mis ...
: should one neglect or impute the missing data; which imputation technique should be used? *In the case of outliers: 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 boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers ...
? *In case the
randomization Randomization is the process of making something random. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution d ...
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. 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 (''Sailor Moon'') * Chaos (''Sesame Park'') * Chaos (''Warhammer'') * Chaos, in ''Fabula Nova Crystallis Final Fantasy'' * Cha ...
,
harmonics A harmonic is a wave with a frequency that is a positive integer multiple of the '' fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', ...
and subharmonics that cannot be analyzed using simple linear methods. Nonlinear data analysis is closely related to
nonlinear system identification System identification is a method of identifying or measuring the mathematical model of a system from measurements of the system inputs and outputs. The applications of system identification include any system where the inputs and outputs can be mea ...
.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, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but pri ...
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 In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the f ...
. It is important to always adjust the significance level when testing multiple models with, for example, a
Bonferroni correction In statistics, the Bonferroni correction is a method to counteract the multiple comparisons problem. Background The method is named for its use of the Bonferroni inequalities. An extension of the method to confidence intervals was proposed by Ol ...
. 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 In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the f ...
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 and econometrics, panel data and longitudinal data are both multi-dimensional data involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time. Time series and ...
. Hence other methods of validation sometimes need to be used. For more on this topic, see statistical model validation. * ''
Sensitivity analysis Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty anal ...
''. 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 boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers ...
.


Free software for data analysis

Notable free software for data analysis include: *
DevInfo DevInfo was a database system developed under the auspices of the United Nations and endorsed by the United Nations Development Group for monitoring human development with the specific purpose of monitoring the Millennium Development Goals (MDGs), ...
– 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 funds, programs, specialized agencies, departments and offices that play a role in development ...
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 developed for use in research and teaching. It was originally at the database ...
– Data mining framework in Java with data mining oriented visualization functions. *
KNIME KNIME (), the Konstanz Information Miner, is a free and open-source data analytics, reporting and integration platform. KNIME integrates various components for machine learning and data mining through its modular data pipelining "Building Blocks ...
– The Konstanz Information Miner, a user friendly and comprehensive data analytics framework. *
Orange Orange most often refers to: *Orange (fruit), the fruit of the tree species '' Citrus'' × ''sinensis'' ** Orange blossom, its fragrant flower *Orange (colour), from the color of an orange, occurs between red and yellow in the visible spectrum * ...
– A visual programming tool featuring
interactive data visualization Data and information visualization (data viz or info viz) is an interdisciplinary field that deals with the graphic representation of data and information. It is a particularly efficient way of communicating when the data or information is nu ...
and methods for statistical data analysis, data mining, and
machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
. *
Pandas Pediatric autoimmune neuropsychiatric disorders associated with streptococcal infections (PANDAS) is a controversial hypothetical diagnosis for a subset of children with rapid onset of obsessive-compulsive disorder (OCD) or tic disorders. Sy ...
– Python library for data analysis. *
PAW A paw is the soft foot-like part of a mammal, generally a quadruped, that has claws. Common characteristics The paw is characterised by thin, pigmented, keratinised, hairless epidermis covering subcutaneous collagenous and adipose tissue, ...
– FORTRAN/C data analysis framework developed at CERN. * R – A programming language and software environment for statistical computing and graphics. *
ROOT In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the su ...
– C++ data analysis framework developed at CERN. *
SciPy SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing. SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, ...
– Python library for data analysis. *
Julia Julia is usually a feminine given name. It is a Latinate feminine form of the name Julio and Julius. (For further details on etymology, see the Wiktionary entry "Julius".) The given name ''Julia'' had been in use throughout Late Antiquity (e.g ...
- 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, is an online community of data scientists and machine learning practitioners. Kaggle allows users to find and publish data sets, explore and build models in a web-based data-science environment, work with oth ...
. * LTPP data analysis contest held by FHWA and ASCE.


See also

* Actuarial science * Analytics * Big data *
Business intelligence Business intelligence (BI) comprises the strategies and technologies used by enterprises for the data analysis and management of business information. Common functions of business intelligence technologies include reporting, online analytical p ...
*
Censoring (statistics) In statistics, censoring is a condition in which the value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known tha ...
*
Computational physics Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics was the first application of modern computers in science, ...
* Computational science *
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 acro ...
*
Data blending Data blending is a process whereby big data from multiple sources are merged into a single data warehouse or data set. It concerns not merely the merging of different file formats or disparate sources of data but also different varieties of data. Da ...
*
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; the latter is a data management concept and forms part of corporate data govern ...
* Data mining *
Data Presentation Architecture Data and information visualization (data viz or info viz) is an interdisciplinary field that deals with the graphic representation of data and information. It is a particularly efficient way of communicating when the data or information is num ...
* Data science * Digital signal processing *
Dimensionality 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 Early case assessment refers to estimating risk (cost of time and money) to prosecute or Lawyer, defend a legal case. Global organizations deal with legal discovery and Discovery (law), disclosure requests for electronically stored information "ES ...
*
Exploratory data analysis In statistics, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but pri ...
* Fourier analysis *
Machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
*
Multilinear PCA Within statistics, Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA). MPCA is employed in the analysis of M-way arrays, i.e. a cube or hyper-cube of numbers, also informally referred ...
*
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 Multiway data analysis is a method of analyzing large data sets by representing a collection of observations as a multiway array, \in^. The proper choice of data organization into ''(C+1)''-way array, and analysis techniques can reveal patterns in ...
*
Nearest neighbor search Nearest 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 is a method of identifying or measuring the mathematical model of a system from measurements of the system inputs and outputs. The applications of system identification include any system where the inputs and outputs can be mea ...
*
Predictive analytics Predictive analytics encompasses a variety of statistical techniques from data mining, predictive modeling, and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events. In busine ...
* Principal component analysis *
Qualitative research Qualitative research is a type of research that aims to gather and analyse non-numerical (descriptive) data in order to gain an understanding of individuals' social reality, including understanding their attitudes, beliefs, and motivation. This ...
*
Structured data analysis (statistics) Structured data analysis is the 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 that fits t ...
* System identification *
Test method A test method is a method for a test in science or engineering, such as a physical test, chemical test, or statistical test. It is a definitive procedure that produces a test result. In order to ensure accurate and relevant test results, a test m ...
*
Text mining Text mining, also referred to as ''text data mining'', similar to text analytics, is the process of deriving high-quality information from text. It involves "the discovery by computer of new, previously unknown information, by automatically extract ...
*
Unstructured data Unstructured data (or unstructured information) is information that either does not have a pre-defined data model or is not organized in a pre-defined manner. Unstructured information is typically text-heavy, but may contain data such as dates, num ...
*
Wavelet A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the num ...
*
List of big data companies This is an alphabetical list of notable IT companies using the marketing term big data: * Alpine Data Labs, an analytics interface working with Apache Hadoop and big data * Azure Data Lake is a highly scalable data storage and analytics service. T ...


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. & 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 Richard Veryard FRSA (born 1955) is a British computer scientist, author and business consultant, known for his work on service-oriented architecture and the service-based business. Biography Veryard attended Sevenoaks School from 1966 to 1972, ...
(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 processing Scientific method Computational fields of study Big data Data management