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Wikipedia

Data analysis

October 14, 2023

Data analysis is the process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making.[1] 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.[2] In today's business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively.[3]

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 covers data analysis that relies heavily on aggregation, focusing mainly on business information.[4] In statistical applications, data analysis can be divided into descriptive statistics, exploratory data analysis (EDA), and confirmatory data analysis (CDA).[5] EDA focuses on discovering new features in the data while CDA focuses on confirming or falsifying existing hypotheses.[6][7] Predictive analytics focuses on the application of statistical models for predictive forecasting or classification, while text analytics applies statistical, linguistic, and structural techniques to extract and classify information from textual sources, a species of unstructured data. All of the above are varieties of data analysis.[8]

Data integration is a precursor to data analysis, and data analysis is closely linked to data visualization and data dissemination.[9]

The process of data analysis Edit

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

Analysis refers to dividing a whole into its separate components for individual examination.[10] Data analysis is a process for obtaining raw data, and subsequently converting it into information useful for decision-making by users.[1] Data is collected and analyzed to answer questions, test hypotheses, or disprove theories.[11]

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."[12]

There are several phases that can be distinguished, described below. The phases are iterative, in that feedback from later phases may result in additional work in earlier phases.[13] The CRISP framework, used in data mining, has similar steps.

Data requirements Edit

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).[14][15] The general type of entity upon which the data will be collected is referred to as an experimental unit (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).[13]

Data collection Edit

Data is collected from a variety of sources.[16][17] A list of data sources are available for study & research. The requirements may be communicated by analysts to custodians of the data; such as, Information Technology personnel within an organization.[18] 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.[13]

Data processing Edit

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

Data, when initially obtained, must be processed or organized for analysis.[19][20] For instance, these may involve placing data into rows and columns in a table format (known as structured data) for further analysis, often through the use of spreadsheet or statistical software.[13]

Data cleaning Edit

Main article: Data cleansing

Once processed and organized, the data may be incomplete, contain duplicates, or contain errors.[21][22] The need for data cleaning will arise from problems in the way that the datum are entered and stored.[21] 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.[23] 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.[24][25] 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.[26][27] 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.[28] Textual data spell checkers can be used to lessen the amount of mistyped words. However, it is harder to tell if the words themselves are correct.[29]

Exploratory data analysis Edit

Once the datasets are cleaned, they can then be analyzed. Analysts may apply a variety of techniques, referred to as exploratory data analysis, to begin understanding the messages contained within the obtained data.[30] 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.[31] Descriptive statistics, such as, the average or median, can be generated to aid in understanding the data.[32][33] 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.[13]

Modeling and algorithms Edit

Mathematical formulas or models (also known as algorithms), may be applied to the data in order to identify relationships among the variables; for example, using correlation or causation.[34][35] 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).[36][11]

Inferential statistics includes utilizing techniques that measure the relationships between particular variables.[37] For example, regression analysis may be used to model whether a change in advertising (independent variable X), provides an explanation for the variation in sales (dependent variable Y).[38] In mathematical terms, Y (sales) is a function of X (advertising).[39] 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.[40] Analysts may also attempt to build models that are descriptive of the data, in an aim to simplify analysis and communicate results.[11]

Data product Edit

A data product is a computer application that takes data inputs and generates outputs, feeding them back into the environment.[41] 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.[42][13]

Communication Edit

 
Data visualization is used to help understand the results after data is analyzed.[43]
Main article: Data and information visualization

Once data is analyzed, it may be reported in many formats to the users of the analysis to support their requirements.[44] The users may have feedback, which results in additional analysis. As such, much of the analytical cycle is iterative.[13]

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.[45] Data visualization uses information displays (graphics such as, tables and charts) to help communicate key messages contained in the data.[46] Tables 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.[47]

Quantitative messages Edit

Main article: Data and information visualization
 
A time series illustrated with a line chart demonstrating trends in U.S. federal spending and revenue over time.
 
A scatterplot illustrating the correlation between two variables (inflation and unemployment) measured at points in time.

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.[48] Customers specifying requirements and analysts performing the data analysis may consider these messages during the course of the process.[49]

  1. Time-series: A single variable is captured over a period of time, such as the unemployment rate over a 10-year period. A line chart may be used to demonstrate the trend.[50]
  2. 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.[51] A bar chart may be used to show the comparison across the salespersons.[52]
  3. 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.[53]
  4. 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.[54]
  5. 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.[55]
  6. 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.[56]
  7. 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.[57]
  8. Geographic or geospatial: Comparison of a variable across a map or layout, such as the unemployment rate by state or the number of persons on the various floors of a building. A cartogram is a typical graphic used.[58][59]

Techniques for analyzing quantitative data Edit

See also: Problem solving

Author Jonathan Koomey has recommended a series of best practices for understanding quantitative data.[60] 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 of return on equity.[25]

For the variables under examination, analysts typically obtain descriptive statistics for them, such as the mean (average), median, and standard deviation.[61] They may also analyze the distribution of the key variables to see how the individual values cluster around the mean.[62]

 
An illustration of the MECE principle used for data analysis.

The consultants at McKinsey and Company named a technique for breaking a quantitative problem down into its component parts called the MECE principle.[63] Each layer can be broken down into its components; each of the sub-components must be mutually exclusive of each other and collectively add up to the layer above them.[64] 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.[65] 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).[66]

Analysts may use robust statistical measurements to solve certain analytical problems.[67] Hypothesis testing is used when a particular hypothesis about the true state of affairs is made by the analyst and data is gathered to determine whether that state of affairs is true or false.[68][69] For example, the hypothesis might be that "Unemployment has no effect on inflation", which relates to an economics concept called the Phillips Curve.[70] Hypothesis testing involves considering the likelihood of Type I and type II errors, which relate to whether the data supports accepting or rejecting the hypothesis.[71][72]

Regression analysis may be used when the analyst is trying to determine the extent to which independent variable X affects dependent variable Y (e.g., "To what extent do changes in the unemployment rate (X) affect the inflation rate (Y)?").[73] This is an attempt to model or fit an equation line or curve to the data, such that Y is a function of X.[74][75]

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)?").[73] 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),[76] 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.[77]

Analytical activities of data users Edit

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.[78][79][80][81]

# Task General
Description		 Pro Forma
Abstract		 Examples
1 Retrieve Value Given a set of specific cases, find attributes of those cases. What are the values of attributes {X, Y, Z, ...} in the data cases {A, B, C, ...}? - What is the mileage per gallon of the Ford Mondeo?

- How long is the movie Gone with the Wind?

2 Filter Given some concrete conditions on attribute values, find data cases satisfying those conditions. Which data cases satisfy conditions {A, B, C...}? - What Kellogg's cereals have high fiber?

- What comedies have won awards?

- Which funds underperformed the SP-500?

3 Compute Derived Value Given a set of data cases, compute an aggregate numeric representation of those data cases. What is the value of aggregation function F over a given set S of data cases? - What is the average calorie content of Post cereals?

- What is the gross income of all stores combined?

- How many manufacturers of cars are there?

4 Find Extremum Find data cases possessing an extreme value of an attribute over its range within the data set. What are the top/bottom N data cases with respect to attribute A? - What is the car with the highest MPG?

- What director/film has won the most awards?

- What Marvel Studios film has the most recent release date?

5 Sort Given a set of data cases, rank them according to some ordinal metric. What is the sorted order of a set S of data cases according to their value of attribute A? - Order the cars by weight.

- Rank the cereals by calories.

6 Determine Range Given a set of data cases and an attribute of interest, find the span of values within the set. What is the range of values of attribute A in a set S of data cases? - What is the range of film lengths?

- What is the range of car horsepowers?

- What actresses are in the data set?

7 Characterize Distribution Given a set of data cases and a quantitative attribute of interest, characterize the distribution of that attribute's values over the set. What is the distribution of values of attribute A in a set S of data cases? - What is the distribution of carbohydrates in cereals?

- What is the age distribution of shoppers?

8 Find Anomalies Identify any anomalies within a given set of data cases with respect to a given relationship or expectation, e.g. statistical outliers. Which data cases in a set S of data cases have unexpected/exceptional values? - Are there exceptions to the relationship between horsepower and acceleration?

- Are there any outliers in protein?

9 Cluster Given a set of data cases, find clusters of similar attribute values. Which data cases in a set S of data cases are similar in value for attributes {X, Y, Z, ...}? - Are there groups of cereals w/ similar fat/calories/sugar?

- Is there a cluster of typical film lengths?

10 Correlate Given a set of data cases and two attributes, determine useful relationships between the values of those attributes. What is the correlation between attributes X and Y over a given set S of data cases? - Is there a correlation between carbohydrates and fat?

- Is there a correlation between country of origin and MPG?

- Do different genders have a preferred payment method?

- Is there a trend of increasing film length over the years?

11 Contextualization[81] Given a set of data cases, find contextual relevancy of the data to the users. Which data cases in a set S of data cases are relevant to the current users' context? - Are there groups of restaurants that have foods based on my current caloric intake?

Barriers to effective analysis Edit

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.[82]

Confusing fact and opinion Edit

You are entitled to your own opinion, but you are not entitled to your own facts.

Daniel Patrick Moynihan

Effective analysis requires obtaining relevant facts to answer questions, support a conclusion or formal opinion, or test hypotheses.[83][84] Facts by definition are irrefutable, meaning that any person involved in the analysis should be able to agree upon them.[85] For example, in August 2010, the Congressional Budget Office (CBO) estimated that extending the Bush tax cuts of 2001 and 2003 for the 2011–2020 time period would add approximately $3.3 trillion to the national debt.[86] 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.[87]

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".[88] 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.[89]

Cognitive biases Edit

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.[90] In addition, individuals may discredit information that does not support their views.[91]

Analysts may be trained specifically to be aware of these biases and how to overcome them.[92] 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.[93] He emphasized procedures to help surface and debate alternative points of view.[94]

Innumeracy Edit

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.[95] Persons communicating the data may also be attempting to mislead or misinform, deliberately using bad numerical techniques.[96]

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.[97] This numerical technique is referred to as normalization[25] 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.[98] Analysts apply a variety of techniques to address the various quantitative messages described in the section above.[99]

Analysts may also analyze data under different assumptions or scenario. For example, when analysts perform financial statement analysis, they will often recast the financial statements under different assumptions to help arrive at an estimate of future cash flow, which they then discount to present value based on some interest rate, to determine the valuation of the company or its stock.[100][101] 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.[102]

Other topics Edit

Smart buildings Edit

A data analytics approach can be used in order to predict energy consumption in buildings.[103] 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.[104]

Analytics and business intelligence Edit

Main article: Analytics

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, which is a set of technologies and processes that uses data to understand and analyze business performance to drive decision-making .[105]

Education Edit

 
Analytic activities of data visualization users

In education, most educators have access to a data system for the purpose of analyzing student data.[106] 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.[107]

Practitioner notes Edit

This section contains rather technical explanations that may assist practitioners but are beyond the typical scope of a Wikipedia article.[108]

Initial data analysis Edit

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.[109] The initial data analysis phase is guided by the following four questions:[110]

Quality of data Edit

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.[111]

  • Analysis of extreme observations: outlying observations in the data are analyzed to see if they seem to disturb the distribution.[112]
  • 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.[113]
  • 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.[114]

Quality of measurements Edit

The quality of the measurement instruments should only be checked during the initial data analysis phase when this is not the focus or research question of the study.[115][116] 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), which gives an indication of the reliability of a measurement instrument.[117] 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[118]

Initial transformations Edit

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.[119]
Possible transformations of variables are:[120]

  • 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? Edit

One should check the success of the randomization procedure, for instance by checking whether background and substantive variables are equally distributed within and across groups.[121]
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.[122]
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).[123]

Characteristics of data sample Edit

In any report or article, the structure of the sample must be accurately described.[124][125] 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.[126]
The characteristics of the data sample can be assessed by looking at:

  • Basic statistics of important variables
  • Scatter plots
  • Correlations and associations
  • Cross-tabulations[127]

Final stage of the initial data analysis Edit

During the final stage, the findings of the initial data analysis are documented, and necessary, preferable, and possible corrective actions are taken.[128]
Also, the original plan for the main data analyses can and should be specified in more detail or rewritten.[129][130]
In order to do this, several decisions about the main data analyses can and should be made:

  • In the case of non-normals: should one transform variables; make variables categorical (ordinal/dichotomous); adapt the analysis method?
  • In the case of missing data: 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 case the randomization procedure seems to be defective: can and should one calculate propensity scores and include them as covariates in the main analyses?[131]

Analysis Edit

Several analyses can be used during the initial data analysis phase:[132]

  • 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:[133]

  • 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 Edit

Nonlinear analysis is often necessary when the data is recorded from a nonlinear system. Nonlinear systems can exhibit complex dynamic effects including bifurcations, chaos, harmonics and subharmonics that cannot be analyzed using simple linear methods. Nonlinear data analysis is closely related to nonlinear system identification.[134]

Main data analysis Edit

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.[135]

Exploratory and confirmatory approaches Edit

In the main analysis phase, either an exploratory or confirmatory approach can be adopted. Usually the approach is decided before data is collected.[136] 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.[137] In a confirmatory analysis clear hypotheses about the data are tested.[138]

Exploratory data analysis should be interpreted carefully. When testing multiple models at once there is a high chance on finding at least one of them to be significant, but this can be due to a type 1 error.[139] It is important to always adjust the significance level when testing multiple models with, for example, a Bonferroni correction.[140] Also, one should not follow up an exploratory analysis with a confirmatory analysis in the same dataset.[141] An exploratory analysis is used to find ideas for a theory, but not to test that theory as well.[141] When a model is found exploratory in a dataset, then following up that analysis with a confirmatory analysis in the same dataset could simply mean that the results of the confirmatory analysis are due to the same type 1 error that resulted in the exploratory model in the first place.[141] The confirmatory analysis therefore will not be more informative than the original exploratory analysis.[142]

Stability of results Edit

It is important to obtain some indication about how generalizable the results are.[143] 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.[144]

  • 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.[145] Cross-validation is generally inappropriate, though, if there are correlations within the data, e.g. with panel data.[146] Hence other methods of validation sometimes need to be used. For more on this topic, see statistical model validation.[147]
  • Sensitivity analysis. A procedure to study the behavior of a system or model when global parameters are (systematically) varied. One way to do that is via bootstrapping.[148]

Free software for data analysis Edit

Notable free software for data analysis include:

  • DevInfo – A database system endorsed by the United Nations Development Group for monitoring and analyzing human development.[149]
  • ELKI – Data mining framework in Java with data mining oriented visualization functions.
  • KNIME – The Konstanz Information Miner, a user friendly and comprehensive data analytics framework.
  • Orange – A visual programming tool featuring interactive data visualization and methods for statistical data analysis, data mining, and machine learning.
  • Pandas – Python library for data analysis.
  • PAW – FORTRAN/C data analysis framework developed at CERN.
  • R – A programming language and software environment for statistical computing and graphics.[150]
  • ROOT – C++ data analysis framework developed at CERN.
  • SciPy – Python library for data analysis.
  • Julia – A programming language well-suited for numerical analysis and computational science.

International data analysis contests Edit

Different companies or organizations hold data analysis contests to encourage researchers to utilize their data or to solve a particular question using data analysis.[151][152] A few examples of well-known international data analysis contests are as follows:[153]

See also Edit

References Edit

Citations Edit

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Bibliography Edit

  • Adèr, Herman J. (2008a). "Chapter 14: Phases and initial steps in data analysis". In Adèr, Herman J.; Mellenbergh, Gideon J.; Hand, David J (eds.). Advising on research methods : a consultant's companion. Huizen, Netherlands: Johannes van Kessel Pub. pp. 333–356. ISBN 9789079418015. OCLC 905799857.
  • Adèr, Herman J. (2008b). "Chapter 15: The main analysis phase". In Adèr, Herman J.; Mellenbergh, Gideon J.; Hand, David J (eds.). Advising on research methods : a consultant's companion. Huizen, Netherlands: Johannes van Kessel Pub. pp. 357–386. ISBN 9789079418015. OCLC 905799857.
  • Tabachnick, B.G. & Fidell, L.S. (2007). Chapter 4: Cleaning up your act. Screening data prior to analysis. In B.G. Tabachnick & L.S. Fidell (Eds.), Using Multivariate Statistics, Fifth Edition (pp. 60–116). Boston: Pearson Education, Inc. / Allyn and Bacon.

Further reading Edit

 
Wikiversity has learning resources about Data analysis
  • 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. ISBN 978-90-79418-01-5
  • Chambers, John M.; Cleveland, William S.; Kleiner, Beat; Tukey, Paul A. (1983). Graphical Methods for Data Analysis, Wadsworth/Duxbury Press. ISBN 0-534-98052-X
  • Fandango, Armando (2017). Python Data Analysis, 2nd Edition. Packt Publishers. ISBN 978-1787127487
  • Juran, Joseph M.; Godfrey, A. Blanton (1999). Juran's Quality Handbook, 5th Edition. New York: McGraw Hill. ISBN 0-07-034003-X
  • Lewis-Beck, Michael S. (1995). Data Analysis: an Introduction, Sage Publications Inc, ISBN 0-8039-5772-6
  • NIST/SEMATECH (2008) Handbook of Statistical Methods,
  • Pyzdek, T, (2003). Quality Engineering Handbook, ISBN 0-8247-4614-7
  • Richard Veryard (1984). Pragmatic Data Analysis. Oxford : Blackwell Scientific Publications. ISBN 0-632-01311-7
  • Tabachnick, B.G.; Fidell, L.S. (2007). Using Multivariate Statistics, 5th Edition. Boston: Pearson Education, Inc. / Allyn and Bacon, ISBN 978-0-205-45938-4

October 14, 2023
data, analysis, process, inspecting, cleansing, transforming, modeling, data, with, goal, discovering, useful, information, informing, conclusions, supporting, decision, making, multiple, facets, approaches, encompassing, diverse, techniques, under, variety, n. Data analysis is the process of inspecting cleansing transforming and modeling data with the goal of discovering useful information informing conclusions and supporting decision making 1 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 2 In today s business world data analysis plays a role in making decisions more scientific and helping businesses operate more effectively 3 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 covers data analysis that relies heavily on aggregation focusing mainly on business information 4 In statistical applications data analysis can be divided into descriptive statistics exploratory data analysis EDA and confirmatory data analysis CDA 5 EDA focuses on discovering new features in the data while CDA focuses on confirming or falsifying existing hypotheses 6 7 Predictive analytics focuses on the application of statistical models for predictive forecasting or classification while text analytics applies statistical linguistic and structural techniques to extract and classify information from textual sources a species of unstructured data All of the above are varieties of data analysis 8 Data integration is a precursor to data analysis and data analysis is closely linked to data visualization and data dissemination 9 Contents 1 The process of data analysis 1 1 Data requirements 1 2 Data collection 1 3 Data processing 1 4 Data cleaning 1 5 Exploratory data analysis 1 6 Modeling and algorithms 1 7 Data product 1 8 Communication 2 Quantitative messages 3 Techniques for analyzing quantitative data 4 Analytical activities of data users 5 Barriers to effective analysis 5 1 Confusing fact and opinion 5 2 Cognitive biases 5 3 Innumeracy 6 Other topics 6 1 Smart buildings 6 2 Analytics and business intelligence 6 3 Education 7 Practitioner notes 7 1 Initial data analysis 7 1 1 Quality of data 7 1 2 Quality of measurements 7 1 3 Initial transformations 7 1 4 Did the implementation of the study fulfill the intentions of the research design 7 1 5 Characteristics of data sample 7 1 6 Final stage of the initial data analysis 7 1 7 Analysis 7 1 8 Nonlinear analysis 7 2 Main data analysis 7 2 1 Exploratory and confirmatory approaches 7 2 2 Stability of results 8 Free software for data analysis 9 International data analysis contests 10 See also 11 References 11 1 Citations 11 2 Bibliography 12 Further readingThe process of data analysis Edit nbsp Data science process flowchart from Doing Data Science by Schutt amp O Neil 2013 Analysis refers to dividing a whole into its separate components for individual examination 10 Data analysis is a process for obtaining raw data and subsequently converting it into information useful for decision making by users 1 Data is collected and analyzed to answer questions test hypotheses or disprove theories 11 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 12 There are several phases that can be distinguished described below The phases are iterative in that feedback from later phases may result in additional work in earlier phases 13 The CRISP framework used in data mining has similar steps Data requirements Edit 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 14 15 The general type of entity upon which the data will be collected is referred to as an experimental unit 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 13 Data collection Edit Data is collected from a variety of sources 16 17 A list of data sources are available for study amp research The requirements may be communicated by analysts to custodians of the data such as Information Technology personnel within an organization 18 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 13 Data processing Edit nbsp The phases of the intelligence cycle used to convert raw information into actionable intelligence or knowledge are conceptually similar to the phases in data analysis Data when initially obtained must be processed or organized for analysis 19 20 For instance these may involve placing data into rows and columns in a table format known as structured data for further analysis often through the use of spreadsheet or statistical software 13 Data cleaning Edit Main article Data cleansing Once processed and organized the data may be incomplete contain duplicates or contain errors 21 22 The need for data cleaning will arise from problems in the way that the datum are entered and stored 21 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 23 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 24 25 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 26 27 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 28 Textual data spell checkers can be used to lessen the amount of mistyped words However it is harder to tell if the words themselves are correct 29 Exploratory data analysis Edit Once the datasets are cleaned they can then be analyzed Analysts may apply a variety of techniques referred to as exploratory data analysis to begin understanding the messages contained within the obtained data 30 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 31 Descriptive statistics such as the average or median can be generated to aid in understanding the data 32 33 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 13 Modeling and algorithms Edit Mathematical formulas or models also known as algorithms may be applied to the data in order to identify relationships among the variables for example using correlation or causation 34 35 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 36 11 Inferential statistics includes utilizing techniques that measure the relationships between particular variables 37 For example regression analysis may be used to model whether a change in advertising independent variable X provides an explanation for the variation in sales dependent variable Y 38 In mathematical terms Y sales is a function of X advertising 39 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 40 Analysts may also attempt to build models that are descriptive of the data in an aim to simplify analysis and communicate results 11 Data product Edit A data product is a computer application that takes data inputs and generates outputs feeding them back into the environment 41 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 42 13 Communication Edit nbsp Data visualization is used to help understand the results after data is analyzed 43 Main article Data and information visualization Once data is analyzed it may be reported in many formats to the users of the analysis to support their requirements 44 The users may have feedback which results in additional analysis As such much of the analytical cycle is iterative 13 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 45 Data visualization uses information displays graphics such as tables and charts to help communicate key messages contained in the data 46 Tables 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 47 Quantitative messages EditMain article Data and information visualization nbsp A time series illustrated with a line chart demonstrating trends in U S federal spending and revenue over time nbsp A scatterplot illustrating the correlation between two variables inflation and unemployment measured at points in time 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 48 Customers specifying requirements and analysts performing the data analysis may consider these messages during the course of the process 49 Time series A single variable is captured over a period of time such as the unemployment rate over a 10 year period A line chart may be used to demonstrate the trend 50 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 51 A bar chart may be used to show the comparison across the salespersons 52 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 53 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 54 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 55 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 56 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 57 Geographic or geospatial Comparison of a variable across a map or layout such as the unemployment rate by state or the number of persons on the various floors of a building A cartogram is a typical graphic used 58 59 Techniques for analyzing quantitative data EditSee also Problem solving Author Jonathan Koomey has recommended a series of best practices for understanding quantitative data 60 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 of return on equity 25 For the variables under examination analysts typically obtain descriptive statistics for them such as the mean average median and standard deviation 61 They may also analyze the distribution of the key variables to see how the individual values cluster around the mean 62 nbsp An illustration of the MECE principle used for data analysis The consultants at McKinsey and Company named a technique for breaking a quantitative problem down into its component parts called the MECE principle 63 Each layer can be broken down into its components each of the sub components must be mutually exclusive of each other and collectively add up to the layer above them 64 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 65 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 66 Analysts may use robust statistical measurements to solve certain analytical problems 67 Hypothesis testing is used when a particular hypothesis about the true state of affairs is made by the analyst and data is gathered to determine whether that state of affairs is true or false 68 69 For example the hypothesis might be that Unemployment has no effect on inflation which relates to an economics concept called the Phillips Curve 70 Hypothesis testing involves considering the likelihood of Type I and type II errors which relate to whether the data supports accepting or rejecting the hypothesis 71 72 Regression analysis may be used when the analyst is trying to determine the extent to which independent variable X affects dependent variable Y e g To what extent do changes in the unemployment rate X affect the inflation rate Y 73 This is an attempt to model or fit an equation line or curve to the data such that Y is a function of X 74 75 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 73 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 76 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 77 Analytical activities of data users EditUsers 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 78 79 80 81 Task GeneralDescription Pro FormaAbstract Examples1 Retrieve Value Given a set of specific cases find attributes of those cases What are the values of attributes X Y Z in the data cases A B C What is the mileage per gallon of the Ford Mondeo How long is the movie Gone with the Wind 2 Filter Given some concrete conditions on attribute values find data cases satisfying those conditions Which data cases satisfy conditions A B C What Kellogg s cereals have high fiber What comedies have won awards Which funds underperformed the SP 500 3 Compute Derived Value Given a set of data cases compute an aggregate numeric representation of those data cases What is the value of aggregation function F over a given set S of data cases What is the average calorie content of Post cereals What is the gross income of all stores combined How many manufacturers of cars are there 4 Find Extremum Find data cases possessing an extreme value of an attribute over its range within the data set What are the top bottom N data cases with respect to attribute A What is the car with the highest MPG What director film has won the most awards What Marvel Studios film has the most recent release date 5 Sort Given a set of data cases rank them according to some ordinal metric What is the sorted order of a set S of data cases according to their value of attribute A Order the cars by weight Rank the cereals by calories 6 Determine Range Given a set of data cases and an attribute of interest find the span of values within the set What is the range of values of attribute A in a set S of data cases What is the range of film lengths What is the range of car horsepowers What actresses are in the data set 7 Characterize Distribution Given a set of data cases and a quantitative attribute of interest characterize the distribution of that attribute s values over the set What is the distribution of values of attribute A in a set S of data cases What is the distribution of carbohydrates in cereals What is the age distribution of shoppers 8 Find Anomalies Identify any anomalies within a given set of data cases with respect to a given relationship or expectation e g statistical outliers Which data cases in a set S of data cases have unexpected exceptional values Are there exceptions to the relationship between horsepower and acceleration Are there any outliers in protein 9 Cluster Given a set of data cases find clusters of similar attribute values Which data cases in a set S of data cases are similar in value for attributes X Y Z Are there groups of cereals w similar fat calories sugar Is there a cluster of typical film lengths 10 Correlate Given a set of data cases and two attributes determine useful relationships between the values of those attributes What is the correlation between attributes X and Y over a given set S of data cases Is there a correlation between carbohydrates and fat Is there a correlation between country of origin and MPG Do different genders have a preferred payment method Is there a trend of increasing film length over the years 11 Contextualization 81 Given a set of data cases find contextual relevancy of the data to the users Which data cases in a set S of data cases are relevant to the current users context Are there groups of restaurants that have foods based on my current caloric intake Barriers to effective analysis EditBarriers 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 82 Confusing fact and opinion Edit You are entitled to your own opinion but you are not entitled to your own facts Daniel Patrick Moynihan Effective analysis requires obtaining relevant facts to answer questions support a conclusion or formal opinion or test hypotheses 83 84 Facts by definition are irrefutable meaning that any person involved in the analysis should be able to agree upon them 85 For example in August 2010 the Congressional Budget Office CBO estimated that extending the Bush tax cuts of 2001 and 2003 for the 2011 2020 time period would add approximately 3 3 trillion to the national debt 86 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 87 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 88 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 89 Cognitive biases Edit 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 90 In addition individuals may discredit information that does not support their views 91 Analysts may be trained specifically to be aware of these biases and how to overcome them 92 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 93 He emphasized procedures to help surface and debate alternative points of view 94 Innumeracy Edit 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 95 Persons communicating the data may also be attempting to mislead or misinform deliberately using bad numerical techniques 96 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 97 This numerical technique is referred to as normalization 25 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 98 Analysts apply a variety of techniques to address the various quantitative messages described in the section above 99 Analysts may also analyze data under different assumptions or scenario For example when analysts perform financial statement analysis they will often recast the financial statements under different assumptions to help arrive at an estimate of future cash flow which they then discount to present value based on some interest rate to determine the valuation of the company or its stock 100 101 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 102 Other topics EditSmart buildings Edit A data analytics approach can be used in order to predict energy consumption in buildings 103 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 104 Analytics and business intelligence Edit Main article Analytics 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 which is a set of technologies and processes that uses data to understand and analyze business performance to drive decision making 105 Education Edit nbsp Analytic activities of data visualization usersIn education most educators have access to a data system for the purpose of analyzing student data 106 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 107 Practitioner notes EditThis section contains rather technical explanations that may assist practitioners but are beyond the typical scope of a Wikipedia article 108 Initial data analysis Edit 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 109 The initial data analysis phase is guided by the following four questions 110 Quality of data Edit 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 111 Analysis of extreme observations outlying observations in the data are analyzed to see if they seem to disturb the distribution 112 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 113 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 114 Quality of measurements Edit The quality of the measurement instruments should only be checked during the initial data analysis phase when this is not the focus or research question of the study 115 116 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 which gives an indication of the reliability of a measurement instrument 117 During this analysis one inspects the variances of the items and the scales the Cronbach s a of the scales and the change in the Cronbach s alpha when an item would be deleted from a scale 118 Initial transformations Edit 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 119 Possible transformations of variables are 120 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 Edit One should check the success of the randomization procedure for instance by checking whether background and substantive variables are equally distributed within and across groups 121 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 122 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 123 Characteristics of data sample Edit In any report or article the structure of the sample must be accurately described 124 125 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 126 The characteristics of the data sample can be assessed by looking at Basic statistics of important variables Scatter plots Correlations and associations Cross tabulations 127 Final stage of the initial data analysis Edit During the final stage the findings of the initial data analysis are documented and necessary preferable and possible corrective actions are taken 128 Also the original plan for the main data analyses can and should be specified in more detail or rewritten 129 130 In order to do this several decisions about the main data analyses can and should be made In the case of non normals should one transform variables make variables categorical ordinal dichotomous adapt the analysis method In the case of missing data 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 case the randomization procedure seems to be defective can and should one calculate propensity scores and include them as covariates in the main analyses 131 Analysis Edit Several analyses can be used during the initial data analysis phase 132 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 133 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 plotsNonlinear analysis Edit Nonlinear analysis is often necessary when the data is recorded from a nonlinear system Nonlinear systems can exhibit complex dynamic effects including bifurcations chaos harmonics and subharmonics that cannot be analyzed using simple linear methods Nonlinear data analysis is closely related to nonlinear system identification 134 Main data analysis Edit 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 135 Exploratory and confirmatory approaches Edit In the main analysis phase either an exploratory or confirmatory approach can be adopted Usually the approach is decided before data is collected 136 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 137 In a confirmatory analysis clear hypotheses about the data are tested 138 Exploratory data analysis should be interpreted carefully When testing multiple models at once there is a high chance on finding at least one of them to be significant but this can be due to a type 1 error 139 It is important to always adjust the significance level when testing multiple models with for example a Bonferroni correction 140 Also one should not follow up an exploratory analysis with a confirmatory analysis in the same dataset 141 An exploratory analysis is used to find ideas for a theory but not to test that theory as well 141 When a model is found exploratory in a dataset then following up that analysis with a confirmatory analysis in the same dataset could simply mean that the results of the confirmatory analysis are due to the same type 1 error that resulted in the exploratory model in the first place 141 The confirmatory analysis therefore will not be more informative than the original exploratory analysis 142 Stability of results Edit It is important to obtain some indication about how generalizable the results are 143 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 144 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 145 Cross validation is generally inappropriate though if there are correlations within the data e g with panel data 146 Hence other methods of validation sometimes need to be used For more on this topic see statistical model validation 147 Sensitivity analysis A procedure to study the behavior of a system or model when global parameters are systematically varied One way to do that is via bootstrapping 148 Free software for data analysis EditNotable free software for data analysis include DevInfo A database system endorsed by the United Nations Development Group for monitoring and analyzing human development 149 ELKI Data mining framework in Java with data mining oriented visualization functions KNIME The Konstanz Information Miner a user friendly and comprehensive data analytics framework Orange A visual programming tool featuring interactive data visualization and methods for statistical data analysis data mining and machine learning Pandas Python library for data analysis PAW FORTRAN C data analysis framework developed at CERN R A programming language and software environment for statistical computing and graphics 150 ROOT C data analysis framework developed at CERN SciPy Python library for data analysis Julia A programming language well suited for numerical analysis and computational science International data analysis contests EditDifferent companies or organizations hold data analysis contests to encourage researchers to utilize their data or to solve a particular question using data analysis 151 152 A few examples of well known international data analysis contests are as follows 153 Kaggle competition which is held by Kaggle 154 LTPP data analysis contest held by FHWA and ASCE 155 156 See also EditActuarial science Analytics Big data Business intelligence Censoring statistics Computational physics Computational science Data acquisition Data blending Data governance Data mining Data Presentation Architecture Data science Digital signal processing Dimensionality reduction Early case assessment Exploratory data analysis Fourier analysis Machine learning Multilinear PCA Multilinear subspace learning Multiway data analysis Nearest neighbor search Nonlinear system identification Predictive analytics Principal component analysis Qualitative research Structured data analysis statistics System identification Test method Text mining Unstructured data Wavelet List of big data companies List of datasets for machine learning researchReferences EditCitations Edit a b Transforming Unstructured Data into Useful Information Big Data Mining and Analytics Auerbach Publications pp 227 246 2014 03 12 doi 10 1201 b16666 14 ISBN 978 0 429 09529 0 retrieved 2021 05 29 The Multiple Facets of Correlation Functions Data Analysis Techniques for Physical Scientists Cambridge University Press pp 526 576 2017 doi 10 1017 9781108241922 013 ISBN 978 1 108 41678 8 retrieved 2021 05 29 Xia B S amp Gong P 2015 Review of business intelligence through data analysis Benchmarking 21 2 300 311 doi 10 1108 BIJ 08 2012 0050 Exploring Data Analysis Data Coding and Exploratory Analysis EDA Rules for Data Coding Exploratory Data Analysis EDA Statistical Assumptions 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22 2017 Data Gov Long Term Pavement Performance LTPP May 26 2016 Archived from the original on November 1 2017 Retrieved November 10 2017 Bibliography Edit Ader Herman J 2008a Chapter 14 Phases and initial steps in data analysis In Ader Herman J Mellenbergh Gideon J Hand David J eds Advising on research methods a consultant s companion Huizen Netherlands Johannes van Kessel Pub pp 333 356 ISBN 9789079418015 OCLC 905799857 Ader Herman J 2008b Chapter 15 The main analysis phase In Ader Herman J Mellenbergh Gideon J Hand David J eds Advising on research methods a consultant s companion Huizen Netherlands Johannes van Kessel Pub pp 357 386 ISBN 9789079418015 OCLC 905799857 Tabachnick B G amp Fidell L S 2007 Chapter 4 Cleaning up your act Screening data prior to analysis In B G Tabachnick amp L S Fidell Eds Using Multivariate Statistics Fifth Edition pp 60 116 Boston Pearson Education Inc Allyn and Bacon Further reading Edit nbsp Wikiversity has learning resources about Data analysis Ader H J amp 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 ISBN 978 90 79418 01 5 Chambers John M Cleveland William S Kleiner Beat Tukey Paul A 1983 Graphical Methods for Data Analysis Wadsworth Duxbury Press ISBN 0 534 98052 X Fandango Armando 2017 Python Data Analysis 2nd Edition Packt Publishers ISBN 978 1787127487 Juran Joseph M Godfrey A Blanton 1999 Juran s Quality Handbook 5th Edition New York McGraw Hill ISBN 0 07 034003 X Lewis Beck Michael S 1995 Data Analysis an Introduction Sage Publications Inc ISBN 0 8039 5772 6 NIST SEMATECH 2008 Handbook of Statistical Methods Pyzdek T 2003 Quality Engineering Handbook ISBN 0 8247 4614 7 Richard Veryard 1984 Pragmatic Data Analysis Oxford Blackwell Scientific Publications ISBN 0 632 01311 7 Tabachnick B G Fidell L S 2007 Using Multivariate Statistics 5th Edition Boston Pearson Education Inc Allyn and Bacon ISBN 978 0 205 45938 4 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