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**Analysis of data** is a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, in different business, science, and social science domains.

Data mining is a particular data analysis technique that focuses on modeling and knowledge discovery for predictive rather than purely descriptive purposes. Business intelligence covers data analysis that relies heavily on aggregation, focusing on business information. In statistical applications, some people divide data analysis into descriptive statistics, exploratory data analysis (EDA), and confirmatory data analysis (CDA). EDA focuses on discovering new features in the data and CDA on confirming or falsifying existing hypotheses. Predictive analytics focuses on application of statistical or structural 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 are varieties of data analysis.

Data integration is a precursor to data analysis, and data analysis is closely linked to data visualization and data dissemination. The term *data analysis* is sometimes used as a synonym for data modeling.

Data analysis is a process, within which several phases can be distinguished:^{[1]} Processing of data refers to concentrating, recasting and dealing with data in such a way that they become as amenable to analysis as possible.

The need for data cleaning will arise from problems in the way that data is entered and stored. Data cleaning is the process of preventing and correcting these errors. Common tasks include record matching, deduplication, and column segmentation.^{[2]} There are several types of data cleaning that depend on the type of data. Quantitative data methods for outlier detection can be used to get rid of likely incorrectly entered data. Textual data spellcheckers can be used to lessen the amount of mistyped words, but it is harder to tell if the words themselves are correct.^{[3]}

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:^{[4]}

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

- 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.^{[5]}

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

There are two ways to assess measurement

- Analysis of homogeneity (internal consistency), which gives an indication of the reliability of a measurement instrument. During this analysis, one inspects the variances of the items and the scales, the Cronbach's α of the scales, and the change in the Cronbach's alpha when an item would be deleted from a scale.
^{[6]}

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.^{[7]}

Possible transformations of variables are:^{[8]}

- 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)

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.

If the study did not need and/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 nonresponse (whether this is random or not should be assessed during the initial data analysis phase)
- Treatment quality (using manipulation checks).
^{[9]}

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
^{[10]}

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 and/or rewritten.

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?
^{[11]}

Several analyses can be used during the initial data analysis phase:^{[12]}

- 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:^{[13]}

- 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

- Distribution

Nonlinear analysis will be 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.^{[14]}

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.^{[15]}

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 should be interpreted carefully. When testing multiple models at once there is a high chance on finding at least one of them to be significant, but this can be due to a type 1 error. It is important to always adjust the significance level when testing multiple models with, for example, a Bonferroni correction. Also, one should not follow up an exploratory analysis with a confirmatory analysis in the same dataset. An exploratory analysis is used to find ideas for a theory, but not to test that theory as well. When a model is found exploratory in a dataset, then following up that analysis with a comfirmatory analysis in the same dataset could simply mean that the results of the comfirmatory analysis are due to the same type 1 error that resulted in the exploratory model in the first place. The comfirmatory analysis therefore will not be more informative than the original exploratory analysis.^{[16]}

It is important to obtain some indication about how generalizable the results are.^{[17]} While this is hard to check, one can look at the stability of the results. Are the results reliable and reproducible? There are two main ways of doing this:

- Cross-validation: By splitting the data in 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.
- Sensitivity analysis: A procedure to study the behavior of a system or model when global parameters are (systematically) varied. One way to do this is with bootstrapping.

Many statistical methods have been used for statistical analyses. A very brief list of four of the more popular methods is:

- General linear model: A widely used model on which various methods are based (e.g. t test, ANOVA, ANCOVA, MANOVA). Usable for assessing the effect of several predictors on one or more continuous dependent variables.
- Generalized linear model: An extension of the general linear model for discrete dependent variables.
- Structural equation modelling: Usable for assessing latent structures from measured manifest variables.
- Item response theory: Models for (mostly) assessing one latent variable from several binary measured variables (e.g. an exam).

- Data Applied - an online data mining and data visualization solution.
- DevInfo - a database system endorsed by the United Nations Development Group for monitoring and analyzing human development.
- ELKI - data mining framework in Java with data mining oriented visualization functions.
- KNIME - the Konstanz Information Miner, a user friendly and comprehensive data analytics framework.
- PAW - FORTRAN/C data analysis framework developed at CERN
- SCaViS - a multiplatform (Java-based) data analysis framework from the jWork.ORG community of developers led by Dr. S.Chekanov
- R - a programming language and software environment for statistical computing and graphics.
- ROOT - C++ data analysis framework developed at CERN
- dotplot - cloud based visual designer to create analytic models
^{[18]} - SciPy - A set of Python tools for data analysis http://scipy.org/stackspec.html

In education, most educators have access to a data system for the purpose of analyzing student data.^{[19]} 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.^{[20]}

In nuclear and particle physics the data usually originate from the experimental apparatus via a data acquisition system. They are then processed, in a step usually called *data reduction*, to apply calibrations and to extract physically significant information. Data reduction is most often, especially in large particle physics experiments, an automatic, batch-mode operation carried out by software written ad-hoc. The resulting data *n-tuples* are then scrutinized by the physicists, using specialized software tools like ROOT or PAW, comparing the results of the experiment with theory.

The theoretical models are often difficult to compare directly with the results of the experiments, so they are used instead as input for Monte Carlo simulation software like Geant4, in order to predict the response of the detector to a given theoretical event, thus producing **simulated events** which are then compared to experimental data.

- Analytics
- Business intelligence
- Censoring (statistics)
- Computational physics
- Data acquisition
- Data governance
- Data mining
- Data Presentation Architecture
- Digital signal processing
- Dimension 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
- Scientific computing
- Structured data analysis (statistics)
- system identification
- Test method
- Text analytics
- Unstructured data
- Wavelet

**^**Adèr, 2008, p. 334-335.**^**"Data Cleaning". Microsoft Research. Retrieved 26 October 2013.**^**Hellerstein, Joseph (27 February 2008). "Quantitative Data Cleaning for Large Databases".*EECS Computer Science Division*: 3. Retrieved 26 October 2013.**^**Adèr, 2008, p. 337.**^**Adèr, 2008, p. 338-341.**^**Adèr, 2008, p. 341-3342.**^**Adèr, 2008, p. 344.**^**Tabachnick & Fidell, 2007, p. 87-88.**^**Adèr, 2008, p. 344-345.**^**Adèr, 2008, p. 345.**^**Adèr, 2008, p. 345-346.**^**Adèr, 2008, p. 346-347.**^**Adèr, 2008, p. 349-353.**^**Billings S.A. "Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains". Wiley, 2013**^**Adèr, 2008, p. 363.**^**Adèr, 2008, p. 361-362.**^**Adèr, 2008, p. 368-371.**^**"dotplot designer - Official Website". Retrieved 19 February 2014.**^**Aarons, D. (2009). Report finds states on course to build pupil-data systems.*Education Week, 29*(13), 6.**^**Rankin, J. (2013, March 28). How data Systems & reports can either fight or propagate the data analysis error epidemic, and how educator leaders can help.*Presentation conducted from Technology Information Center for Administrative Leadership (TICAL) School Leadership Summit.*

- Adèr, H.J. (2008). Chapter 14: Phases and initial steps in data analysis. In H.J. Adèr & G.J. Mellenbergh (Eds.) (with contributions by D.J. Hand), Advising on Research Methods: A consultant's companion (pp. 333–356). Huizen, the Netherlands: Johannes van Kessel Publishing.
- Adèr, H.J. (2008). Chapter 15: The main analysis phase. In H.J. Adèr & G.J. Mellenbergh (Eds.) (with contributions by D.J. Hand), Advising on Research Methods: A consultant's companion (pp. 333–356). Huizen, the Netherlands: Johannes van Kessel Publishing.
- 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.

Wikiversity has learning materials 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.
- ASTM International (2002).
*Manual on Presentation of Data and Control Chart Analysis*, MNL 7A, ISBN 0-8031-2093-1 - Juran, Joseph M.; Godfrey, A. Blanton (1999).
*Juran's Quality Handbook*. 5th ed. 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/SEMATEK (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, Fifth Edition. Boston: Pearson Education, Inc. / Allyn and Bacon, ISBN 978-0-205-45938-4
- Vance (September 8, 2011). "Data Analytics: Crunching the Future". Bloomberg Businessweek. Retrieved 26 September 2011.
- Hair, Joseph (2008). Marketing Research 4th ed. McGraw Hill.
*Data Analysis: Testing for Association*ISBN 0-07-340470-5