DATA ANALYSIS

Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making. Data analysis has multiple facts 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.

The process of data analysis

Data analysis is a process, within which several phases can be distinguished:

Data cleaning

Data cleaning is an important procedure during which the data are inspected, and erroneous data are—if necessary, preferable, and possible—corrected. Data cleaning can be done during the stage of data entry. If this is done, it is important that no subjective decisions are made. The guiding principle provided by Adèr (ref) is: during subsequent manipulations of the data, information should always be cumulatively retrievable. In other words, it should always be possible to undo any data set alterations. Therefore, it is important not to throw information away at any stage in the data cleaning phase. All information should be saved (i.e., when altering variables, both the original values and the new values should be kept, either in a duplicate data set or under a different variable name), and all alterations to the data set should be carefully and clearly documented, for instance in a syntax or a log.

Initial data analysis

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

Quality of data

The quality of the data should be checked as early as possible. Data quality can be assessed in several ways, using different types of analyses: 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.

Quality of measurements

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 quality:

Confirmatory factor analysis

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.

Initial transformations

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

Possible transformations of variables are:

·         Square root transformation (if the distribution differs moderately from normal)

·         Log-transformation (if the distribution differs substantially from normal)

·         Inverse transformation (if the distribution differs severely from normal)

·         Make categorical (ordinal / dichotomous) (if the distribution differs severely from normal, and no transformations help)

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

One should check the success of the randomization 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).

Characteristics of data sample

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

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

·         Basic statistics of important variables

·         Scatter plots

·         Correlations and associations

·         Cross-tabulations

Final stage of the initial data analysis

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

Also, the original plan for the main data analyses can and should be specified in more detail 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?

Analyses

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

·         Univariate statistics(single variable)

·         Bivariate associations (correlations)

·         Graphical techniques (scatter plots)

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

·         Nominal and ordinal variables

·         Frequency counts (numbers and percentages)

·         Associations

·         circumambulations (crosstabulations)

·         hierarchical loglinear analysis (restricted to a maximum of 8 variables)

·         loglinear analysis (to identify relevant/important variables and possible confounders)

·         Exact tests or bootstrapping (in case subgroups are small)

·         Computation of new variables

·         Continuous variables

·         Distribution

·         Statistics (M, SD, variance, skewness, kurtosis)

·         Stem-and-leaf displays

·         Box plots

References

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. & 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