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When determining how to communicate the results, the analyst may consider data visualization techniques to help clearly and efficiently communicate the message to the audience. Data visualization uses information displays such as tables and charts to help communicate key messages contained in the data. Tables are helpful to a user who might lookup specific numbers, while charts e.

Stephen Few described eight types of quantitative messages that users may attempt to understand or communicate from a set of data and the associated graphs used to help communicate the message.

Customers specifying requirements and analysts performing the data analysis may consider these messages during the course of the process. Author Jonathan Koomey has recommended a series of best practices for understanding quantitative data. For the variables under examination, analysts typically obtain descriptive statistics for them, such as the mean average , median , and standard deviation.

They may also analyze the distribution of the key variables to see how the individual values cluster around the mean. The consultants at McKinsey and Company named a technique for breaking a quantitative problem down into its component parts called the MECE principle.

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. For example, profit by definition can be broken down into total revenue and total cost.

In turn, total revenue can be analyzed by its components, such as revenue of divisions A, B, and C which are mutually exclusive of each other and should add to the total revenue collectively exhaustive. Analysts may use robust statistical measurements to solve certain analytical problems. Hypothesis testing is used when a particular hypothesis about the true state of affairs is made by the analyst and data is gathered to determine whether that state of affairs is true or false.

For example, the hypothesis might be that "Unemployment has no effect on inflation", which relates to an economics concept called the Phillips Curve. 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. Regression analysis may be used when the analyst is trying to determine the extent to which independent variable X affects dependent variable Y e.

This is an attempt to model or fit an equation line or curve to the data, such that Y is a function of X. Necessary condition analysis NCA may be used when the analyst is trying to determine the extent to which independent variable X allows variable Y e. Each single necessary condition must be present and compensation is not possible. Users may have particular data points of interest within a data set, as opposed to 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: 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. Effective analysis requires obtaining relevant facts to answer questions, support a conclusion or formal opinion , or test hypotheses.

Facts by definition are irrefutable, meaning that any person involved in the analysis should be able to agree upon them. This makes it a fact.

Whether persons agree or disagree with the CBO is their own opinion. As another example, the auditor of a public company must arrive at a formal opinion on whether financial statements of publicly traded corporations are "fairly stated, in all material respects. When making the leap from facts to opinions, there is always the possibility that the opinion is erroneous. There are a variety of cognitive biases that can adversely affect analysis.

In addition, individuals may discredit information that does not support their views. Analysts may be trained specifically to be aware of these biases and how to overcome them.

In his book Psychology of Intelligence Analysis , retired CIA analyst Richards Heuer wrote that analysts should clearly delineate their assumptions and chains of inference and specify the degree and source of the uncertainty involved in the conclusions. He emphasized procedures to help surface and debate alternative points of view.

Effective analysts are generally adept with a variety of numerical techniques. However, audiences may not have such literacy with numbers or numeracy ; they are said to be innumerate. Persons communicating the data may also be attempting to mislead or misinform, deliberately using bad numerical techniques. For example, whether a number is rising or falling may not be the key factor. More important may be the number relative to another number, such as the size of government revenue or spending relative to the size of the economy GDP or the amount of cost relative to revenue in corporate financial statements.

This numerical technique is referred to as normalization [7] or common-sizing. There are many such techniques employed by analysts, whether adjusting for inflation i. Analysts apply a variety of techniques to address the various quantitative messages described in the section above.

Analysts may also analyze data under different assumptions or scenarios. 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.

A data analytics approach can be used in order to predict energy consumption in buildings. Analytics is the "extensive use of data, statistical and quantitative analysis, explanatory and predictive models, and fact-based management to drive decisions and actions. In education , most educators have access to a data system for the purpose of analyzing student data. This section contains rather technical explanations that may assist practitioners but are beyond the typical scope of a Wikipedia article.

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: 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: 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.

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.

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

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

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. Data analysis, being one of the most popular services offered at Statistics Consultation, has a detailed process chalked out for completion of the work.

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