Data analysis

Data analysis is a process for obtaining raw data, and subsequently converting it into information useful for decision-making by users.^[1] 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."^[7]

There are several phases, and they are iterative, in that feedback from later phases may result in additional work in earlier phases.^[8]

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).^[9] 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).^[8]

Data may be collected from a variety of sources.^[10] 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.^[11] Data collection or data gathering is the process of gathering and measuring information on targeted variables in an established system, which then enables one to answer relevant questions and evaluate outcomes. 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.^[8]

Data integration is a precursor to data analysis: Data, when initially obtained, must be processed or organized for analysis. For instance, this 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(excel) or statistical software.^[8]

Once processed and organized, the data may be incomplete, contain duplicates, or contain errors.^[12] The need for data cleaning will arise from problems in the way that the data is entered and stored.^[12][13] 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.^[14][15]

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.^[16] 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.^[17] 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. Text data spell checkers can be used to lessen the amount of mistyped words. However, it is harder to tell if the words are contextually (i.e., semantically and idiomatically) correct.

Once the datasets are cleaned, they can then begin to be analyzed using exploratory data analysis. The process of data exploration may result in additional data cleaning or additional requests for data; thus, the initialization of the iterative phases mentioned above.^[18] Descriptive statistics, such as the average, median, and standard deviation, are often used to broadly characterize the data.^[19][20] Data visualization is also used, in which the analyst is able to examine the data in a graphical format in order to obtain additional insights about messages within the data.^[8]

Mathematical formulas or models (also known as algorithms), may be applied to the data in order to identify relationships among the variables; for example, checking for correlation and by determining whether or not there is the presence of causality. 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).^[21]

Inferential statistics utilizes techniques that measure the relationships between particular variables.^[22] 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), i.e. is Y a function of X? This can 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.^[23]

A data product is a computer application that takes data inputs and generates outputs, feeding them back into the environment.^[24] 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.^[25][8]

Once data is analyzed, it may be reported in many formats to the users of the analysis to support their requirements.^[27] The users may have feedback, which results in additional analysis.

When determining how to communicate the results, the analyst may consider implementing a variety of data visualization techniques to help communicate the message more clearly and efficiently to the audience. Data visualization uses information displays (graphics such as, tables and charts) to help communicate key messages contained in the data. Tables 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.^[28]

Stephen Few described eight types of quantitative messages that users may attempt to communicate from a set of data, including the associated graphs.^[29][30]

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.
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. A bar chart may be used to show the comparison across the salespersons.^[31]
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.^[32]
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.^[33]
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.
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.^[34]
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.^[35]
8. Geographic or geo-spatial: 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 typically used.^[29]

Author Jonathan Koomey has recommended a series of best practices for understanding quantitative data. These include:^[16]

• 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.

For the variables under examination, analysts typically obtain descriptive statistics, 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.^[16]

McKinsey and Company named a technique for breaking down a quantitative problem into its component parts called the MECE principle. MECE means "Mutually Exclusive and Collectively Exhaustive".^[36] 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.^[37]

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 hypothesis is true or false.^[38] For example, the hypothesis might be that "Unemployment has no effect on inflation", which relates to an economics concept called the Phillips Curve.^[39] 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.^[40]

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)?").^[41]

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)?").^[41] 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),^[42] 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.^[43]

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.^[44][45][46]

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.^[47]

Effective analysis requires obtaining relevant facts to answer questions, support a conclusion or formal opinion, or test hypotheses.^[48] Facts by definition are irrefutable, meaning that any person involved in the analysis should be able to agree upon them. 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".^[49] This requires extensive analysis of factual data and evidence to support their opinion.

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.^[50] In addition, individuals may discredit information that does not support their views.^[51]

Analysts may be trained specifically to be aware of these biases and how to overcome them.^[52] 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.^[53] He emphasized procedures to help surface and debate alternative points of view.^[54]

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.^[55] Persons communicating the data may also be attempting to mislead or misinform, deliberately using bad numerical techniques.^[56]

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.^[57] This numerical technique is referred to as normalization^[16] 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.^[58]

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.^[59] 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.^[60]

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.^[61]

In education, most educators have access to a data system for the purpose of analyzing student data.^[62] 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.^[63]

Free software for data analysis include:

• DevInfo – A database system endorsed by the United Nations Development Group for monitoring and analyzing human development.^[95]
• 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.^[96]
• ROOT – C++ data analysis framework developed at CERN.
• SciPy – Python library for scientific computing.
• Julia – A programming language well-suited for numerical analysis and computational science.

The typical data analysis workflow involves collecting data, running analyses, creating visualizations, and writing reports. However, this workflow presents challenges, including a separation between analysis scripts and data, as well as a gap between analysis and documentation. Often, the correct order of running scripts is only described informally or resides in the data scientist's memory. The potential for losing this information creates issues for reproducibility.

To address these challenges, it is essential to document analysis script content and workflow. Additionally, overall documentation is crucial, as well as providing reports that are understandable by both machines and humans, and ensuring accurate representation of the analysis workflow even as scripts evolve.^[97]

Different companies and organizations hold data analysis contests to encourage researchers to utilize their data or to solve a particular question using data analysis. A few examples of well-known international data analysis contests are:

• Kaggle competitions; the Kaggle platform is owned and run by Google.^[98]
• LTPP data analysis contest^[99] held by FHWA and ASCE.^[100]