Data analysis Examination Study Notes Latest Updated Guide 2024/2025, Exams of Finance

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Data analysis

Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering usefulinformation, 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 models for predictive forecasting or classification, whiletext 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.

Contents [hide]

• 1The process of data analysis

o 1.1Data requirements

o 1.2Data collection

o 1.3Data processing

o 1.4Data cleaning

o 1.5Exploratory data analysis

o 1.6Modeling and algorithms

o 1.7Data product

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o 1.8Communication

• 2Quantitative messages
• 3Techniques for analyzing quantitative data
• 4Analytical activities of data users
• 5Barriers to effective analysis

o 5.1Confusing fact and opinion

o 5.2Cognitive biases

o 5.3Innumeracy

• 6Other topics

o 6.1Analytics and business intelligence

o 6.2Education

• 7Practitioner notes

o 7.1Initial data analysis

▪ 7.1.1Quality of data

▪ 7.1.2Quality of measurements

▪ 7.1.3Initial transformations

▪ 7.1.4Did the implementation of the study fulfill the intentions of the research design?

▪ 7.1.5Characteristics of data sample

▪ 7.1.6Final stage of the initial data analysis

▪ 7.1.7Analysis

▪ 7.1.8Nonlinear analysis

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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.

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). [3]

Data collection [edit]

Data is collected from a variety of sources. The requirements may be communicated by analysts to custodians of the data, such as information technology personnel within an organization. The data may also be collected from sensors in the environment, such as traffic cameras, satellites, recording devices, etc. It may also be obtained through interviews, downloads from online sources, or reading documentation.[3]

Data processing [edit]

Data initially obtained must be processed or organized for analysis. For instance, this may involve placing data into rows and columns in a table format for further analysis, such as within a spreadsheet or statistical software.[3]

Data cleaning [edit]

Once processed and organized, the data may be incomplete, contain duplicates, or contain errors. 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 co lumn segmentation.[4]^ 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 believed to be reliable. [5] (^) Unusual amounts above or below pre-determined thresholds may also be reviewed. There are

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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.[6]

Exploratory data analysis [edit]

Once the data is cleaned, it can be analyzed. Analysts may apply a variety of techniques referred to as exploratory data analysi s to beg in understanding the messages conta ined in the data.[7][8]^ The process of exploration may result in additional data cleaning or additional requests for data, so these activities may be iterative in nature. Descriptive statistics such as the average or median may be generated to help understand the data. Data visualization may also be used to examine the data in graph ical format, to obta in add itiona l insight regard ing the messages with in the data.[3]

Modeling and algorithms [edit]

Mathematical formulas or models called algorithms may be applied to the data to identify relationships among the variables, such as correlation or causation. In general terms, models may be developed to evaluate a particular variable in the data based on other variable(s) in the data, with some residual error depend ing on mode l accuracy (i.e., Data = Model + Error).[1] Inferential statistics includes techniques to measure relationships between particular variables. For example, regression analysis may be used to model whether a change in advertising (independent variable X) explains the variation in sales (dependent variable Y). In mathematical terms, Y (sales) is a function of X (advertising). 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. Analysts may attempt to build models that are descriptive of the data to simplify analysis and commun icate resu lts.[1]

Data product [edit]

A data product is a computer application that takes data inputs and generates outputs, feeding them back into the environment. It may be based on a model or algorithm. An example is an application that analyzes data about customer purchasing history and recommends other purchases the customer might en joy.[3]

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Author 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.

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 sales persons (the category , with each sales person a categorical subdivision ) during a single period. A bar chartmay be used to show the comparison across the sales persons.
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.
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 comparison of the actual versus the reference amount.
5. Frequency distribution: Shows the number of observations of a particular variable for 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

A scatterplot illustrating correlation between two variables (inflation and unemployment) measured at points in time.

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unemployment (X) and inflation (Y) for a sample of months. A scatter plot is typically used for this message.

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.
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 typ ical graphic used.[10][11]

Techniques for analyzing quantitative data[edit]

See also: Problem solving

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

• Check raw data for anomalies prior to performing your 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 ana lysis of return on equity.[5] 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.

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Description Abstract

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 Audi TT?

• How long is the movie Gone with the Wind?_

2 Filter

Given some concrete conditions on attribute values, find data cases

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?_

satisfying those conditions.

Compute Derived Value

Given a set of data cases, compute an aggregate numeric representation of those data cases.

What is the value of

_- 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?_

3 aggregation over a given^ functionset S of data^ F cases?

Find Extremum

Find data cases possessing an (^) 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 Robin Williams film has the most recent release date?_

4 extreme attribute^ valueover itofs^ an range within the data set.

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

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?_ values set. within the - What actresses are in the data set?

7 Characterize Given a set of data What is the distribution of - What is the distribution of

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

Distribution

cases and a quantitative attribute of interest, characterize the distribution of that attribute’s values

values of attribute A in a set S of data cases?

carbohydrates in cereals?

- What is the age distribution of shoppers? over the set.

Find Anomalies

Identify any anomalies within a given set of data (^) 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?_

8 cases to a given^ with respect relationship or expectation, e.g. statistical outliers.

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?_

0 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?_

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.

Confusing fact and opinion [edit]

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Analytic activities of data visualization users

present value based on some interest rate, to determine the valuation of the company or its stock. 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.

Other topics[edit]

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 use data to understand and ana lyze business performance.[19]

Education [edit]

In education, most educators have access to a data system for the purpose of analyzing student data.[20]^ 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/d isplay and content decisions) to improve the accuracy of educators’ data ana lyses.[21]

Practitioner notes[edit]

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

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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 origina l research question. The initial data ana lysis phase is guided by the fo llow ing four questions:[22] 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, 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 ma in ana lys is phase.[23] 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. 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 de leted from a sca le.[24] 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 du ring the ma in ana lysis phase.[25] Possib le transformations of va riab les are:[26]
• 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)

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• 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 ca lcu late propensity scores and include them as covariates in the ma in analyses?[29] Analysis [edit] Severa l ana lyses can be used during the in itial data ana lysis phase:[30]
• 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 statistica l techniques are available for each level :[31]
• 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

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• Continuous variables
  • Distribution
    • Statistics (M, SD, variance, skewness, kurtosis)
    • Stem-and-leaf displays
    • Box plots Nonlinear analysis [edit] 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 c losely re lated to nonlinear system identification.[32]^ Main

data analysis [edit]

In the main analysis phase analyses aimed at answering the research question are performed as we ll as any other relevant ana lysis needed to w rite the fi rst draft of the research report.[33] 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. 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 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. The confirmatory analysis therefore will not be more informative than the original exploratory analysis.[34] Stability of results [edit]

It is important to obta in some ind ication about how generalizab le the resu lts are.[35]^ 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:

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statistics portal

• R - a programming language and software environment for statistical computing and graphics.
• ROOT - C++ data analysis framework developed at CERN
• dotp lot — cloud based visua l designer to create analytic mode ls[36]
• SciPy - A set of Python tools for data analysis http://scipy.org/stackspec.html
• Statsmodels - a Python module that allows users to explore data, estimate statistical models, and perform statistical tests http://statsmodels.sourceforge.net/
• Pandas - A software library written for the Python programming language for data manipulation and analysis.

See also[edit]

• Analytics
• Business intelligence
• Censoring (statistics)
• Computational physics
• Data acquisition
• Data governance
• Data mining
• Data Presentation Architecture
• Digital signal processing
• Dimension reduction
• Early case assessment

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• 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

References[edit]

Citations [edit]

1. ^ Jump up to: a^ b^ c^ Judd, Charles and, McCleland, Gary (1989). Data Analysis. Harcourt Brace Jovanovich. ISBN 0-15-516765-0.