Data Gathering and Analysis

 

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Multivariate Analysis

 

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Data Gathering and Analysis

 

Rationale

Research is often described as an active, diligent, and systematic process of inquiry aimed at discovering, interpreting, and revising facts. This intellectual investigation produces a greater knowledge of events, behaviors, theories, and laws and makes practical applications possible. The term research is also used to describe an entire collection of information about a particular subject, and is usually associated with the output of science and the scientific method. The word research derives from the French recherche, from rechercher, to search closely where "chercher" means "to search" (see French language); its literal meaning is 'to investigate thoroughly'. Research is funded by public authorities, by charitable organisations and by private groups, including many companies.

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Data Analysis is the act of transforming data with the aim of extracting useful information and facilitating conclusions. Depending on the type of data and the question, this might include application of statistical methods, curve fitting, selecting or discarding certain subsets based on specific criteria, or other techniques. Respect to Data mining, data analysis is usually more narrowly intended as not aiming to the discovery of unforeseen patterns hidden in the data, but to the verification or disproval of an existing model, or to the extraction of parameters necessary to adapt a theoretical model to (experimental) reality.

 

Choropleth Mapping with Exploratory Data Analysis

 

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Investigate Useful Ways to Conceptualise or Group Items

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A Conceptual Framework is used in research to outline possible courses of action or to present a preferred approach to a system analysis project. The framework is built from a set of concepts linked to a planned or existing system of
methods, behaviors, functions, relationships, and objects. A conceptual framework might, in computing terms, be thought of as a relational model.

 

 

A Comprehensive Analysis of Permission Marketing

 

The idea of a conceptual framework that is separated in some way from the content of the framework was criticized in philosopher Donald Davidson's essay "On the Very Idea of a Conceptual Scheme".

Conceptual framework of accounting “seeks to identify the nature, subject, purpose and broad content of general-purpose financial reporting and the qualitative characteristics that financial information should possess”. (Deegan, 2005, p.1184)

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Multidimensional Scaling (MDS) is a set of related statistical techniques often used in data visualisation for exploring similarities or dissimilarities in data. An MDS algorithm starts with a matrix of item-item similarities, then assigns a location of each item in a low-dimensional space, suitable for graphing or 3D visualisation.

 

 

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Classical Multidimensional Scaling Classical Multidimensional Scaling

 

 

Generate Hypothesis

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A Hypothesis (from Greek ὑπόθεσις) consists either of a suggested explanation for a phenomenon or of a reasoned proposal suggesting a possible correlation between multiple phenomena. The term derives from the ancient Greek, hypotithenai meaning "to put under" or "to suppose". The scientific method requires that one can test a scientific hypothesis. Scientists generally base such hypotheses on previous observations or on extensions of scientific theories.

 

 

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Generating hypotheses: A method for the madness

 

 

Test Hypothesis

One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. A Statistical Hypothesis Test, or more briefly, hypothesis test, is an algorithm to state the alternative (for or against the hypothesis) which minimizes certain risks.

 

Hypothesis Testing - Statistical Test of Population Mean with known Variance - Theory & Examples

 

This article describes the commonly used frequentist treatment of hypothesis testing. From the Bayesian point of view, it is appropriate to treat hypothesis testing as a special case of normative decision theory (specifically a model selection problem) and it is possible to accumulate evidence in favor of (or against) a hypothesis using concepts such as likelihood ratios known as Bayes factors.

There are several preparations we make before we observe the data.

The hypothesis must be stated in mathematical/statistical terms that make it possible to calculate the probability of possible samples assuming the hypothesis is correct. For example: The mean response to treatment being tested is equal to the mean response to the placebo in the control group. Both responses have the normal distribution with this unknown mean and the same known standard deviation ... (value).

A test statistic must be chosen that will summarize the information in the sample that is relevant to the hypothesis. Such a statistic is known as a sufficient statistic. In the example given above, it might be the numerical difference between the two sample means, m1 − m2.

The distribution of the test statistic is used to calculate the probability sets of possible values (usually an interval or union of intervals). In this example, the difference between sample means would have a normal distribution with a standard deviation equal to the common standard

 

deviation times the factor where n1 and n2 are the sample sizes.

 

Among all the sets of possible values, we must choose one that we think represents the most extreme evidence against the hypothesis. That is called the critical region of the test statistic. The probability of the test statistic falling in the critical region when the hypothesis is correct is called the alpha value (or size) of the test.

The probability that a sample falls in the critical region when the parameter is θ, where θ is for the alternative hypothesis, is called the power of the test at θ. The power function of a critical region is the function that maps θ to the power of θ.

After the data is available, the test statistic is calculated and we determine whether it is inside the critical region.

If the test statistic is inside the critical region, then our conclusion is one of the following:

The hypothesis is incorrect, therefore reject the null hypothesis. (Therefore the critical region is sometimes called the rejection region, while its complement is the acceptance region.)

An event of probability less than or equal to alpha has occurred.

The researcher has to choose between these logical alternatives. In the example we would say: the observed response to treatment is statistically significant.

If the test statistic is outside the critical region, the only conclusion is that

There is not enough evidence to reject the hypothesis.

This is not the same as evidence in favor of the hypothesis. That we cannot obtain using these arguments, since lack of evidence against a hypothesis is not evidence for it. On this basis, statistical research progresses by eliminating error, not by finding the truth.
 

 

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Undertake Factor Analysis

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Factor Analysis is a statistical technique used to explain variability among observed random variables in terms of fewer unobserved random variables called factors. The observed variables are modeled as linear combinations of the factors, plus "error" terms. Factor analysis originated in psychometrics, and is used in behavioral sciences, social sciences, marketing, product management, operations research, and other applied sciences that deal with large quantities of data.

 

Factor/Principal Components Analysis

 

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References

Abdi, H. "[1] (2003). Factor Rotations in Factor Analyses. In M. Lewis-Beck, A. Bryman, T. Futing (Eds): Encyclopedia for research methods for the social sciences. Thousand Oaks (CA): Sage. pp. 792-795.]".

Abdi, H. "[2] ((2007). Multiple factor analysis. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage.".

Abdi, H. "[3] ((2007). Multiple correspondence analysis. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage.".

Charles Spearman. Retrieved July 22, 2004, from http://www.indiana.edu/~intell/spearman.shtml

Exploratory Factor Analysis - A Book Manuscript by Tucker, L. & MacCallum R. (1993). Retrieved June 8, 2006, from: http://www.unc.edu/~rcm/book/factornew.htm

Factor Analysis. (2004). Retrieved July 22, 2004, from http://comp9.psych.cornell.edu/Darlington/factor.htm

Factor Analysis. Retrieved July 23, 2004, from http://www2.chass.ncsu.edu/garson/pa765/factor.htm

Raymond Cattell. Retrieved July 22, 2004, from http://www.indiana.edu/~intell/rcattell.shtml

Sternberg, R.J.(1990). The geographic metaphor. In R.J. Sternberg, Metaphors of mind: Conceptions of the nature of intelligence (pp.85-111). New York: Cambridge.

Stills, D.L. (Ed.). (1989). International encyclopedia of the social sciences: Biographical supplement (Vol. 18). New York: Macmillan.

 

 

Know What Special Statistical Techniques are Available for Analysing Most Research Problems

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Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities; it is also used and misused for making informed decisions in all areas of business and government.

Statistical analysis

 

Statistical methods can be used to summarize or describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, to draw inferences about the process or population being studied; this is called inferential statistics. Both descriptive and inferential statistics can be considered part of applied statistics. There is also a discipline of mathematical statistics, which is concerned with the theoretical basis of the subject.

The word statistics is also the plural of statistic (singular), which refers to the result of applying a statistical algorithm to a set of data, as in employment statistics, accident statistics, etc.

 

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Multivariate Analysis (MVA) is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time. In design and analysis, the technique is used to perform trade studies across multiple dimensions while taking into account the effects of all variables on the responses of interest.

 

Uses for multivariate analysis includes:

Design for capability (also known as capability-based design)Inverse design, where any variable can be treated as an independent variableAnalysis of alternatives, the selection of concepts to fulfill a customer needAnalysis of concepts with respect to changing scenarios

Identification of critical design drivers and correlations across hierarchical levels

Multivariate analysis can be complicated by the desire to include physics-based analysis to calculate the effects of variables for a hierarchical "system-of-systems." Often, studies that wish to use multivariate analysis are stalled by the dimensionality of the problem. These concerns are often eased through the use of surrogate models, highly accurate approximations of the physics-based code. Since surrogate models take the form of an equation, they can be evaluated very quickly. This becomes an enabler for large-scale MVA studies: while a Monte Carlo simulation across the design space is difficult with physics-based codes, it becomes trivial when evaluating surrogate models, which often take the form of response surface equations.

Chemometrics & Multivariate Analysis in Food Science

 

References

Abdi, H (2003). "Multivariate analysis. In M. Lewis-Beck, A. Bryman, T. Futing (Eds): Encyclopedia for research methods for the social sciences. Thousand Oaks (CA): Sage. pp. 699-702.". [1]

KV Mardia, JT Kent, and JM Bibby (1979). "Multivariate Analysis. Academic Press,".[2]

 

 

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Consider any plans or problems you have in data gathering and analysis, either in your project or in your work.  Be prepared to discuss these. 

 

Recommended Texts

Business Research Metehods

Business Research Methods, 8/e

Donald R Cooper, Florida Atlantic University
Pamela S Schindler, Wittenberg University

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Evaluation and Control Program Introduction

 

 

 

 

 

 

 

Quantitative Analysis

 

Case Studies

McDonald's

 

McDonald's Corporation (NYSE: MCD) is the world's largest chain of fast-food restaurants, primarily selling hamburgers, chicken, french fries, milkshakes and soft drinks. More recently, it also offers salads, fruit and carrot sticks.

The business began in 1940, with a restaurant opened by siblings Dick and Mac McDonald in San Bernardino, California. Their introduction of the "Speedee Service System" in 1948 established the principles of the modern fast-food restaurant. The present corporation dates its founding to the opening of a franchised restaurant by Ray Kroc, in Des Plaines, Illinois on April 15, 1955, the ninth McDonald's restaurant overall. Kroc later purchased the McDonald brothers' equity in the company and led its worldwide expansion.

With the successful expansion of McDonald's into many international markets, the company became a symbol of globalization and the spread of the American way of life. Its prominence also made it a frequent subject of public debates about obesity, corporate ethics and consumer responsibility.

 

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