The material below comprises excerpts from books by Dr. Johnathan Mun, our CEO and founder, such as Readings in Certified Quantitative Risk Management, 3rd Edition, and Quantitative Research Methods Using Risk Simulator and ROV BizStats Software Applying Econometrics, Multivariate Regression, Parametric and Nonparametric Hypothesis Testing, Monte Carlo Risk Simulation, Predictive Modeling, and Optimization, 4th Edition (https://www.amazon.com/author/johnathanmun). All screenshots and analytical models are run using the ROV Risk Simulator and ROV BizStats software applications. Statistical results shown are computed using Risk Simulator or BizStats. Online Training Videos are also available on these topics as well as the Certified in Quantitative Risk Management (CQRM) certification program. All materials are copyrighted as well as patent protected under international law, with all rights reserved.

This chapter is the heart of the quantitative portion of the book in that it covers the most commonly used analytical methodologies. As in most research projects, whenever data is collected, it will need to be analyzed. Typically, the researcher is attempting to test some theory or hypothesis whereby if a certain situation or condition is applied in an experiment, the data is collected prior to and after said experiment and analyzed to see if the hypothesis is validated or debunked.

For example, if a bank is trying to test whether a new check deposit scanning system and associated training will reduce its operational risks (i.e., making mistakes during deposits), it could start collecting data prior to implementing the new system in a single branch, and continue to collect the same data after the system proof of concept implementation at that single branch. Then, using statistical hypothesis tests, determine whether the differences seen in the before and after data can be attributed to randomness or are a clear indication that the new system is working, and, hence, make a decision about implementing the same system in all its other branches.

Other examples could include the U.S. military testing the effectiveness of implementing a series of equipment and support services to increase the mean time between failures (MTBF); a pharmaceutical company assessing the efficacy of its new experimental drug; a vehicle manufacturer testing a new engineering design that improves engine life compared to a conventional design; and the like.

The chapter begins with simple t-, F-, and z-tests where two variables are tested simultaneously to determine if their means and variances are statistically significantly different or similar. The chapter continues with the application of ANOVA or analysis of variance, where multiple variables are tested at once. Other nonparametric tests are introduced, where normality and large datasets do not have to be assumed, as they are required in standard t- and z-tests. Tests of normality, multicollinearity, and heteroskedasticity are introduced, together with the basic concepts of multivariate linear and nonlinear regression models.

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