Statistical Discussion, Coursework Example

How may variance and standard deviation be applied to a real-world business-related problem? Provide a specific application in which these measures are useful.

The concepts of variance and standard deviation are quite useful in analyzing business issues.  Variance describes roughly how far numbers in a data set are spread out from one another; standard deviation is typically defined as the square root of variance.  Standard deviation is also used to measure spread; however, standard deviation is usually more useful because it measures around the mean- thus giving one a good idea if there are outliers or other factors skewing the mean.

One particular area where variance and standard deviation are useful is real estate transactions.  For example, say there is client who wishes to move into an “upscale” neighborhood, and thus asks you the mean value of a house there.  While an average gives you an approximate estimate, it does not give one an understanding of spread around the mean.  So while the average house value in a neighborhood maybe around $550,000 that could be due to one house valued over one million dollars, and other houses valued under $100,000.  In this case, the variance and standard deviation would give valuable information regarding the neighborhood’s true condition.

When would you use descriptive over inferential statistics? Provide a specific scenario and explain your rationale.

The difference between inferential statistics depends on what question one wants to answer.  For example, if one wanted to know the basic demographic characteristics of a population of the Hispanic population in a district of Kansas City, inferential statistics such as mean age, mean income, mean number of children (and measures of variance) would likely be sufficient.  However, if one wanted to test whether the demographics in this particular region were different than in another region, (say Kansas City versus Los Angeles) one would want to use inferential statistics to understand differences in the two populations.

When would you use Chebyshev’s theorem and the empirical rule in business? How are they calculated? Provide one real-life example that requires Chebyshev’s theorem and one that requires the empirical rule.

Chebyshev’s theorem helps to calculate the placement of a data point, stratified by the number of standard deviations, in any distribution, even one that is not necessarily normal. In particular, the formula states that 1/(n^2) of values are more than n standard deviations away from the mean.  The empirical rule only applies to the normal distribution: That is, 68% of all data points are within one standard deviation of the mean, 95% of all data point are within two standard deviations of the mean.  While  Chebyshev’s theorem is more applicable in different situations, the empirical rule is clearly more simplistic and elegant in use with problems with a normal distribution.

A use of the empirical rule would be if you wanted to know where in the population distribution a male weighing 205 pound was versus all males.  A use of Chebyshev’s theorem would be to understand where in the distribution a stock performed in 2011 versus all other stocks.

Why is using Bayes’ theorem important to help answer business-related questions? What does this theorem allow you to do that traditional statistics do not? What are some prerequisites for using Bayesian statistics?

Traditionally in statistics, there is rivalry between probabilistic and Bayesian statistics.  While probabilistic statistics relies on calculating probabilities based on static data and underling distribution, the Bayesian formula is more dynamic in nature allowing for implementing new information as it become available;  So, for example, if I am trying to calculate the probability of a successful event in an iterative process, I can use the feedback results to constantly revise my estimates.  The main prerequisites for application of Bayesian techniques are that pieces of evidence are conditionally independent- that is, they are not related to one another.

As a manager, what are some benefits of applying probability concepts to solve business-related problems? Would business decisions suffer without probability concepts? Explain.

Probability concepts are important to solve business-related problems in that they provide a rough estimate that allows one to prepare for possible results.  Business decisions would necessarily suffer without probability concepts because there would not be robust tools to estimate would happen when launching a new product or estimating production errors at a manufacturing plant.
Week Two Discussion Questions

Read Albert Einstein’s quote on p. 55 of Business Research Methods. What is the value of this statement in terms of the research process? What is the relevance and relationship of this statement to the technologically advancing business world? Where do these questions allow us to go?

The value of Einstein’s quote can be described in one word: perspective.  If the main value of the research problem lies in asking the right question, the research process can play a key role in understanding which questions have robust evidence and which do not have robust evidence.  As technology continues to develop into areas not necessarily known by man, asking the right research question will become more and more important allowing us to find solutions.

What are some examples of operational definitions in research design within your profession?

As a financial analyst, more of the operational definitions in my job deal with understanding of different financial instruments such as equity, stock, bonds, etc.  For example, stock is equity held in a company; a bond is essentially holding a company’s debt.

Of the exploratory, formalized, and casual research designs types, which would you use to assess the effectiveness of an aspect of your job? Explain.

I think in this question, exploratory would likely be the best way to assess the effectiveness of an aspect of my job.  This is because that question is an essential why question that cannot be answered with the formalized research types.  In addition, this question is not necessarily a causal one: that is, the question is not asking what x causes y.

What is the purpose of sampling? What are some concerns and dangers of sampling? How important is the sample design to data validity? Explain. Provide an example where a sample might misrepresent data validity.

The main point of sampling is to acquire a roughly accurate estimate of what the population characteristics would be.  The main concerns and dangers of sampling is using improper techniques that might result in a biased sample, that in turn, would result in biased inferences regarding the population in question.  For example, if one wanted to  acquire a rough estimate of  political sentiment in a building and picked a floor at random- a floor of all senior citizens- that might not be an objective sample to draw conclusions from.

How does each key managerial dimension promote effective research? How does each dimension help meet desired results? What is the inherent value of these dimensions to a manager and the decision-making process?

Key managerial dimensions provide one with key context in order to understand potential answers and problems.  For example, while one managerial dimension might deal with one set of issues, another might deal with another set of issues.  These dimensions are important because of the information they provide to the manager; that is, the manager can use different dimensions to understand different issues that allows for a more informed decision.

You have received a business research study done by a consultant for a life insurance company. The study is a survey of customer satisfaction based on a sample of 600. You are asked to comment on its quality. What do you look for?

Initially, quality would likely consist of the sample size, assumptions, and study design.  I have no way to assess whether 600 is an appropriate customer size or not; if there are a total of 625 customers, it would probably be a fairly representative study, if there were 100,000 customers, probably not.  Then I would like at the assumptions underpinning the survey and what research design and statistical methods were used to analyze the survey.

In your organization’s management development program, there was a heated discussion between people who claimed that theory is impractical and not effective, and others who claimed that effective theory is the most practical approach to problems. What position would you take and why?

One must start out any robust examination of an issue with a theoretical approach.  That is because all analytical methods used to investigate are essentially based on underlying theories.  If one says all theory is useless, they would likely have to answer how they proceed without a road map.  It may ultimately be the case that the initial theory chosen didn’t work, and thus people posit “theory doesn’t work”; however, but that will allow the researcher to move onto towards developing another one.  .

What is the relationship between deductive and inductive arguments? Why are both types valuable in research? Provide examples of each type, illustrating benefits of their usage.

In general, inductive arguments feed into the information used for deductive arguments.  That is, inductive reasoning from a number of data points turns into the statements typically used for syllogistic reasoning.  An example using deductive reasoning is the following: 1) Socrates is a man; 2) All men are mortal; 3) Socrates is mortal.  The advantage of deductive reasoning is the simplistic nature and generalizations that can be made (if the information is correct).  The disadvantage of using the deductive method is if the information used in the statements is wrong, one will commit a fallacy.  An example of the inductive measure of reasoning is the following: many people in this area are Caucasians and own Lexus automobiles; thus, Caucausians must purchase a majority of automobiles.

You observe female sales representatives having lower customer defections than male sales representatives. What concepts and constructs would you use to study this phenomenon? How might the concepts or constructs relate to explanatory hypotheses? Explain.

In order to study the following phenomenon, I would employ the following concepts:  First, I would want to define customer retention in an objective sense for both male and female employees.  Second, I  would want to conceptualize the different demographic characteristics of the male and female members such as age, marriage status, etc in order to see if there was anything abnormal with the sample.