Applied Managerial Decision-Making: Sample Memo

The purpose of this memorandum is to bring attention to the newest software that Company W is testing out. Although we have hundreds of staff working in four regions, we still need to try and bring each and everyone of them on board to become more proficient with this software so that it can help them maintain a handle on their contacts. It is my desire to enlighten the VP of sales on what null and alternative hypothesis are and how it pertains to business when using non-parametric test on data via chi-square distribution. Hopefully at the end of this memorandum, you will have gained more knowledge of how this process works and what it can do for Company W.

Company W has as I said in the introduction, that it has hundreds of employees which are placed in the four regions which we occupy. The company has upgraded and have decide to use a software that basically keeps an accurate count on the number of sales that each and every employee makes per product for the business. Each employee from the different regions have contracts and as I said also, they are expected to make the same number of sales each month. The problem with this is that over the past few months or so, only a certain percentage of the employees have met that quota or expectation. So it came to my attention that the Sales VP of Company W has gotten highly involved by wanting to know what possible theories could be used or incorporated to make a statistical analysis of this situation and what testing could be done to make for a answer to this problematic situation. In fact, before we can address this situation properly, we have to do the necessary we must do all the statistical testing so that we can make a sound decision to help index this situation. In saying this, I would delve to say that are many ways that this problem could be addressed to do this statistical analysis. Two of which are non-parametric statistics and hypothesis testing just to name a few. In fact, both of these will be further discussed in the following portions of this memorandum.

Statistical Theories used for Analyzing:

Hypothesis Testing

When obtaining conclusions dealing with a population that utilize information that is attained from a sample or portion per se, the use of hypothesis testing is what is done to get this information. The way in which this is done is it is done by getting the information from just that portion so that a decision can be made by the person doing the research to the extent of being able to either reject or accept what the hypothesis says. Null and Alternative hypothesis which are labeled as Ho and H1 are in fact, two ways of hypothesis that researchers can use to make and educated conclusion. Null hypothesis for instance, is just one of the ways and it gives the researcher the information to put the test into motion to establish a rejection per se of the statements made for this hypothesis by saying that they are either untrue or false. When a conclusion is determined, a researcher can then be able to reject or accept a null hypothesis statement. Then again, if the statement is determined to be false and then is then rejected, this is when an alternative hypothesis will then be accepted (CTU, 2012).

Alternative hypothesis plain and simply put, is just the outcome of a statement that is suggested by a researcher and what he or she expects. The symbol for this would be something like (H1or HA) which would come about when a null hypothesis is rejected and it is a researchers' sound conclusion. This will come from the researchers prior studies of literature they have gotten to support their assumptions. Two types of alternative hypothesis are non-directional and directional hypothesis. The non-directional hypothesis is one that has no definite direction of the expected findings that are gotten. With that being said, a researcher may or may not be able to know what prediction to make from that of his or her past literature that was gotten. And the directional hypothesis is one that gives a direction of the expected findings by examining the relationships between variables other than by the comparing of groups. A good way to put it regarding null and alternative hypothesis is that whatever subject area is being studied, either something happened (which is the alternative hypothesis) or nothing at all happened (which is the null hypothesis). In fact, a hypothesis can only be either supported or not supported, it can't be proved or unproved. With all of this being said, an alternative hypothesis might be supported if the truth is not known which could lead to a change if the norm or status quo is gotten or achieved (Sharma, M. and Battina, S., 2009).

Statistics that are Non-parametric

An assessment which applies to categorical information that is used to make an analysis is said to be non-parametric in nature. This type of information can be either ordinal or nominal. Nominal variables actually give a researcher enough information to label it as being able to be categorized into a ranking order. This information actually indexes individual distribution within a particular family and makes for less stringent demands of data. It can also be used to get a quick answer when just a minute bit of calculations are done. The non-parametric analysis will not formulate statements regarding the information being presented by the researcher.

When one wants to do an analysis of variation, a researcher typically uses what is known as ANOVA. This is the type of analysis that tels whether there is a percentag of distinction between certain groups and if their mean is actually the same. In saying this, when testing this ANOVA with a null hypothesis, it will help to determine if the information that is being looked at is of the same mean. Now on the other hand, if this information is being tested usng ANOVA for the alternative hypothesis, it is being checked to determine if the information that is being used has a differnet mean (CTU, 2012).

Actually, a researcher can use one of two ways to do this. They may in fact use the one-way method or that of the two way method as well in order to conduct this ANOVA analysis. To explain what the one-way method is, I would say that it is used when wanting to test the validity of the information being looked at when only using one means to do so. On the other hand, the two-way method is what is used when the researcher uses more than one method to determine or make for a conclusion to this analysis in which can use different ways to look at the possible outcome of this observation (Bowerman, B., and Murphree, E., 2010).

Using Chi-Square Distribution

Chi-Square distribution is labeled as being what is used by a researcher to determine the distinctions between information and to see if the information is independent of one another. These variables actually don't have a perspective pattern and can basically be two kinds of information that are either categorical or numerical in that respect. In saying this, when variables have no numerical value or fixture about them, they are basically said to be categorical. When they are of numerical type though, they then are said to be just numerical. There are numerous ways that you can pose these types of questions. An example of a categorical variable would be something such as: hair color, gender, field of study, college attended, or political affiliation. With that being said, you could say that numerical variables would concern things such as: variables that have numbers associated with them, such as height, weight, or annual income.

Numerical variables can essentially be seen as either discrete or continuous in nature. To further elaborate on these two, discrete means that it basically happens because of a count of just certain thing that is distinct or separate such as saying that "the company is composed of three discrete units." Now, if we say that it is continuous, then we mean that it pertains to something as simple as the measurement of height of an individual.

When using chi-square distribution, the collected testing can essentially be unstable by fluctuating. As it pertains to Widge Corp., this can be looked at from a chi-square analysis perspective as the sales reps that actually attain their target numbers for a particular month up against the ones that do not achieve their desired results and don't reach this desired quota for a particular month. The null hypothesis of this would be "sales reps that used the new software actually made their target numbers for the month versus sales reps that did not make their target numbers for the month because they did not use the software causing them to not meet their target numbers." This particular statement from a null perspective cannot be proven true because it really has not been proven that any particular sales person used the software at hand to meet their target numbers and those just the same, that did not use the software and didn't meet their quotas weren't ever proven either. In saying this too, the theoretical part of this is that the null hypothesis is basically untrue and the alternative to this is that it is accepted because the sales reps did not even sell a certain amount of products by using the software anyway (Bowmerman, B. and Murphree, E., 2010).

If I were to sum this up, I would say that when using a hypothesis to determine a conclusion to a particular issue, it behooves a researcher to put together a report of a population in order to do the analysis. Hypothesis testing is done by researchers to determine if statements are true based on the problem or issue at hand. This information gives the researcher pertinent information that is pretty much solid. He or she must first go through the process by basically getting the information, analyzing it, then discerning the data and this will help him get an understanding of the posed questions that need to be answered and indexed. This statistical data must be analyzed using the types of methods that are out there to do this and once the proper method is determined, will help the powers (leadership at Company W.) to be able to make a proper decision from a business perspective.

References

Bowerman, B., O'Connell, R., Orris, J., & Murphree, E. (2010). Essentials of Business Statistics, (3^rd ed.). McGraw-Hill Irwin: New York, NY.

CTU Online. (2011). Applied Managerial Decision Making. Phase 3 course materials [text]. Retrieved from https://campus.ctuonline.edu/pages/MainFrame.aspx?ContentFrame=/Home/Pag

Dallal, G., (2008). Nonparametric Statistics. Retrieved on January 23, 2012 from http://www.jerrydallal.com/LHSP/npar.htm

Null Hypothesis, (2007). What is a Null Hypothesis. Retrieved on January 24, 2012 from http://www.null-hypothesis.co.uk/science//item/what_is_a_null_hypothesis

Sharma, M. and Battina, S., (2009). Developing Hypothesis and Questions. Retrieved on January 23, 2012 from http://www.public.asu.edu/~kroel/www500/HYPOTHESIS