Abstract
Company W has a sales force of 500 employees that is divided in the Northeast, Southeast, Central, and West regions. Recently the company has put into place a software program that keeps track of the amount of sales each employee generates on products for the business. To help the company with contracts they presently have the employee within each region is expected to sell the same amount of products each month, however within the last three months only half the sales employees of each region have reached these expectations. Due to this the Sales VP of Widgecorp wants to know the possible theories that can be put into place to statistically analyze the issue of some sales employees not reaching their sales quotas for the month. However, before a decision can be made on this issue statistical testing must be done so that an accurate conclusion can be made. With that being said, there are different techniques that Company W can use to statistical analyze the issue at hand, but the ones to be discussed here are non-parametric statistics and hypothesis testing, both of these will be discussed along with chi-square distribution testing of data. To understand these terms let’s first begin by defining them.
Statistically Analyzing Theories
Hypothesis Testing
Hypothesis testing is a technique applied by businesses sequentially to obtain conclusions regarding a population utilizing information taken from a sample. The information taken from the sample is gathered so that a decision can be made by the researcher to either accept or reject the hypothesis. The null (H0) and the alternative (H1) are two types of hypotheses that researchers make decisions upon (Voelz, 2006). The null hypothesis, which is what the researcher actually performs the test on, attempts to establish a rejection of the hypothesis statement by proving it false. The concluding results of the testing done by the researcher will be either a rejection or acceptance of the null hypothesis statement, and if the statement is proven to be false and rejected by the researcher the alternative hypothesis would then be accepted (CTU Online, 2011).
Non-parametric Statistics
A non-parametric statistical analysis is an assessment that applies information categorically. This categorical information can either be nominal or ordinal. Variables that are nominal will allocate the researcher to classify the information presented as qualitative, while variables that are ordinal will allocate the researcher to categorize the information presented in order for ranking to be given. The non-parametric analysis will not formulate statements regarding the information being presented by the researcher. An analysis of variation, which is the ANOVA, is a common non-parametric method used by researchers. With the ANOVA an analysis is done by the researcher to tell whether there is a differentiation among groups, and if the mean of them are the same. With that being said, the testing of the ANOVA with the null hypothesis will check to see if the information presented have the same means, while the testing of the ANOVA with the alternative hypothesis will check to see if the information presented have different means (CTU Online, 2011). The researcher may use the one-way or two-way method for an ANOVA analysis. The one-way has only one factor for the researcher to test the equality of the information being presented, while the two-way lets the researcher distinguish if there might be another factor such as allotment of the information presented in order for every possible outcome to be pointed out in the observation (Engineering Statistics Handbook, n.d.)
Chi-Square Distribution Use
When variables are without pattern they can typically generate two kinds of information which are numerical or categorical. The use of the chi-square distribution is employed by researchers to discover the distinctions among the information and check if they are independent. Variables that are specific and have no fixed numerical value are categorical, and numerical type variables are numerical. In regards to this, questions are used such as, “what is your employment type, or do you have a vehicle?” These types of questions are categorical variables because the answers such as “construction worker” and “yes or no” are different responses than that of other questions such as, “how much do you weigh, or “what is your GPA?”, which would be numerical variables, and can either be discrete or continuous, such as “how many vehicles do you own?” = discrete and how tall are you?” = continuous. The discrete data occurs from the counting a particular thing, such as counting how many vehicles an individual owns and the continuous data occurs from measuring a particular thing, such as measuring how tall an individual is (CTU Online, 2011).
Using Chi-Square Analysis
Depending on the information collected testing using the chi-square analysis can fluctuate, such as in the condition of the sales representatives that reached their quotas for the month and those sales representatives that did not reach their quotas for the month. In this case the statement in this situation related to the null hypothesis is, those sales representatives that used the sales software met their sales quotas vs. those sales representatives that did not use the sales software did not meet their sales quotas. In this statement the null hypothesis cannot be proven true, since in reality it has not been proven that the sales representatives that used the sales software met their sales quotas, and those that did not use the sales software did not meet their sales quotas. With that being said, the theory to this is the null hypothesis is untrue and the alternative hypothesis is accepted which means the sales representatives did not sell that same amount of products using the sales software (Bowerman, O’Connell, Orris, & Murphree, 2010).
Conclusion
A hypothesis is comparable to a dilemma account in that it aids the researcher in developing a report regarding a population aspect for the point of analyzing. Testing a hypothesis is done by researchers to develop true statements regarding a problem or issue so that it can be accurately classified. Collecting, analyzing, and interpreting data requires the researcher to have a solid understanding of the question that needs to be answered or the issue that need to be resolved. In addition, a researcher must statistically analyze different theories in order to aid a company in making educated business decisions (Voelz, 2006).
References
Bowerman, B., O’Connell, R., Orris, J., & Murphree, E. (2010). Essentials of Business Statistics, (3rd 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/Pages/Default.aspx
Engineering Statistics Handbook. (n.d.). Retrieved from http://www.itl.nist.gov/div898/handbook/prc/section4/prc43.htm
Voelz, V. (2006). Hypothesis testing. Retrieved from http://www.stanford.edu/~vvoelz/lectures/hypotesting.pdf