Statistics in business model development

¶ … assist the Nyke Shoe Company in determining what size shoe to produce at the most efficient cost and highest value. The Company has decided that it would be a more profitable company if it was able to produce one shoe for the marketplace instead of a variety of sizes. The one shoe that the company produces will have to provide the opportunity for the greatest amount of people to purchase and therefore will have to (statistically speaking) appeal to the largest audience. There are a number of statistical methods that would help in determining just what that audience is and who would fall into that category.

According to Charles Wheelan, author of Naked Statistics; "Many businesses must assess the risks associated with assorted adverse outcomes" (Wheelan, 2013, p. 7). One can hardly imagine a more adverse outcome than to go out of business, and it would seem on the face of it that a shoe company that decides to only produce one size of shoe, no matter what the gender, or size of the consumer, would essentially be courting disaster. That is where statistics comes in. Wheelan states however that "statistics cannot be any smarter than the people who use them" (p. 95). Therefore it behooves this paper's author to ensure that the statistics used in evidence herein are as easy to understand as possible. Will they show that the Nyke Company can be profitable by producing (en masse) just one size of shoe, no matter the gender or size of the person buying them? Perhaps.

The first thing to do is determine what the most common shoe size is. This can be done by collecting data (see Appendix A).

It's important to understand that the data gathered is certain to contain certain biases. Since this is only a preliminary study it was not necessary to gather a vast amount of data, and in most cases, at least according to Wheelan, "we conduct statistical analysis using the best data and methodologies and resources available" (p. 14). The data in this particular case was gathered from a random sampling of a male and female population at a local shoe establishment. The data, like all data, contains a bias, in this case the shoe store was one that catered to a population looking for inexpensive shoes. This type of population is not necessarily looking for high quality shoes, instead they may oftentimes be looking for shoes that are made to look good for a relatively low expense.

The data gathered in this case included gender, size of the person in inches, and regular shoe size (the individual's size of a normal purchase of an athletic shoe). There were 35 individuals who participated in the survey. 17 individuals were male, and 18 were female. No ages were asked, although a future study might wish to incorporate that variable.

The data shows that the most common size shoe purchased by females ranges between 6.5 and 7.5. There were four 6.5's and four 7's and four 7.5's. Out of 18 individuals, 12 purchased either 6.5, 7 or 7.t sized shoes. That's a percentage of almost 66%. The male side was a little more diverse. The most common size purchased by men was 11 and 12. Three men purchased 11's and three men purchased 12's. The percentage of purchases for the most common size on the men's side is approximately 35%. That thirty five percent is a far lower percentage of common purchases than on the female side of the equation.

One method for comparing data is using a paired comparison experiment. As one recent study showed "for each pair of objects, the judge decides which of the two objects is preferred (or judged to be bigger, better, faster, etc.); the aim is to estimate the desirability or worth of each object and this to rank the objects in preference order" (Dittrich, Francis, Hatzinger, Katzenbeisser, 2012, p. 118). In this case, the comparison can be made that men will purchase larger sizes than women (on the whole part) but that they are also more diverse in the sizes they purchase. Woman are much more likely to stick with a size range that would be more efficient if a company were interested in only producing one shoe size.

The data also shows that the average shoe size purchased by a woman is a 7.1. The average size purchased by a male is a 10.8. The average size purchased overall is 8.9. The average size overall really has no bearing on this particular study, but the average size for woman does. If the company were to produce a shoe size of 7, they would be catering almost strictly to females. However, another method for looking at the data could include a normal distribution to see how many individuals would make a likely purchase of a shoe size of 7 if the shoe were set to generically appeal to both women and men. Using an approach like the frequent outcome approach might work in this instance. As one study determined "we analyze sequences of values that are almost-uniform and we discuss a prediction method called the frequent outcome approach, in which the outcome that has occurred the most in the observed trials is the most likely to occur again" (O'Neill, 2012, p. 106). The outcome that would most likely occur in this study would be that females would purchase shoe sizes of either 6.5, 7 or 7.5.

Another method to analyze the data would be to find the mean and use the normal distribution from that mean. The mean for the female purchases is exactly seven. There were just as many female purchases made over seven as there were purchases made under seven. Paul Erdos, a reknowned mathematician, once stated that "a mathematician is a device for turning coffee into theorems" (Peterson, 1998, p. 41). The theorem in this case could be that the one size fits all mode of production might be cost efficient and profitable; however, that is true only if there are enough females (coupled with a small number of males) that would purchase the one size in enough numbers to ensure the company's profitability.