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Statistics Suck; So Why Do I Need to Learn About It?

1.1 Introduction

The question is a fair one, considering how many people feel about the subject. In this chapter, we go over some interesting aspects of the topic to convince the reader of the need to learn about statistics. Then we provide a formal definition.

Statistics Are All Around Us

Nowadays, we see and hear about statistics everywhere. Whether it is in statements about the median student loan amount of college students, the probability of rain tomorrow, association between two financial variables, or how an environmental factor may increase the risk of being diagnosed with a medical condition. These are all brief examples that rely on statistics. Information extracted from data is so ubiquitous these days that not understanding statistics limits our comprehension of the information coming to us. Therefore, understanding the main concepts from statistics has become imperative. In the world of business, making decisions based on evidence leads to a competitive advantage. For example, retailers can use data from customers to determine appropriate marketing campaigns, and manufacturing experiments can help establish the best settings to reduce costs. Investors can combine assets according to an adequate expected return on investment with an appropriate risk. We go over some specific applications of statistical methods in business in Section 1.2.

The Importance of Understanding the Concepts

Suppose you are invited to invest in a fund with an expected yearly return of 10%. Therefore, if you invest $100 at 10% yearly return, you expect to have $110 by the end of the year. So you decide to invest money; but at the end of the year, your portfolio is worth $90 (ignoring all fees). Specifically, the return on your money has been negative. That raises the question, based on the information you were given about the return you would receive, was your investment a mistake? Think about this question before reading ahead. The trick is in understanding the meaning of expected value. The information provided to you was that the fund had an “expected” yearly return of 10%. In some scenarios, such as a deposit account in a bank, the return given to you is guaranteed, and your principal (the money you start with) is protected. But in other scenarios, such as the stock market, the return you receive is not guaranteed, and, in fact, your principal may not be protected. Consequently, in any given year, you may have an outstanding return, much higher than the expected 10%, or you may get a return lower than the expected return of1 10%. To counter this risk, possible returns are higher in these investments than safer alternatives, such as a bank savings account. The expected return is what the company has determined you should receive over the long term. Because of this aspect, an investment such as a stock has to be looked at differently than a bank savings account, and if after a year your portfolio is worth $90, your decision to invest in the portfolio was not necessarily a bad decision. What matters is the return you obtain over the long term, say, 10 or 20 years, and how much risk you are willing to take as an investor.

Another relevant component in understanding statistics is being able to distinguish between good information and bad information. An example is a spurious relationship. A spurious relationship between two variables occurs when an association is not due to a direct relationship between them, but from their association with other variables or coincidence. Strange associations are not the only way we can wrongly use statistics. Many media outlets (and politicians) often misquote scientific studies, which often rely on statistical methods, to reach their conclusions.

Example 1.1

In the summer of 2014, several media outlets reported on a new scientific study; one of the titles was2 “Study: Smelling farts may be good for your health.” In reality the study was about a developed compound that delivered small amounts of hydrogen sulfide that helped protect cells.3 Hydrogen sulfide is known to be a foul‐smelling gas; hence the misunderstanding of the study results occurred. It is not enough to be able to correctly perform statistical analysis, but understanding the results is also key.

The issues brought up are rather common and tend to occur for two reasons:

• Inappropriate use of statistics.
• Wrong interpretation of results (poor statistical literacy skills).

Either of these two issues will potentially lead to reaching a wrong conclusion, hence making the wrong managerial decision. In contrast, avoiding these issues offers valuable knowledge for a given context.

Satiated Judge, More Lenient Ruling

Did you know that judges used to give more lenient decisions after meals compared to before meals?4 The finding comes from a study that looked at 1112 judicial rulings on parole. It was found that judge rulings were more likely to be favorable to the prisoner earlier in the day and that there was a jump in probability of parole ruling after a break. The study even considered the length of sentence, incarceration history of the prisoner, etc. Of course, the time of day of a parole hearing should not be a factor in determining a decision. The findings of this study helped establish a protocol to help eliminate the impact of time of day on parole ruling. Thus, an unintentional benefit of reading this book is that if you are facing the possibility of jail time, you should ask your lawyer to delay the sentencing until after lunch, just in case!

Case study 1

A professor wants to answer the following question: Do quizzes help business undergraduate students get a better grade in their introductory statistics course? In academia, it is often simply assumed that quizzes will force students to study, leading to better course grades. The goal here is to answer the question based on evidence. There are two possible answers:

• They do not work: No difference between grades of students who took quizzes and students who did not take quizzes, or students who took quizzes perform worse.
• They do work: Grades of students who took quizzes are better than students who did not take quizzes.

Next is to determine how the comparison will be made. More specifically, what aspects associated with students will be taken into account? Hours of study per week, undergrad concentration, high school they went to, and the education level of parents are just some examples of “variables” that could be considered. Yet, the simplest way to make the comparison is based on two groups of students:

• One group that took quizzes during the course.
• The other group that did not take quizzes during the course.

Then, it is assumed that both groups are homogeneous in all their attributes, except that one group of students took the course with quizzes, while the other did not. This way, the average exam scores of both groups can be compared.

To compare average exam scores, two semesters were selected: one with quizzes and the other without. It was verified that the number of students that dropped the course or stopped attending class for both groups was similar (why do you think it is necessary to check this?).

• The group that took quizzes had an average test score of 79.95.
• The average of the group that had no quizzes was 75.54.

Now, these averages are just estimates, and different semesters will have different students in each group leading to new average values. This leads to uncertainty. Informally, what is known as statistical inference accounts for this uncertainty. When the inferential procedure was implemented, it was found that in reality there was no difference in average exam score among the two groups. Thus, there was no evidence that quizzes helped students improve their test scores.

Now, let's not get too excited about this. The interpretation is that quizzes do not help improve the performance of students who take the class with that professor. The conclusion does not necessarily extend to quizzes in other subjects, and it doesn't even necessarily extend to all introductory business statistics courses.

Practice Problems

1. 1.1 In Case Study 1, it was stated that “It was verified that the number of students that dropped the course or stopped attending class for both groups were similar.” Why do you think it is necessary to check this condition?
2. 1.2 In September 20, 2017, Puerto Rico was struck by Hurricane Maria, a powerful storm with 155 mph sustained winds. In May 2018, multiple media outlets reported the findings of a study5 in which researchers used September to December 2017 data to estimate that 4645 people had died in Puerto Rico, directly or indirectly, due to Hurricane Maria. The news shocked many, since at the time the local government had stated a total of 64 people had died due to the storm. Indeed, the study was one of several indicating the official estimate of 64 was too low. Before the news broke, the Puerto Rican government had not publicly shared death certificate6 data. Due to growing pressure from the study results, the government released data on the number of death certificates (Table 1.1). How...