PDF Summary:Naked Statistics, by Charles Wheelan

Statistics help us use data to make sense of the world, and statistical insights help guide modern society, informing medical practices, public and fiscal policy, education initiatives, business and marketing decisions, and so on. But statistics aren’t just for “experts.” Thanks to Charles Wheelan, statistics don’t need to be intimidating. Naked Statistics puts the math behind statistics into digestible terms and explains statistics concepts with relatable, relevant, and even humorous examples. Readers also benefit from additional socio-political insight from the book, as Wheelan uses real-world anecdotes to explore how statistics can inform collective decision-making.

As Wheelan does in Naked Statistics, this guide focuses on the meaning and context of commonly used statistics rather than on their calculations. After explaining the insight each statistics concept provides and how to interpret it, this guide uses real and fictional examples for added context.

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Vigen’s work has been highlighted by the Harvard Business Review and received positive reviews from the Boston Globe and Washington Post, among others, in part because these ridiculous examples highlight the fact that equating causation with correlation is incorrect, no matter how close the relationship.

Another statistics technique, regression analysis, goes beyond describing the relationship between two variables and allows us to make mathematical predictions based on those relationships. For example, the nursery owner above could generate an equation with regression analysis to predict how many flowers her plants would have based on the amount of sunlight she gave them.

Regression Analysis for Smoking and Lung Cancer

As Wheelan explains, regression analysis is a staple in medical and social sciences research. A study in the National Library of Medicine used regression analysis to calculate that for every 1% more collective smoking American adults do, lung cancer rates rise by 164 cases per 1,000 citizens.

Statistics Help Answer Complicated Questions

Probability is one way statistics can help us make more informed decisions. It allows us to manage uncertainty, calculate risks, and put possible outcomes in perspective. Wheelan explains that understanding probability can be especially relevant to our daily lives because we make decisions based on our perception of probability all the time. However, our perception of likely outcomes is often mathematically irrational. For example, the probability of getting in a car accident while driving to a beach is far higher than the probability of being attacked by a shark there, but we often—irrationally—fear the shark risk more.

Probability Isn’t Intuitive

There are several reasons for our mathematically irrational perception of probability, including:

Confirmation Bias: When we focus on what we expect and ignore the rest. Using our shark attack example above, we might justify our fear of swimming at the beach with a statement like, “well, that one guy was bitten by a shark at Cape Cod last year!” ignoring the tens of thousands of swimmers who weren’t attacked.

Anecdotal Logic: Improbable events are statistically bound to happen, and people notice and talk about them when they do. These stories of improbable occurrences stick in our minds and shape our perception of what is likely. For example, say you have a friend diagnosed with an exceedingly rare cancer. Even though your friend’s diagnosis is an anomaly, the rare form of cancer suddenly feels more prevalent.

Short-Term Thinking: Humans are evolutionally hardwired to think in the short and middle-term, which can make us feel like we're witnessing statistically improbable events when we're not (for example, witnessing a 100-year flood) and make us unable to process long-term data (for example, focusing on the cold snap over the last several days and ignoring climate change).

Our brains’ tendency to misunderstand probability makes it a useful subject to study if we want to use statistics to make more informed decisions.

People often use probability to assess risk when making financial decisions. Wheelan explains that a statistic called the “expected value” can help us determine whether we want to take a financial risk when we know the probability of each possible outcome and its respective payoff. Real-estate developers, for instance, can use this tool to make sure that their multiple investments are likely to make money as a whole. Even if one property loses money or underperforms in a given year, as long as the expected value of their portfolio is profitable overall, they are likely to make money.

Probability and Purchasing Stock

As Wheelan explains, probability is an effective tool for managing risk. Unfortunately, many of us underutilize probability when investing in the stock market. Research shows that we tend to overestimate the probability of rare events and our ability to foresee them. For example, people will often invest in a single stock that they think will be the next Apple instead of spreading their investment across a diverse portfolio. Therefore, people tend to under-diversify their stock, costing them an average of $2,500 per year.

Using statistics like the expected value is likely a good idea before investing in the stock market as it can temper our “gut feeling” about a stock with math and help us make smarter investments.

In addition to helping us make more informed decisions, statistics can offer insight into questions we couldn’t possibly design an experiment to answer. For example, say we wanted to know whether exposure to a certain chemical (we’ll call it chemical X) corresponds to higher rates of cancer. Ethics precludes purposefully exposing people to chemical X in a laboratory setting for the sake of science. Additionally, so many other variables impact a person’s personal cancer risk that we can’t possibly know if chemical X was the sole cause of anyone’s cancer diagnosis. Without statistics, complex but important questions like this would remain unanswered.

To answer the question of whether chemical X is associated with higher rates of cancer, researchers could collect a large dataset including people who were and were not exposed to chemical X and record their rates of cancer diagnoses. Then the researchers could use regression analysis to determine the association between exposure to chemical X and a cancer diagnosis, independent of other factors such as smoking, exercise, family history, and so on. Statistics can even tell us what percent of a person’s overall cancer risk is mathematically associated with exposure to chemical X rather than other factors.

As Wheelan explains, the ability to mathematically separate individual variables (like exposure to a particular chemical) in the complexity of the real world makes statistical analysis an invaluable part of medical and social sciences research.

Using Statistics to Assess Whether Money Can Buy Happiness

Researchers have even used statistics to try to answer the age-old question of whether money can buy happiness. In a 2010 study from Princeton University, researchers gathered data from 450,000 responses to a Gallup survey about day-to-day emotions and overall life evaluation (how people rate their life in the “big picture”). Next, researchers used multivariate regression analysis to analyze whether a high income is correlated with increased emotional well-being and better life evaluation.

The results of the study suggest that money can buy happiness to a point. Income was positively associated with life evaluation in general (people had a more favorable opinion of their lives overall if they made more money) and associated with emotional well-being up to an income of $75,000. Beyond $75,000, income no longer predicted emotional well-being.

Learning Statistics Is Empowering

Learning statistics is an exercise in self-empowerment. Wheelan explains that thanks to modern society’s affinity for and reliance on technology, we're constantly surrounded and impacted by data. This abundance of data is a blessing in that it gives researchers a chance to study society’s most pressing issues, for example, using student outcomes to highlight racial and social inequities in our education system. But, the amount of data we're bombarded with every day through targeted marketing, political campaigns, and social media can also be a challenge when we don’t know how to gauge its reliability. Studying statistics can give us a better sense of how much trust we should put in different sources of information and can help us interpret published statistics correctly.

Data Literacy

Learning statistics to be an informed citizen is part of a larger skill set called “data literacy.” Data literacy refers to the ability to analyze and interpret data correctly. Just as a literate person can understand a story by reading the words on a page, a data-literate person can look at a statistic, chart, graph, and so on and correctly interpret its “story.”

Data literacy is a critical yet neglected skill. Poor data literacy skills hamper our individual and societal ability to make informed decisions. For example, Wheelan cites mainstream confusion about the difference between correlation and causation, combined with a lack of awareness of modern vaccine-safety research, as the cause of the anti-vaccination movement.

The gap between data literacy skills and data literacy needs in the modern workplace is costly. Many jobs require working with and making decisions using data, yet many employees lack the skills to do this effectively. Estimates show that over $109 billion are lost to the US economy every year due to underdeveloped data literacy skills in the workforce. In response, most corporations are adopting data literacy as a critical skill.

Studying statistics also makes us less susceptible to being purposefully misled. Unfortunately, Wheelan explains that the purposeful misuse of statistics is more common than we may think. While the statistics values themselves can't lie, the statistical tests that people choose to use, the data they choose to calculate statistics with, and the choice to include or not include specific statistics from datasets can construct various versions of “the truth.” For example, consider the following statements based on the same hypothetical dataset:

• Vote for Mark Smith! His tax cuts have saved the people in this town an average of $1,000 per year!
• Don’t vote for Mark Smith! His “tax cuts” have saved the wealthiest 1% of town residents tons of money and have saved low-income residents almost nothing!

Neither of these statements is a lie. Instead, different uses of data and statistics construct versions of the truth that best suit differing perspectives. While we can't expect ourselves to dive into the underlying data for every statistic we read or hear, Wheelan explains that we can better spot incomplete or misleading information with a basic understanding of statistics.

Dishonest Statistics

In his 1954 book How to Lie With Statistics (republished in 1993), Darell Huff explores several ways that statistics are used to deliberately mislead an audience. His examples include using small sample sizes to inflate results, taking biased samples, and omitting values that are critical for context.

As an example of the latter, take the following hypothetical marketing for a weight loss supplement:

Headline: “Supplement Users Lost Twice as Much Weight During Their First Month as Those Taking a Placebo!”

This sounds appealing and might tempt many people to spend big on the supplements. However, it gives no context given for what “twice as much” means because no actual weight loss figures are included. Perhaps those on the supplement lost just one pound, while those on the placebo lost just half a pound. While it's true that one pound is twice as much as half a pound, the actual figures are far less impressive than the report makes them appear.

Huff cautions that dishonest or incomplete statistics combined with a data-illiterate audience render many published statistics meaningless at best and harmful at worst.