Naked Statistics: Stripping the Dread from the Data

The rise of social media we have massive amounts of data at our fingertips. What we do with all this information is up to us. Have you ever have logged on to face the only to discover the friend who has a post with one single data point and uses that as the basis of their argument? It’s perfectly acceptable to take a stance on a hot topic but you’ll come out looking foolish if you don’t understand the statistics and data points behind your argument. Don’t be that person.In comes Naked StatisticsGrowing up, I was never fond of mathematics. I struggled in high school with a solid 65 average (that is borderline failing in the United States), and a long believed that now just wasn’t for me. It was until recently ago that I discovered I really do love numbers and specifically statistics. It’s around this all the time whether through social media or my favorite thing, gaming. Looking back, I think educators were not ever explaining to me in a way that grabbed my attention that made me want to further my math education. The blame can’t lie solely on the educators I grew up with, so I recently took it into my own hands to further my own understanding of math.I stumbled across the audio book Naked Statistics by Charles Wheelan, a professor at Dartmouth college. I found the narration to the enticing and upon finishing the audio book actually bought the physical copy and marked it up heavily with notes of my own.Throughout the book the author gives great detail about how statistics can truly improve our lives while the same time helping readers understand the power that comes with it and how the power can be used and negative ways as well.Now there are a few key points I want to highlight about the book:Statistics rarely offer a single “right” way of doing anythingStatistics can be powerful for establishing an argumentHoweverStatistics can also be very easy to misuseThe book opens with an explanation of the classic Monty Hall problem, which is a brain teaser in the form of a probability puzzle loosely based on the 1980’s television show “Let’s Make a Deal”. I’d never quite comprehend it the full detail of this problem until this book. I encourage you to look into unknown because not only to find to be interesting but also provided a great starting point for understanding for help powerful statistics can truly be.Uses of StatisticsDescription and comparisonInferenceAssessing risk and probabilityIdentifying important relationships (correlation)Descriptive Statistics“Who was the best baseball player of all time?”Descriptive statistics can be technically accurate yet pretty misleading. The author explains that “The good news is that these descriptive statistics gives us a manageable and meaningful summary of the underlying phenomenon,” and continues with “the bad news is that any simplification invites abuse.”Wheelan highlights the Gini Index, which is a measure of statistical dispersion intended to represent the income distribution of the nation’s residents and most commonly used to measure inequality. The problem however is that this is a mere useless stat. It simply takes the per capita income of a nation and divides it by the number of people. But who was actually earning how much of that income? That is the key missing piece.Precision vs AccuracyThe author goes on to describe the differences between precision and accuracy.Precision: “The exactitude with which we can express something”Accuracy: “Measure of whether a figure is broadly consistent with the truth”Correlation“Measures the degree to which two phenomena are related to one another.Correlation coefficient: Expressed on a scale of -1 -> 11: every change in one variable is associated with an equivalent change in the other variable in the same direction-1: every change in one variable is associated with an equivalent change in the other variable in the opposite directionProbability:“Study of events in outcomes including elements of uncertainty.”There were a few key takeaways from this chapter:Don’t play Lotto (Pg. 80)You should invest in the stock market if you have a long-term investment horizon (because stocks typically have the best long-term returns)Probability is not deterministicThere are several problems with probability, however. The 2008 Wall Street crash and financial crisis largely had to do with computers misusing probability. The VaR model, or Value at Risk, which was called “potentially catastrophic”. Value at risk is a measure of risk in investments, and estimates how much a set of investments might lose given normal market conditions and a set time period, such as any day. This model offered 99% reassurance about 1% is the difference between success and failure.The importance of data (Garbage in and out)When working with numbers you assume that you retrieve and good data, but no amount of fancy analysis can make up for fundamentally flawed data.Selection bias: “How have you chosen the samples you are evaluating?”Self-selection bias: “Will arise whenever individuals volunteer to be any treatment group.”Publication bias: “positive findings are more likely to be published”This distorts the research that we see, or more evidently, do not see. This pious comes from not directly his studies themselves but from the skewed information that reaches the public. Typically, medical journals now require that any study be registered at the beginning of the project to help combat this problem of only publishing information that researchers want to see.Inference“The process by which data speaks to us enabling us to draw meaningful conclusions.” The typical tool that researchers will use is a hypothesis, which is a proposed explanation made on the basis of limited evidence as a starting point for further investigation.While statistical inference offers many benefits it also comes with some significant pitfalls. Notably, statistical inference is based on a probability, And not some sort of absolute certainty.PollingThe power polling comes also comes from the central limit theorem, similar to other forms of sampling. Where it differs however, is that we don’t care about the mean, but we actually care about the percentage, or proportion relative to our results. But again, this can be powerful for example the poll of 1000 individuals can offer meaningful insight into the attitudes of an entire nation.Regression Analysis“Allows us to quantify the relationship between a particular variable and how come we care about, while controlling for other factors.” It’s important to note there are many pitfalls of regression analysis, and is the hydrogen bomb of the statistical arsenal! Most of the studies that you read about in the newspaper are based on regression analysis.Bringing it all togetherNow that you’re more informed, consider these aspects of statistics the next time you stumble across an infographic on social media which illustrates only one point, or discover an article which takes a stand on a topic. I never realized how large of a role statistics plays in my life, but the author’s enthusiasm and clear instruction helped me to not only appreciate it, but has also further sparked my interest.If you have other books you’d like to recommend regarding math, business, or computer science, I’d love to hear about them.Key Takeaways:Statistics rarely offer a single “right” way of doing anythingStatistics can be powerful for establishing an argumentHoweverStatistics can also be very easy to misuse

This book made statistics actually enjoyable to read. Wheelan explains things in a way that’s clear, funny, and surprisingly relevant to everyday life. I never thought I’d laugh while reading about regression or probability, but here we are. If stats ever felt intimidating or boring, this is the perfect way to change that.

How many times have you wondered how two different people looking at the same report managed to draw totally opposite conclusions? How many times have you looked at a set of data yourself and decided that the data must be wrong because it doesn't show what you "know" to be true? Well, I suspect that you aren't alone. I suspect that you also have an aversion to "doing the math" necessary to convince yourself that the data is actually correct.Wheelan claims that "Statistics is like a high-caliber weapon: helpful when used correctly and potentially disastrous in the wrong hands." This is an incredibly important topic as we move forward into our increasingly connected world where we are creating data at an accelerating rate. The data is only raw knowledge, how we analyze that data is what allows us to derive useful information to create actionable knowledge. The tools we use to analyze the data is, like it or not, statistics. Wheelan gives us an easy to follow and understand overview of statistics. Even if you didn't like math in school, you will find this book useful as well as insightful.Here's the rub. No matter how hard we try, when using descriptive statistics, we lose the detail in the data. We've "summarized" it and just like the summary of a good book, we will miss a lot of the nuance in the story. Neither this review nor the summary of data known as descriptive statistics is an exception to that rule. And because of that loss of fidelity, we will find as Wheelan puts its, "Smart and honest people will often disagree about what the data are trying to tell us."Wheelan includes many examples of how statistics is enlightening and infuriating. The examples are from everyday life and you are likely to recognize them; things like "Money Ball" and the "Wall Street failure." You will learn about correlation, basic probability, the Central Limit Theorem, Inferences, Polling, Regression Analysis and more. All without tears!So why should you be interested? Because the big questions will be answered by statistical analysis and you will want to know at least enough to not be "taken in" by those who would purposely try and confuse you or convert you to their views using statistics and data. Wheelan believes that there are five "large" questions that statistics will help us answer in the future.1. What is the future of football? Will it die of concussions?2. What (if anything) is causing the dramatic rise in the incidence of autism?3. How can we identify and reward good teachers and schools?4. What are the best tools for fighting global poverty?5. Who gets to know what about you?Wheelan doesn't answer these questions. The data is still being collected and analyzed. What he has done, however, is set the reader on the right path to understanding the complexity of those questions and why there aren't any easy answers. He has given the reader at least a working knowledge of statistics so that we can decide for ourselves who is doing the best job of presenting the information and knowledge buried in ever expanding universe of dots for us to connect. The sub title of this excellent book is "Stripping the dread from the data." What I found is that now I know how to make sure that I strip the dread from the statistics which applies to the data. The dread is when the proper use of statistics on that data shows my cherished beliefs to be ill conceived!