Applied Statistics and Critical Thinking
Introduction
Do you know that:
 on average, smokers are said to die 10 years earlier than nonsmokers?
 64% of Americans will retire broke?
 in the fall of 2020, 56.4 million students were expected to attend schools in the USA:
 50.7 million students within a public school context;
 5.7 million students within a private school one;
 it’s estimated that 1.5 million will go to prekindergarten;
 3.7 million will attend kindergarten;
 35.3 million will go to prekindergarten  grade 8;
 15.4 million will to go to grades 9  12;
 and 4.1 million will go to 9th grade?
 according to the US Travel Association, Americans travel because:
 85% want to see their children excited about the travel experience;
 82% wish to relax;
 81% are on the lookout to make memories;
 78% seek adventure, fun, and excitement;
 73% want to do/see new things;
 72% wish to explore the world more;
 66% want to enhance their relationship with their partners;
 65% seek to straighten their relationship with friends and family members;
 60% want to improve the outlook they have on life;
 55% wish to learn new things about a specific place, history, and/or culture;
 40% want to continue their family travel tradition;
 35% try to cross items off their bucket lists.
Statistics.
They’re all around us, regardless of whether we want to be exposed to them or not.
But how can we distinguish between statistics that stick to the truth and statistics that sway us away from it?
We have your back, as our article’s purpose is precisely that: to get you to think critically about statistics, which is something everyone should do. Let’s start!
What Is Applied Statistics?
To understand applied statistics, we need to understand statistics first. According to Investopedia, statistics is
a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data. The mathematical theories behind statistics rely heavily on differential and integral calculus, linear algebra, and probability theory. Statisticians, people who do statistics, are particularly concerned with determining how to draw reliable conclusions about large groups and general phenomena from the observable characteristics of small samples that represent only a small portion of the large group or a limited number of instances of a general phenomenon.
In essence, statistics is concerned with statistical problems. It includes deep analysis, logic, and interpretation of data. As an extension of this process, applied statistics refers to using statistics for solving other problems.
Applying statistics to any type of social, professional, scientific, and/or industrial problem is a serious undertaking. It involves a lot of statistical methods, tools, data, research, and interpretation, to name a few.
At the same time, however, it’s something that’s done on a daily basis. In other words, applied statistics shows itself in various ways. It’s a decisionmaking tool in the business world; it’s a source of information for everyday questions; and it’s a supportive method for when we need to backup our claims/stories/views.
Applied Statistics and Critical Thinking
Analyzing statistics without being critical toward them is a recipe for disaster. In fact, statistics and critical thinking should go hand in hand at all times. This is not only because critical thinking will help us understand stats better, but because it will make us challenge them too.
It will force us to ask questions, wonder more about what we read/see/hear, go deeper with things, and take information with a grain of salt. As Daniel J. Levitin put it:
Just because someone quotes you a statistic or shows you a graph, it doesn’t mean it’s relevant to the point they’re trying to make. It’s the job of all of us to make sure we get the information that matters, and to ignore the information that doesn’t.
Being able to understand any piece of information with data and statistics is known as statistical literacy. This necessitates that people are able to “use” the Internet, read newspapers and magazines, listen to the radio, and engage in conversations without problems or challenges. In other words, they need to be capable of understanding the different material presented through various media.
That said, understanding it is just the beginning. You need to be able to filter out information from misinformation, truth from lies, important data from obsolete data, and so on. And as we said, that’s when critical thinking comes into play.
For instance, if you’re reading a review about a new skin product, which is said to aggressively deal with acne and other skin imperfections, and you see there’s a 99.9% success, but you have an extremely sensitive skin, you may need to think twice about buying it. In other words, you need to ask yourself:
 Can this product make my skin worse?
 Is this really a product I want to experiment with?
 Is my skin a suitable candidate for this product? What side effects should I expect?
 How many people were the products tested on to come up with that percentage (statistic)?
 Were the test subjects chosen based on particular characteristics? For instance, maybe none of them had acne at the beginning of the trial, so it’s no wonder most of them left it without acne as well.
 How do you know you can trust a statistic printed on the side of a bottle?
Extra help
So, how can you make sure you’re critical toward data and stats? How can you know you’re not being manipulated?
Of course, there are certain tips and tricks to help you stay on the right path when you’re dealing with statistics. Namely, Darell Huff suggests using the following five questions in order to avoid being tricked by statistics and statisticians:
 “Who says so?”
The first thing you need to focus on is identifying bias. For instance, a newspaper that wishes to publish something only because it's a good story (without much concern for context and truthfulness), a laboratory trying to prove something only to sell a product, and so on, will cause red flags because they have motives that go beyond sharing the truth.
 “How does he know?”
Here, you should ask yourself whether the information presented is enough to draw a conclusion. If yes, how reliable is that conclusion? In essence, look for evidence of whether the sample is biased.
 “What’s missing?”
Be on the lookout for statistics where the mean and the median are suspiciously different. For instance, if a statistic says that 100% of female students at a university married professors, but there’s only one female student at that university, the statistic is purposefully misleading (albeit technically correct).
 “Did somebody change the subject?”
Are you dealing with real statistics, or what someone else may have reported? Entities and institutions may give different numbers (or “bother” to get more or less truthful numbers) depending on their current interests.
 “Does it make sense?”
This one is pretty much selfexplanatory. You need to use your own critical reasoning. Does the statistic sound plausible?
Applied Statistics Definition
Applied statistics is:
 a legitimate discipline;
 said to collect and arrange numerical data and meant to deal with every aspect of that data;
 supposed to classify the data in a systematic and meaningful way, so that it’s understandable to different groups of people;
 meant to include a varios procedures for organizing, gathering, presening, and interpreting quantitative data;
 said to include a lot of experiments and fluctuations, but its results should be definite and presentable;
 sometimes funny which might make it sound untrustworthy at first; for instance, there’s a quote by Kato Lomb that reads like this: “Whenever I read statistical reports, I try to imagine my unfortunate contemporary, the Average Person, who, according to these reports, has 0.66 children, 0.032 cars, and 0.046 TVs.”;
 a discipline comprised of various statistical tests and tools such as:
 analysis of variance (ANOVA);
 chisquared test;
 regression analysis;
 Pearson productmoment correlation coefficient (PPMCC);
 student's ttest;
 Spearman's rank correlation coefficient;
 conjoint analysis;
 time series analysis;
 mean square weighted deviation (MSWD);
 Mann–Whitney U;
 and correlation.
 is also obtained through various means including:
 surveys;
 questionnaires;
 experiments;
 case studies;
 observational studies;
 interviews;
 field research, and so on.
Applied statistics isn’t:
 random numbers and inaccurate facts;
 exactly the same as math  of course, math plays a part in it, but it’s a separate discipline; that said, some consider statistics as a branch of mathematics, and not a distinct science;
 also, it’s worth mentioning there’s mathematical statistics too, which is a subset of statistics that includes:
 mathematical analysis;
 differential equations;
 linear algebra;
 probability theory, and so on.
 open only for statisticians/mathematicians  all of us use it, although sometimes unknowingly;
 for those who:
 don’t trust data;
 who believe numbers always manipulate;
 who wish to get results immediately;
 are constantly impatient;
 don’t wish to consult others;
 don’t want to follow certain rules, use various tools, and learn from their mistakes;
 analyze things in a rather shallow manner  statistics requires you to truly get to the heart of the matter, that is, if you wish to get credible data.
The History of Applied Statistics
The term statistics comes from the New Latin statisticum collegium which means "council of state", as well as the Italian word statista which means a "statesman" or "politician".
It was first introduced into the English language in 1791 by Sir John Sinclair when he published the Statistical Account of Scotland. This was the first of twentyone volumes. The book was basically a series of documentary publications covering the subject of living in Scotland.
That said, some of the earliest writing on statistics and probability go way back to the Arab statisticians during the socalled Islamic Golden Age (between the eight and the thirteenth century). Namely, AIKhalil, an Arab philologist and lexicographer, wrote the Book of Cryptographic Messages, considered to be among the first books on cryptography and cryptanalysis. The book employs “the first use of permutations and combinations” to list all Arabic words based on whether they contain vowels or not.
Then, there’s the Manuscript on Deciphering Cryptographic Messages, written by AIKindi, another Arab scholar. In his book, AIKIndi mostly dwells on how to use statistics in order to decipher encrypted messages. This is what basically laid the foundation for statistics.
But when it comes to modern statistics, or statistics as a discipline today, we can probably say that the current version of the field emerged somewhere in the late 19th and the beginning of 20th century.
This started with the work of Karl Pearson and Francis Galton (both were English statisticians), who basically transformed statistics into a much more powerful discipline than it was. They reinforced the opinion that statistics can be used not only in science, but in politics and industry as well.
Galton is also known for introducing concepts such as regression analysis, standard deviation, and correlation, along with models for their application. Pearson developed the Pearson productmoment correlation coefficient.
Probably one of their most significant contributions was founding Biometrika, the first journal of biostatistics and mathematical statistics. The journal originally appeared quarterly.
Other significant figures are William Sealy Gosset, an English statistician, and Ronald Fisher, also a statistician. Fisher’s publications are quite notable, and they include The Correlation between Relatives on the Supposition of Mendelian Inheritance, Statistical Methods for Research Workers, The Genetical Theory of Natural Selection, and The Design of Experiments. He introduced concepts such as variance, ancillary statistics, sufficiency, and so on. Fisher also coined the term null hypothesis, and this happened during the “Lady Tasting Tea” experiment, a “randomized” experiment carried out by Fisher.
Finally, we have to mention Egon Pearson and Jerzy Neyman, too. They’re known for introducing the concepts of “Type II” error, as well as the power of a test, and confidence intervals.
Today, statistical models and tools are applied across a wide range of disciplines. In fact, it’s hard to think of a field unaffected by statistics. As a discipline, statistics has evolved so much that what’s left is to simply ask ourselves what’s next, and how much further it can expand.
Why Are Applied Statistics Important?
It goes without saying that the world can’t run on the basis of predictions, approximate numbers, assumptions, and speculations (and by the way, many people tend to look at stats and numerical data in this way too). Of course, they have their own place, but there are many instances where we’re in need of exact numbers.
And that’s where statistics come into play.
Statistics are said to help us become better decision makers. This is so because a lot of decisions are better made when using logic based on facts, and data, rather than just our gut feeling. This especially applies to professional decisions, but also serious life decisions in general, such as getting vaccinated, getting insurance, asking for a loan, and so on.
That said, we don’t mean to diminish the importance of following your gut and feelings. In fact, they’re very much valid in matters of love, passions, and desires. But that’s a whole other area of life.
Statistics make us understand how lengthy research can get. You start off by collecting data, doing deep analysis, reevaluating things, questioning your own skills and those of your team (if you’re collaborating), and above all, doing it all with as few mistakes as possible. When a notable mistake does occur, you know you need to start right from the beginning because even a single discrepancy can cost you your whole statistical research. In essence, statistics are important because they teach us about patience, perseravence, and devotion.
They also teach us that sometimes teamwork may be a challenge for some, but ultimately it’s a rewarding experience too. We can’t do everything on our own (especially when it comes to long research projects and arranging large numerical data).
But the highest significance of statistics stems from the information they can provide for us. That information helps us make sense of our world; understand the events unfolding around us; and simply give us a perspective that can help us take action in our personal, professional, and political lives.
It also helps us identify with the numerical data  especially when we find ourselves resonating with it. For instance, if a smoker comes across smoking statistics, it’s more than likely that they’ll continue reading those statistics.
Finally, statistics are important because they help us to predict, measure, explore and construct new concepts, present information in a new manner, come up with conclusions about different matters, make relevant comparisons, describe something that’s happening, test hypotheses, explain behaviors, attitudes, and/or activities, develop theories, and so on.
How To Develop Applied Statistics?
Developing applied statistics as a skill means gaining knowledge on the tools and methodology that you can use to conduct relevant research and come up with meaningful results.
Statistical models and tools are indeed developed. We already converted some of them in the “History of Applied Statistics” section, along with the people responsible for their conception.
So, why does developing such methods matter?
Well, statistical methods are basically mathematical models, formulas, methods and techniques which are used as part of the statistical analysis of research data. Building such a model requires more than just a basic knowledge in statistics.
Here are some steps and useful guidelines for statistical model building*:
 Keep in mind that regression coefficients are, in fact, marginal results. Coefficients can change, so you’re far from the final result.
 Begin with the graphs and the univariate descriptives. This will help you identify any potential errors. Also, don’t just focus on bell curves  look for anything that stands out such as breaks in the middle.
 Run the bivariate descriptives and include the graphs. Here, it’s important to understand how each predictor functions on its own, but also in relation to the other predictors and the final outcome.
 Take into account the predictors in sets. Such sets include demographics (socioeconomic status and age), psychological health (depression, stress, anxiety), and so on.
 Don’t forget to analyze your results. Keep in mind that model building and result analysis go together.
 Each variable which is involved in any kind of interaction has to be in the model by itself. When you’re deciding what to leave out and what to keep, it’s easy to get confused. You might end up leaving significant things out, so a sound piece of advice is to focus on the nonsignificant interactions, and get rid of those first.
 Don’t lose sight of the research question.This can happen if you’re dealing with a huge data set. So, every now and then, go back to your main, central question and remind yourself what its purpose is.
Finally, do remember that building a model is not a onesizefitsall activity. A lot of it depends on the field of application, that is, what it is that the model is supposed to do.
*For those of you really interested in model building, we invite you to read the whole article to get a better understanding not only of the steps involved, but also the process as a whole.
Examples of Applied Statistics in Everyday Life
Various scientific fields
Statistics has its implications within different scientific fields, and the list is constantly growing. Here are some examples*:
 Actuarial science: This is the discipline that uses various statistical and mathematical methods in order to assess risks in the finance and insurance industries.
 Epidemiology: This discipline studies factors that affect the health and illness of populations. It’s crucial when it comes to making strategies and interventions in the interest of public health.
 Astrostatistics: This is a discipline that makes use of statistical analysis to interpret astronomical data.
 Business analytics: This is a business process which uses statistical tools and methods to data sets in order to gain insights into business opportunities and performance.
 Geostatistics: This is a geography branch which is concerned with data analysis from different disciplines such as:
 hydrology;
 meteorology;
 oceanography;
 geochemistry;
 geography;
 petroleum geology.
 Demography: Demography deals with populations. It can be applied to section out entire societies/groups in terms of criteria such as ethnicity, nationality, religion, education, and so on.
 Environmental statistics: This refers to the application of certain statistical methods to environmental science. Aspects such as water and air quality, climate, and weather are included, along with animal and plant populations.
 Machine learning: This is a subfield of computer science and it formulates algorithms so that it can make certain predictions from the available data.
 Jurimetrics: It refers to the application of quantitative methods (specifically statistics and probability) to law.
 Biostatistics: A branch of biology that analyzes biological phenomena via statistical analysis (and includes medical statistics).
 Forensic statistics: It denotes the application of probability models as well as statistical methods to scientific evidence (very often DNA evidence).
 Psychometrics: This is the field of psychological and educational assessment of abilities, personality traits, attitudes, knowledge, etc. in terms of statistical analysis.
 Operations research: This branch of applied mathematics (also referred to as operational research), uses methods such as statistics, algorithms, and mathematical modeling to come up with optimal solutions to complicated issues.
 Quality control: This process focuses on reviewing the factors engaged in production and manufacturing.
 Population ecology: This is a subfield of ecology which is concerned with the dynamics of species populations and how they interact with the surrounding environment and ecosystem.

 Quantitative psychology: It refers to statistically analyzing mental processes and people’s behaviors.

 Statistical physics: A subtheory of physics that uses probability theory methods to solve physics problems.
*Keep in mind that some of these disciplines/fields already contain the word “statistics” in their names, but they refer to probability distributions rather than them being a type of statistical analysis.
How to approach this?
 Which fields do you think are impacted the most by statistics? Why?
 Does your line of work require employees to use any statistical tools/methods? If yes, which ones? Also, do you feel comfortable using them?
 How keen are you on expanding your knowledge on statistics if you know it would help with your work?
 David Spiegelhalter said:
 We have seen the problems that result when researchers only report significant findings, but perhaps more important are the conscious or unconscious set of minor decisions that might be made by the researcher depending on what the data seem to be showing. These 'tweaks' might include decisions about changes in the design of the experiment, when to stop collecting data, what data to exclude, what factors to adjust for, what groups to emphasize, what outcome measures to focus on, how to split continuous variables into groups, how to handle missing data, and so on.
 Do you agree with his statement? Why? Why not?
 Do you find statistics in research troublesome in any way? If yes, why?

Do you agree with the following paragraph?

Research in statistics finds applicability in virtually all scientific fields and research questions in the various scientific fields motivate the development of new statistical methods and theory. In developing methods and studying the theory that underlies the methods statisticians draw on a variety of mathematical and computational tools.
 Do you think this is the influence statistics has within a research context? How do you feel about the development of new statistical tools? Who should test their feasibility?
 What’s the most challenging thing about carrying out research in statistics?
 Do you think statistics add credibility to any type of research field? How so? Also, do you think statistics are sometimes manipulated in favor of a certain hypothesis that benefits a particular person, company, institution, or cause?
Getting a university degree
Apart from using statistics in everyday life, you may opt to major in it. In other words, a lot of universities across the world offer degrees in statistics, so a lot of people are actually keen to professionally engage in it.
Should you choose to follow such a path, you need to be aware of some of the possibilities. For instance, if you decide to get a BA in Statistics, you’ll learn subjects such as:
 Probability and statistics;
 Applied statistics;
 Linear algebra;
 Discrete data analysis;
 and Experiments and sampling.
A BA in Statistics prepares you to conduct serious research, collect, analyze, and interpret various data, take a look at numerical information, and come up with credible conclusions. Statistics graduates are asked to explain and elaborate on technical data, and understand the advantages that come with acquiring specific pieces of information.
All in all, graduates are not only asked to analyze and understand data  they’re required to present it properly to others too.
That said, many don’t stop here and move onto getting an MA in Statistics. Such a degree prepares individuals to use statistical data and tools in order to make more specific inquiries, go deeper into the theory, and engage in more meaningful research.
Of course, some of these students move on to PhD programs, too. On this level they deal with formulation and application of scientific methods and models, and PhD programs usually encourage students to focus on the interconnectedness between theory and observation.
Finally, it’s worth noting that many consider statistics to be a valuable subject not only for those who eventually decide to major in it, but highschoolers, too. Tony Wagner stated:
If college admissions officers are going to encourage kids to take the same AP math class, why not statistics? Almost every career (whether in business, nonprofits, academics, law, or medicine) benefits from proficiency in statistics. Being an informed, responsible citizen requires a sound knowledge of statistics, as politicians, reporters, and bloggers all rely on "data" to justify positions.
In other words, no matter what college degree you’re interested in obtaining  you’ll benefit from having a statistics subject at some point as part of your education.
Where to find such a major?
You can check out the website of the university you’d like to attend (in whatever country or city it is) to make sure that they offer a BA in statistics.
If you’re looking to study at an American university, for instance, here are colleges that offer a major in statistics:
 Albion College;
 American University;
 Arizona State University  West;
 Bowling Green State University;
 Brown University;
 California Polytechnic State University  San Luis Obispo;
 California University of Pennsylvania;
 Case Western Reserve University;
 Colorado School of Mines;
 Colorado State University;
 Florida State University;
 Grand Valley State University;
 Harvard University (probably every student’s academic dream, right?);
 Illinois Institute of Technology;
 Iowa State University;
 North Carolina State University;
 San Diego State University, and so on.
Statistics about statistics
Finally, let’s talk statistics.
According to the U.S. Bureau of Labor Statistics, the employment in the statistics sector is expected to grow 35% from 2019 through 2029. This is probably because as technology grows and develops further, data is made more accessible, so opportunities in statistics are projected to increase as well. Also, as of 2019, the median salary for staticians is approximated to be $92,270 per year.
How to approach this?
 Why do you want this major?
 Do you know enough about this major?
 What are the exact requirements for this major and can you meet them?
 Do you know enough about this major and how can you get further informed?
 Have you ever talked to someone who majored in statistics? If yes, did their experience impact you? In what way?
 Who should be getting a major in statistics? Why?
 Do you think statistics is a difficult degree to obtain?
 Do you think you need a lot of mathematical knowledge in order to get a degree in statistics?
 What aspect of statistics interests you the most? And vice versa  which one bores you?
 What kind of job can you get with a major in (applied) statistics? What can you do? And more importantly, what is it that you want to do?
 Do you think statistics can pave the way to a good career? If yes, how so?
 What type of statistics courses are you interested in attending at a university level? What do you expect to learn from them?
 What should you consider when choosing the university?
 What are some of the challenges that come with majoring in statistics?
 How can this degree help you in everyday life? Think of several examples and come up with as many details as you can.
 What qualities and skills do students interested in statistics need to possess? And how can they work on improving them? Also, what qualities/skills do statisticians need to obtain?
 According to you, what’s a successful statistician?
 Do you think a person majoring in statistics should be patient, knowing that gathering data, analyzing, and doing research all the time can be exhausting and challenging?
 Do you feel any pressure to choose this major? If yes, why? Who’s pressuring you and what can you do about it?
 Finally, is getting a degree in statistics worth it?
Everyday situations
Why would statistics be a useful thing in everyday life?
How do we use it?
Why would we use it?
And more importantly, are we aware that we use it at all?
Since statistics help us make sense of the world around us, it shouldn’t come as a surprise they’re part of our daily lives.
Since the moment we have our first coffee in the morning and read the newspaper, to the moment we turn on the TV before we go to bed, we’re surrounded by a bunch of stats.
In fact, there’s rarely a job position that doesn’t deal with some form of statistics. Even if it’s not the job itself, consider the following: almost every company out there has at least one social media platform where they promote their business/services/products. So, the people responsible for this are constantly checking how much engagement there is; when are people the most active on their page; how many comments they have under a specific post; what posts are the most popular; and so on. These are all statistics.
In fact, some are so complex (yet important) that business owners even opt for various social analytics tools instead, to get more detailed information.
We witness more or less the same with political campaigns. During election periods, many news organizations predict who the winner is. Of course, that’s done based on voter polls and voter comments, how the candidates’ overall campaigns are received, and so on.
Moreover, statistics has a role when it comes to our insurance, too. We have car insurance, health insurance, house insurance, life insurance, and so on. How much we’re charged is based upon statistics. For instance, if you’re older and suffer from certain chronic diseases  then the insurance company gives you less points based on their scale (each company has a different approach to this, but the result is more or less the same). So, companies determine how much of a risk a specific person poses to the company; what percentage of policies is the company likely to pay out; how much money the company can lose in specific cases, and so on.
All in all, statistics plays a part even in the most mundane activities we’re faced with each day.
How to approach this?
 How much do you rely on statistics when you make decisions?
 In general, what do you think about statistics? Do you feel they mislead you, guide you, inform you, lie to you, and so on? What kind of attitude do you have towards them?
 How knowledgeable are you about statistics? Do you have a general understanding of the concept or you’ve gone deeper with it?
 Why do you think people often say “statistics don’t really apply to me”?
 What do you dislike the most about statistics? And vice versa  what do you appreciate the most about them?
 Why are statistics useful in real life?
 How can you focus on finding statistics that help you instead of focusing on unnecessary data and information? Also, how do you know what set of statistics are reliable?
 Can statistics be harmful in any way?
 When you read statistics that include your age/level of education/race and so on, and don’t resonate with them  how does that make you feel? Do you think there’s something wrong with you, with the research, or perhaps with other people? Maybe you don’t think much and simply move on to the next piece of information?
 How do you feel about people that rely heavily on statistics and try to convince others that they’re right simply because certain statistics support their claims?
 How do statistics contribute to our lives? Can you imagine our lives without any numerical data, statistics, technical data, and so on? Why would that be a problem? What challenges might come with it? Or maybe you think that will make things better? Elaborate.
 How much value do you feel statistics add to your life? In other words, do you feel more:
 informed about the world?
 knowledgeable about different areas?
 eager to discuss things further?
 curious?
 aware?
 competent?
 enlightened?
Famous Quotes About Applied Statistics
“Another mistaken notion connected with the law of large numbers is the idea that an event is more or less likely to occur because it has or has not happened recently. The idea that the odds of an event with a fixed probability increase or decrease depending on recent occurrences of the event is called the gambler's fallacy. For example, if Kerrich landed, say, 44 heads in the first 100 tosses, the coin would not develop a bias towards the tails in order to catch up! That's what is at the root of such ideas as "her luck has run out" and "He is due." That does not happen. For what it's worth, a good streak doesn't jinx you, and a bad one, unfortunately , does not mean better luck is in store.”
“I just wish that Statistics was as easy as arranging numbers in chronological order, finding the median, lower and upper quartiles, and placing them on a Box and whisker's chart”
“While most of us are comfortable acknowledging that luck plays a role in what we do, we have difficulty assessing its role after the fact. Once something has occurred and we can put together a story to explain it, it starts to seem like the outcome was predestined. Statistics don't appeal to our need to understand cause and effect, which is why they are so frequently ignored or misinterpreted. Stories, on the other hand, are a rich means to communicate precisely because they emphasize cause and effect.”
“One is born an individual; one becomes a statistic.”
“The statistical rate of mortality means nothing. It is the rate of invisible mortality that counts. That is much higher, but incalculable, since death is here, growing everywhere and mounting up in the social body as a whole.
In the same way, there's no comparison between the index of visible corruption and that of invisible corruption (which it contributes to masking). The rate of political indifference is much higher than the abstention rate. As for the rate of invisible stupidity, it is far beyond the stupidity that actually shows up.
But perhaps the rate of secret intelligence and the rates of passion and imagination are also far higher than they appear?”
“There are two kinds of statistics, the kind you look up and the kind you make up.”
“Statistics are somewhat like old medical journals, or like revolvers in newly opened mining districts. Most men rarely use them, and find it troublesome to preserve them so as to have them easy of access; but when they do want them, they want them badly.”
“Be wary, though, of the way news media use the word “significant,” because to statisticians it doesn’t mean “noteworthy.” In statistics, the word “significant” means that the results passed mathematical tests such as ttests, chisquare tests, regression, and principal components analysis (there are hundreds). Statistical significance tests quantify how easily pure chance can explain the results. With a very large number of observations, even small differences that are trivial in magnitude can be beyond what our models of change and randomness can explain. These tests don’t know what’s noteworthy and what’s not—that’s a human judgment.”
“Statistical malfeasance has very little to do with bad math. Judgement an integrity turn out to be surprisingly important. A detailed knowledge of statistics does not deter wrongdoing any more than a detailed knowledge of the law averts criminal behavior.”
“To call in the statistician after the experiment is done may be no more than asking him to perform a postmortem examination: he may be able to say what the experiment died of.”
Frequently Asked Questions (FAQ)
What are some different types of statistics?
When we talk about statistics people usually think of applied statistics, mathematical statistics, theoretical statistics, and so on. And while there’s nothing wrong with these statistics, there’s another classification that’s more common.
Namely, there are two major branches of statistics:
 Descriptive statistics;
 Inferential statistics.
Descriptive Statistics
Descriptive statistics denotes a summary statistic which quantitatively summarizes data sets or pieces of information. These statistics are very brief descriptive coefficients, and they can be both representations of the entire population or a sample of a population. Please note that in statistics, the term population refers to the pool of individuals from which statistical samples are gathered.
Also, descriptive statistics are usually divided into measures of variability and measures of central tendency. The former include variance, kurtosis, standard deviation, skewness, minimum and maximum variables, whereas the latter include median, mean, and mode.
The measures of variability of speed are used to describe the dispersion of data within the given set, and the measures of central tendency serve to explain the center of the data set.
A lot of people wonder why we need such descriptive statistics. In other words, why do we need to describe data? The answer is that these statistics help us understand certain collective properties of the data sample’s elements. Such measures give the overall shape of the collected data. This can be depicted on a chart or a dot plot.
A good example of descriptive statistics is calculating a student’s GPA (grade point average). Each student’s GPA is a reflection of their academic performance, and it takes data points from grades received via exams (and/or midterms), and averages them together in order to arrive at a more general understanding of a student’s academic achievements.
Inferential Statistics
According to Investopedia, inferential statistics “are tools that statisticians use to draw conclusions about the characteristics of a population from the characteristics of a sample and to decide how certain they can be of the reliability of those conclusions”.
Such statistics are used to make generalizations about very large groups, such as speculating about future events, analyzing consumers’ various purchasing habits, and so on.
Common statistical models applied in inferential statistics contexts are regression analysis hypothesis tests, correlation, and confidence intervals.
What exactly does a statistician do?
By now you probably understand a lot about (applied) statistics, and what its purpose is, but there could be some dilemmas regarding a statistician’s job. In other words, you may not fully understand what it is that a statistician does exactly.
A statistician is required to communicate effectively with a team in receiving but also providing detailed feedback. They also need to work individually, and convey information to nonstatisticians in an accurate and understandable manner. This means statisticians are involved in more or less all the stages of the “thing” being analyzed. The “thing” can vary, of course, depending on whether we’re talking about drug development, product development, or launching a new service, to name a few.
They should also be able to integrate disparate and random sources of data, and then prepare them for detailed analysis. In other words, statisticians may not be aware of the challenges that come with each set of data before they actually sit down and get to work.
Statisticians should use advanced statistical models both accurately and professionally, and handle huge chunks of data. They also need programming knowledge, collaborative skills, and high levels of concentration, as they’re constantly surrounded by numbers, data, and a plethora of information. This means that even the slightest mistake can totally cause chaos and produce wrong results.
Can statistics sometimes be misleading?
Can they?
Well, it depends on what we perceive to be misleading.
Is it because the research was conducted in a poor manner, so now we’re exposed to “wrong” results? Is it because we’re misinterpreting what we’re reading?
Or is it because sometimes, only convenient statistics are shared? For instance, a new product is released, and the brand only emphasizes this product’s perks and the percentage of people who have benefited from it, but disregards the group of people who may have experienced some side effects from using that product. Charles Wheelan said: “Statistics cannot be any smarter than the people who use them. And in some cases, they can make smart people do dumb things.”
What’s more, sometimes statistics may mislead people when they’re (deliberately or by accident) altered, that is, the numerical data gets changed and/or omitted. Steven Magee gives the following example: “Many people that have been through the unemployment system realize that the corporate government unemployment statistics only report the short term unemployed and the long term unemployed and disabled are ignored.”
This is again where the critical thinking factor comes into play. It’s up for us to decipher what we trust, what we’re exposing ourselves to, what piece of information gets to us, and which one doesn’t.
This is much easier said than done. Statistics are nowadays so randomly “thrown” at us, that it’s impossible to fully “protect” yourself from being overwhelmed by numerical data and weird information. But it’s up to us to do our best, and try to at least double check sources, people’s claims, and news  especially about serious matters.
After all, as Mark Suster put it: “Anyone with a great deal of experience in dealing with numbers knows to be careful about the seduction of them”.
Suggestions for Further Reading
Statistics is a field that’s often a topic of debate. Some discuss what it is or why it is the way it is; others dwell on its shortcomings and the challenges that come with it. However, one thing’s for sure  it’s a field we are all interested in.
You don’t have to be a statistician or a mathematician to benefit from reading about statistics. In fact, educating yourself about statistics can only help you further understand the complexity behind it.
That said, many believe they may only get more confused about it. That’s why we chose books that will only clear things up, and not make them even more complicated
Without any ado, here’s our list.*
 How to Lie with Statistics, by Darrell Huff
 The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition (Springer Series in Statistics), by Jerome H. Friedman, Robert Tibshirani, and Trevor Hastie
 Naked Statistics: Stripping the Dread from the Data, by Charles Wheelan
 The Signal and the Noise: Why So Many Predictions Failbut Some Don't, by Nate Silver
 The Model Thinker: What You Need to Know to Make Data Work for You, by Scott E. Page
 Statistics Done Wrong: The Woefully Complete Guide, by Alex Reinhart
 Statistics for People Who (Think They) Hate Statistics, by Neil J. Salkind
 Bayesian Statistics the Fun Way: Understanding Statistics and Probability with Star Wars, LEGO, and Rubber Ducks, by Will Kurt
 Factfulness: Ten Reasons We're Wrong About the Worldand Why Things Are Better Than You Think, by Anna Rosling Rönnlund, Hans Rosling, and Ola Rosling
 Statistics without Tears: An Introduction for NonMathematicians, by Derek Rowntree
 How to Make the World Add Up: Ten Rules for Thinking Differently About Numbers, by Tim Harford
 The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy, by Sharon Bertsch McGrayne
Final Thoughts
All in all, statistics is a very versatile field. It has practical applications within various research fields, but it’s also a part of our daily lives. In the end, how much we’re willing to welcome it and accept it is up to us.
Of course, there’s always something else to be added. Statistics is a complex discipline. And while we may not have to understand every single bit of it, it can definitely be helpful to upgrade our current knowledge.
If you feel that way too, then you’re in the right place. We’re happy to share that we've prepared an online applied statistics and critical thinking course, and we’d be thrilled if you joined us!
Together we’ll learn about:
 collecting data, random sampling, and sampling bias;
 principles of data representation, histograms, pie graphs, box and whisker, and bar graphs;
 regressions models, mediation and moderation, multicollinearity, and heterogeneity bias;
 statistics and the media (statistics and advertising);
 median, mode, rage and percentiles (descriptive statistics), and so on.
Finally, Charmaine J. Forde said: “I have studied many languagesFrench, Spanish and a little Italian, but no one told me that Statistics was a foreign language.”
Let us be the ones to teach you how to speak it.
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