Statistics in a Nutshell
T he world today is overflowing with data to the point where anyone (even me!) can be overwhelmed. I wouldn’t blame you if you were cynical right now about statistics you read about in the media — I am too at times. The good news is that while a great deal of misleading and incorrect information is lying out there waiting for you, a lot of great stuff is also being produced; for example, many studies and techniques involving data are helping improve the quality of our lives. Your job is to be able to sort out the good from the bad and be confident in your ability to do that. Through a strong understand ing of statistics and statistical procedures, you gain power and confidence with numbers in your everyday life, in your job, and in the classroom. That’s what this book is all about.
In this chapter, I give you an overview of the role statistics plays in today’s data-packed society and what you can do to not only survive but thrive. You get a much broader view of statistics as a partner in the scientific method — designing effective studies, collecting good data, organizing and analyzing the information, interpreting the results, and making appropriate conclusions. (And you thought statistics was just number-crunching!)
Thriving in a Statistical World
It’s hard to get a handle on the flood of statistics that affect your daily life in large and small ways. It begins the moment you wake up in the morning and check the news and listen to the meteorologist give you her predictions for the weather based on her statistical analyses of past data and present weather conditions. You pore over nutritional information on the side of your cereal box while you eat breakfast. At work you pull numbers from charts and tables, enter data into spreadsheets, run diagnostics, take measure ments, perform calculations, estimate expenses, make decisions using statis tical baselines, and order inventory based on past sales data.
At lunch you go to the No. 1 restaurant based on a survey of 500 people. You eat food that was priced based on marketing data. You go to your doctor’s appointment where they take your blood pressure, temperature, weight, and do a blood test; after all the information is collected, you get a report show ing your numbers and how you compare to the statistical norms.
You head home in your car that’s been serviced by a computer running sta tistical diagnostics. When you get home, you turn on the news and hear the latest crime statistics, see how the stock market performed, and discover how many people visited the zoo last week
At night, you brush your teeth with toothpaste that’s been statistically proven to fight cavities, read a few pages of your New York Times Best-Seller (based on statistical sales estimates), and go to sleep — only to start it all over again the next morning. But how can you be sure that all those statistics you encounter and depend on each day are correct? In Chapter 2, I discuss in more depth a few examples of how statistics is involved in our lives and workplaces, what its impact is, and how you can raise your awareness of it.
Some statistics are vague, inappropriate, or just plain wrong. You need to become more aware of the statistics you encounter each day and train your mind to stop and say “wait a minute!”, sift through the information, ask ques tions, and raise red flags when something’s not quite right. In Chapter 3, you see ways in which you can be misled by bad statistics and develop skills to think critically and identify problems before automatically believing results.
Like any other field, statistics has its own set of jargon, and I outline and explain some of the most commonly used statistical terms in Chapter 4. Knowing the language increases your ability to understand and communicate statistics at a higher level without being intimidated. It raises your credibil ity when you use precise terms to describe what’s wrong with a statistical result (and why). And your presentations involving statistical tables, graphs, charts, and analyses will be informational and effective. (Heck, if nothing else, you need the jargon because I use it throughout this book; don’t worry though, I always review it.)
In the next sections, you see how statistics is involved in each phase of the scientific method.
Designing Appropriate Studies
Everyone’s asking questions, from drug companies to biologists; from mar keting analysts to the U.S. government. And ultimately, everyone will use sta tistics to help them answer their questions. In particular, many medical and psychological studies are done because someone wants to know the answer to a question. For example,
Will this vaccine be effective in preventing the flu?
What do Americans think about the state of the economy?
Does an increase in the use of social networking Web sites cause depres sion in teenagers?
The first step after a research question has been formed is to design an effective study to collect data that will help answer that question. This step amounts to figuring out what process you’ll use to get the data you need. In this section, I give an overview of the two major types of studies — surveys and experiments — and explore why it’s so important to evaluate how a study was designed before you believe the results
Surveys
An observational study is one in which data is collected on individuals in a way that doesn’t affect them. The most common observational study is the survey. Surveys are questionnaires that are presented to individuals who have been selected from a population of interest. Surveys take many differ ent forms: paper surveys sent through the mail, questionnaires on Web sites, call-in polls conducted by TV networks, phone surveys, and so on.
If conducted properly, surveys can be very useful tools for getting informa tion. However, if not conducted properly, surveys can result in bogus informa tion. Some problems include improper wording of questions, which can be misleading, lack of response by people who were selected to participate, or failure to include an entire group of the population. These potential problems mean a survey has to be well thought out before it’s given.
Many researchers spend a great deal of time and money to do good surveys, and you’ll know (by the criteria I discuss in Chapter 16) that you can trust them. However, as you are besieged with so many different types of surveys found in the media, in the workplace, and in many of your classes, you need to be able to quickly examine and critique how a survey was designed and conducted and be able to point out specific problems in a well-informed way. The tools you need for sorting through surveys are found in Chapter 16
Experiments
An experiment imposes one or more treatments on the participants in such a way that clear comparisons can be made. After the treatments are applied, the responses are recorded. For example, to study the effect of drug dosage on blood pressure, one group may take 10 mg of the drug, and another group may take 20 mg. Typically, a control group is also involved, in which subjects each receive a fake treatment (a sugar pill, for example), or a standard, non experimental treatment (like the existing drugs given to AIDS patients.)
Good and credible experiments are designed to minimize bias, collect lots of good data, and make appropriate comparisons (treatment group versus control group). Some potential problems that occur with experiments include researchers and/or subjects who know which treatment they got, factors not controlled for in the study that affect the outcome (such as weight of the sub ject when studying drug dosage), or lack of a control group (leaving no base line to compare the results with)
But when designed correctly, an experiment can help a researcher establish a cause-and-effect relationship if the difference in responses between the treatment group and the control group is statistically significant (unlikely to have occurred just by chance)
Experiments are credited with helping to create and test drugs, determining best practices for making and preparing foods, and evaluating whether a new treatment can cure a disease, or at least reduce its impact. Our quality of life has certainly been improved through the use of well-designed experiments. However, not all experiments are well-designed, and your ability to determine which results are credible and which results are incredible (pun intended) is critical, especially when the findings are very important to you. All the info you need to know about experiments and how to evaluate them is found in Chapter 17
Collecting Quality Data
After a study has been designed, be it a survey or an experiment, the individ uals who will participate have to be selected, and a process must be in place to collect the data. This phase of the process is critical to producing credible data in the end, and this section hits the highlights
Selecting a good sample
Statisticians have a saying, “Garbage in equals garbage out.” If you select your subjects (the individuals who will participate in your study) in a way that is biased — that is, favoring certain individuals or groups of individuals — then your results will also be biased. It’s that simple.
Suppose Bob wants to know the opinions of people in your city regarding a proposed casino. Bob goes to the mall with his clipboard and asks people who walk by to give their opinions. What’s wrong with that? Well, Bob is only going to get the opinions of a) people who shop at that mall; b) on that par ticular day; c) at that particular time; d) and who take the time to respond.
Those circumstances are too restrictive — those folks don’t represent a cross section of the city. Similarly, Bob could put up a Web site survey and ask people to use it to vote. However, only people who know about the site, have Internet access, and want to respond will give him data, and typically only those with strong opinions will go to such trouble. In the end, all Bob has is a bunch of biased data on individuals that don’t represent the city at all.
To minimize bias in a survey, the key word is random. You need to select your sample of individuals randomly — that is, with some type of “draw names out of a hat” process. Scientists use a variety of methods to select individuals at random, and you see how they do it in Chapter 16
Note that in designing an experiment, collecting a random sample of people and asking them to participate often isn’t ethical because experiments impose a treatment on the subjects. What you do is send out requests for volunteers to come to you. Then you make sure the volunteers you select from the group represent the population of interest and that the data is well collected on those individuals so the results can be projected to a larger group. You see how that’s done in Chapter 17
After going through Chapters 16 and 17, you’ll know how to dig down and analyze others’ methods for selecting samples and even be able to design a plan you can use to select a sample. In the end, you’ll know when to say “Garbage in equals garbage out.”
Avoiding bias in your data
Bias is the systematic favoritism of certain individuals or certain responses. Bias is the nemesis of statisticians, and they do everything they can to mini mize it. Want an example of bias? Say you’re conducting a phone survey on job satisfaction of Americans; if you call people at home during the day between 9 a.m. and 5 p.m., you miss out on everyone who works during the day. Maybe day workers are more satisfied than night workers.
You have to watch for bias when collecting survey data. For instance: Some surveys are too long — what if someone stops answering questions halfway through? Or what if they give you misinformation and tell you they make $100,000 a year instead of $45,000? What if they give you answers that aren’t on your list of possible answers? A host of problems can occur when collect ing survey data, and you need to be able to pinpoint those problems.
Experiments are sometimes even more challenging when it comes to bias and collecting data. Suppose you want to test blood pressure; what if the instru ment you’re using breaks during the experiment? What if someone quits the experiment halfway through? What if something happens during the experi ment to distract the subjects or the researchers? Or they can’t find a vein when they have to do a blood test exactly one hour after a dose of a drug is given? These problems are just some examples of what can go wrong in data collection for experiments, and you have to be ready to look for and find these problems
After you go through Chapter 16 (on samples and surveys) and Chapter 17 (on experiments), you’ll be able to select samples and collect data in an unbi ased way, being sensitive to little things that can really influence the results. And you’ll have the ability to evaluate the credibility of statistical results and to be heard, because you’ll know what you’re talking about.
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