What are Statistics?

What are Statistics?

Learning Objectives

1. Describe the range of applications of statistics
2. Identify situations in which statistics can be misleading
3. Define "Statistics"

Statistics include numerical facts and figures. For instance:

• The largest earthquake measured 9.2 on the Richter scale.
• Men are at least 10 times more likely than women to commit murder.
• One in every 8 South Africans is HIV positive.
• By the year 2020, there will be 15 people aged 65 and over for every new baby born.

The study of statistics involves math and relies upon calculations of numbers. But it also relies heavily on how the numbers are chosen and how the statistics are interpreted. For example, consider the following three scenarios and the interpretations based upon the presented statistics. You will find that the numbers may be right, but the interpretation may be wrong. Try to identify a major flaw with each interpretation before we describe it.

As a whole, these examples show that statistics are not only facts and figures; they are something more than that. In the broadest sense, "statistics" refers to a range of techniques and procedures for analyzing, interpreting, displaying, and making decisions based on data.

Source: Mikki Hebl, https://onlinestatbook.com/2/introduction/what_are.html
This work is in the Public Domain.

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Questions

Question 1 out of 2.

Which of the following are part(s) of statistics? Select all that apply.

Question 2 out of 2.

Answers

1. All of the given choices
   Statistics is a field of study concerned with summarizing data, interpreting data, and making decisions based on data. It involves all of those things.
   
   
2. Yes
   There is a third variable involved here--the summer. More people eat ice cream in the summer and more people swim in the summer.

Importance of Statistics

Learning Objectives

1. Give examples of statistics encountered in everyday life
2. Give examples of how statistics can lend credibility to an argument

Like most people, you probably feel that it is important to "take control of your life". But what does this mean? Partly, it means being able to properly evaluate the data and claims that bombard you every day. If you cannot distinguish good from faulty reasoning, then you are vulnerable to manipulation and to decisions that are not in your best interest. Statistics provides tools that you need in order to react intelligently to information you hear or read. In this sense, statistics is one of the most important things that you can study.

To be more specific, here are some claims that we have heard on several occasions. (We are not saying that each one of these claims is true!)

• 4 out of 5 dentists recommend Dentine.
• Almost 85% of lung cancers in men and 45% in women are tobacco-related.
• Condoms are effective 94% of the time.
• Native Americans are significantly more likely to be hit crossing the street than are people of other ethnicities.
• People tend to be more persuasive when they look others directly in the eye and speak loudly and quickly.
• Women make 75 cents to every dollar a man makes when they work the same job.
• A surprising new study shows that eating egg whites can increase one's life span.
• People predict that it is very unlikely there will ever be another baseball player with a batting average over 400.
• There is an 80% chance that in a room full of 30 people that at least two people will share the same birthday.
• 79.48% of all statistics are made up on the spot.

All of these claims are statistical in character. We suspect that some of them sound familiar; if not, we bet that you have heard other claims like them. Notice how diverse the examples are. They come from psychology, health, law, sports, business, etc. Indeed, data and data interpretation show up in discourse from virtually every facet of contemporary life.

Statistics are often presented in an effort to add credibility to an argument or advice. You can see this by paying attention to television advertisements. Many of the numbers thrown about in this way do not represent careful statistical analysis. They can be misleading and push you into decisions that you might find cause to regret. For these reasons, learning about statistics is a long step towards taking control of your life. (It is not, of course, the only step needed for this purpose). The present textbook is designed to help you learn statistical essentials. It will make you into an intelligent consumer of statistical claims.

You can take the first step right away. To be an intelligent consumer of statistics, your first reflex must be to question the statistics that you encounter. The British Prime Minister Benjamin Disraeli is quoted by Mark Twain as having said, "There are three kinds of lies - lies, damned lies, and statistics". This quote reminds us why it is so important to understand statistics. So let us invite you to reform your statistical habits from now on. No longer will you blindly accept numbers or findings. Instead, you will begin to think about the numbers, their sources, and most importantly, the procedures used to generate them.

We have put the emphasis on defending ourselves against fraudulent claims wrapped up as statistics. We close this section on a more positive note. Just as important as detecting the deceptive use of statistics is the appreciation of the proper use of statistics. You must also learn to recognize statistical evidence that supports a stated conclusion. Statistics are all around you, sometimes used well, sometimes not. We must learn how to distinguish the two cases.

Now let us get to work!

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Questions

Question 1 out of 2.
You hear in a commercial that 80% of children prefer to eat a certain kind of cereal for breakfast. What do you conclude?

• This cereal is superior to all others...at least according to kids.
• You need to know more about where these data came from before making any conclusions.
• 20% of kids prefer to eat Trix.

Question 2 out of 2.
What should you take into consideration when evaluating statistical claims? Check all that apply.

• The statistics presented
• The sources of the statistical findings
• The procedures used to generate the claims

Answers

1. You need to know more about where these data came from before making any conclusions
   To be an intelligent consumer of statistics, your first reflex must be to question the statistics that you encounter.
   
   
2. All the given choices
   As opposed to just accepting numbers or findings, you should think about all of these things when evaluating a statistical claim.