What are Statistics?

Site: Saylor Academy
Course: MA121: Introduction to Statistics
Book: What are Statistics?
Printed by: Guest user
Date: Monday, May 27, 2024, 3:38 AM

Description

Read this brief introduction to the field of statistics and some relevant examples of how statistics can lend credibility to making arguments. Complete the practice questions in these sections.

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.

1) A new advertisement for Ben and Jerry's ice cream introduced in late May of last year resulted in a 30% increase in ice cream sales for the following three months. Thus, the advertisement was effective.

A major flaw is that ice cream consumption generally increases in the months of June, July, and August regardless of advertisements. This effect is called a history effect and leads people to interpret outcomes as the result of one variable when another variable (in this case, one having to do with the passage of time) is actually responsible.

2) The more churches in a city, the more crime there is. Thus, churches lead to crime.

A major flaw is that both increased churches and increased crime rates can be explained by larger populations. In bigger cities, there are both more churches and more crime. This problem, which we discuss in more detail in the section on causality, refers to the third-variable problem. Namely, a third variable can cause both situations; however, people erroneously believe that there is a causal relationship between the two primary variables rather than recognize that a third variable can cause both.

3) 75% more interracial marriages are occurring this year than 25 years ago. Thus, our society accepts interracial marriages.

A major flaw is that we don't have the information that we need. What is the rate at which marriages are occurring? Suppose only 1% of marriages 25 years ago were interracial and so now 1.75% of marriages are interracial (1.75 is 75% higher than 1). But this latter number is hardly evidence suggesting the acceptability of interracial marriages. In addition, the statistic provided does not rule out the possibility that the number of interracial marriages has seen dramatic fluctuations over the years and this year is not the highest. Again, there is simply not enough information to understand fully the impact of the statistics.

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
Public Domain Mark 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.

 numerical calculations
 graphs
 interpretations and decisions based on the numbers and graphs


Question 2 out of 2.

Higher rates of ice cream consumption and drowning for a city correspond. This leads people to believe that eating ice cream can somehow put you at risk of drowning. Can you think of another interpretation?

 yes

 no

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.