Introduction to Collecting Data

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 Dentyne.
• 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 streets 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.
• Based on clinical trials the Pfizer-BioNTech vaccine was 95% effective at preventing laboratory-confirmed COVID-19 illness in people without evidence of previous infection.
• 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.)  These chapters will help you learn statistical essentials. It will make you into an intelligent consumer of statistical claims.

Here are a few examples to illustrate why it is important to understand the concepts discussed in these sections (from Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University.)

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 will discuss in more detail in a later module 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.

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 famously 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.  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.  When a research team is testing a new treatment for a disease, statistics allows them to conclude based on a relatively small trial that there is good evidence their drug is effective.  Statistics allowed prosecutors in the 1950’s and 60’s to demonstrate racial bias existed in jury panels.  Statistics are all around you, sometimes used well, sometimes not. We must learn how to distinguish the two cases.

Learning Objectives

Below are the learning objectives for each section of this chapter.

3.1 Basic Concepts

• Identify the population of a study
• Determine whether a value calculated from a group is a statistic or a parameter
• Determine whether a measurement is categorical (qualitative) or quantitative data

3.2 Sampling Method

• Identify different sampling methods
• Select appropriate sampling techniques
• Identify sources of bias

3.3 Experiments

• Identify characteristics of an experiment
• Identify different experiment methods
• Identify experiments that control for the placebo effect

Attributions

• This page contains modified content from David Lippman, “Math In Society, 2nd Edition.” Licensed under CC BY-SA 4.0.
• This page contains content by Robert Foth, Math Faculty, Pima Community College, 2021.