1.2: Importance of Statistics

Learning Objectives

• Motivate the importance of statistical literacy in our daily lives
• Review the scientific method
• Define variable
• Define independent variable
• Define dependent variable
• Outline the basic process of statistics-based research

General Overview of Why/How We Study Statistics

Most of us understand the basic human desire to live a good life. To reach this goal, we all have to make choices based on what we know about the world. One way to make better decisions is to pay attention to things that are consistent and predictable, since they can help us understand what might happen in the future. At the same time, we know that not everything in life follows a pattern. By recognizing both what is predictable and what is not, we can develop tools that help us learn, grow, and make informed decisions.

There are many real-life challenges that push us to understand these tools and how the world works. For example, a candidate for mayor might say that the city's rising crime rate is caused by the policies of his political opponent. How can we know if that is true? How do we decide who to vote for in the upcoming election? Or maybe a salesperson is trying to sell us blackout curtains, claiming that it will lower the heating bill of the house. How do we know if the curtains will actually save us money? Will a new diet actually improve our health? Can we improve the fuel economy of our vehicle by using a different kind of fuel? Is the chance of severe weather high enough to justify canceling an event? These kinds of questions require us to observe, analyze, and think carefully to make the best choices.

Because we have experienced how unpredictable both nature and human societies can be, it’s reasonable to wonder how we can be sure that our understanding of the world is accurate. The world is complex, and many different factors influence every event. People might make claims out of ignorance, or they might have their own motives. Faced with all of this, it would be easy to feel overwhelmed with doubt—but fortunately, we spend most of our lives learning how to deal with uncertainty.

The way we handle this is simple and familiar. Throughout our lives, we observe people and events again and again, paying attention to different situations and outcomes. We think about what we see and form a first impression or idea. Then we test that idea by looking for more examples and adjusting our thinking when necessary. Over time, some of our ideas become strong and reliable because they consistently match what we observe. Still, we stay open to new information that might change our understanding. For most of us, this process happens naturally. In fact, it is the basic idea behind the scientific method.

We can think of the the scientific method as a more organized version of the natural questioning process we outlined above. As we grow in our ability to analyze the world, we learn to avoid common mistakes and improve the way we investigate things. The scientific method starts when we make observations about something that interests us. These observations lead us to ask a research question about a specific topic. Then we create a hypothesis (a possible explanation or prediction that relates to our question). A hypothesis describes how different factors, called variables, might be connected. Variables are traits or characteristics of an event, object, or person that can change. A hypothesis must also be falsifiable, meaning it must be possible to show that it could be wrong.

Once a hypothesis has been created, it must be tested through experimentation. Simply observing something isn't enough, because we can't tell how each variable affects the situation. That's why designing a good experiment is one of the most important parts of the scientific method. It this step, the researcher identifies other factors, called confounding variables, that may influence the results. The researcher then creates a plan to reduce or control the influence of these variables while systematically changing some of the variables being studied.

The variables that are changed systematically by a researcher during an experiment are called independent variables. The dependent variables are the variables measured as the independent variables are manipulated. The experimental design becomes more complicated as the number of independent and dependent variables increases. This is because the researcher must understand how each independent variable interacts with each dependent variable. For this reason, it is usually best to keep the number of variables low in an experiment. More variables can always be tested in later experiments.

Text Exercise \(\PageIndex{1}\)

High schools often help students prepare for graduation by exploring different career options and the paths that lead to them. These presentations usually include information about job satisfaction. Which jobs make people feel the most satisfied? Which careers make people the happiest? A student might see a list of high-satisfaction careers (like chiropractors, clergy, dentists, firefighters, and nurses etc.), and think that choosing one of these jobs will guarantee a happy life.

We can think of job satisfaction studies as a type of experiment. In this case, we can identify the independent, dependent, and confounding variable(s) and examine whether a person's career os truly connected to their happiness.

Answer

In job satisfaction studies, the two main variables of interest are a person's profession and their level of satisfaction with that job. Researchers compare different careers, which are the "values" of the profession variable, and then measure how satisfaction changes from one career to another. This makes the profession someone has the independent variable and their job satisfaction the dependent variable.

However, many other factors can also influence how satisfied someone feels in their job. Personal values, interests, strengths, and personality all play important rolls. These factors (plus many others that we did not discuss), are called confounding variables because they can influence the results even though they aren't the main focus of the study. In reality, career and life satisfaction often depend more on a person's individual qualities than on the job title itself. Because each person is unique, meaningful work usually aligns with who a person is and what they value.

The experimental design process also focuses on collecting and analyzing data. The researcher must decide how to change the independent variables in a consistent way, how to measure the dependent variables accurately, what types of analysis are best for the data, and how those analyses will test the hypothesis. Remember the definition of statistics provided earlier. Being comfortable with statistics helps throughout this process and makes sure that our conclusions are meaningful, even when they are not the results we hoped for.

Once the experimental design is complete, the researcher will conduct the experiment, summarize and analyze the data, and decide whether to support the hypothesis or not. If the original hypothesis turns out to be false, a new hypothesis could be created using the new information. However, if the data supports the original hypothesis, our confidence in it grows stronger. The scientific method also encourages researchers to share their experimental designs and conclusions. We can quickly gain confidence when a hypothesis is proven wrong, but confidence in a hypothesis being true comes only after many experiments produce the same results.

Whether we are using the scientific method on purpose or simply trying to make good decisions, we often go through the steps of observing, making general ideas, testing them, and updating our thinking. This process involves collecting and analyzing data to reach conclusions, which is exactly what statistics helps us do. That's why it's important to take the study of statistics seriously and use it in everyday life. Understanding statistics helps us make sense of the world and judge the claims that others make.

Because of this, it's important to understand the basic steps of research that uses statistics, whether we use them casually in everyday life or formally in important studies. The process of statistic-based research can be explained in four steps:

1. Establish a research question you want to explore.
2. Decide who or what to study and which variables are needed, then collect the data in an appropriate way.
3. Summarize the collected data using appropriate statistical methods. Use inferential methods when needed.
4. Use the summarized data to make careful, reasonable conclusions. Then think about whether the results are meaningful in real life, not just statistically.

Although we will focus mainly on steps \(3\) and \(4\) of this process in this course, the first two steps are just as important. Creating a strong research question and deciding how to collect the right data can be harder than analyzing the data itself. As both creators and consumers of research, we need to understand the entire process so we can recognize both its strengths and its limits.

Statistics are often used to make arguments sound more convincing, especially in advertisements we see every day. But many of the numbers used in these ads are not based on careful research. They can be misleading and may push us into decisions that we might regret. To be smart users of statistics, our first reaction should be to question the numbers we see. We should think carefully about the claims being made, where the numbers came from, and most importantly, how the data was collected.