1.1: How to Start with Statistics

Let’s start with you. By you, we mean how you observe “it.”

We know something is different by observing it. This “it” is another way of saying “construct.” A construct is something that we experience as varying. Obvious examples are height, weight, and age. The reason I say those are “obvious” examples is because we can readily observe the physical indicators of the variations in height, weight, and age. Somewhat obvious examples are intelligence and personality. The reason I saw those are “somewhat obvious” is because while we readily experience people as more or less intelligent that others, or people having different personalities, there is no agreed upon method of definitively stating how people have different intelligence levels or personality traits. These experiences are called “constructs” because we constructed them. We observe one person as being able to solve a problem better than another person, and we call that experience as "intelligence.” We observe one person as having more friends than another person and we call that experience as “extroversion personality.” The term “it” throughout this textbook is shorthand for “construct.”

It is not always easy to describe how “it,” or the construct varies. We first must define what “it” is. When we define something, we do have to agree on what it is that we are observing. Height, weight, and speed seem obvious enough to define. That something has to seem higher than others, heavier than others, or faster than others. Other constructs are not that easy to define, such as depression, attachment, racism, post-traumatic stress disorder, post-traumatic growth. This discussion is beyond this chapter, but suffice to say, we can observe “it” by observing how it varies.

We know something is different based on comparison. All differences, all variations, are based on comparison. In fact, statistics are based on comparison. You are always comparing something to something else. We see that some people are taller than others, some things are heavier than others, and some cars are faster than others. Statistics are based on comparing one person to another person, or one thing to another. Fast forward – when we say something is “statistically significant,” we always need to think, “significant, compared to what?”

This process becomes interesting when there are many ways to describe how “it” varies. Let us say we want to quantify the number of beers you drank over a weekend. The number of beers you drank becomes an interesting observation because there are so many ways to define this variation. How many glasses are the same size? Is drinking cheap beer (insert your beer brand here) the same as drinking craft beer (insert your beer brand here)? Is the alcohol content the same across each beer? Whatever we observe, we notice that it varies, and we use statistics as a framework to organize how we observe this variation.