1.2 – What Are Statistics?

So, what exactly are statistics?

For our purposes, statistics refers to the calculations and strategies that help researchers answer their research questions.  For example, let’s say we want to know if it is warmer today than normal. To answer this question, we would simply take a sufficiently large set of high temperatures on this date from the past and calculate the average high temperature. Then we would compare that average with today’s high temperature. For example, if it reached 94 degrees today, and the average temperature is 88 degrees, you could conclude that today is warmer than average. That average temperature of 88 you calculated is a statistic.

In many cases, though, research questions can be much more complicated.  For example, do extraverts perform better in a group situation than introverts?  To answer a question like this, we would need to complete a more formal research process, probably involving an experimental research design.  Since it would be impossible to test every extravert and every introvert because there are millions or billions of them, we would need to do our research on a much smaller group and see what happens with them.

In this second, more complex type of research situation where we use a smaller group of people to answer a bigger question, we can again use statistics. Suppose, for example, the extraverts in our study had a higher average score on a test when they performed in a group, while the introverts had a higher average score when they performed by themselves.  These averages are again statistics, and they seem to indicate a difference between introverts and extraverts.

However, that conclusion would only apply to the people in our study. It may be that the group of extraverts in our study happen to be people who are used to performing in groups due to some job or experience.  On the other hand, our research question was about all extraverts and introverts.  While our study gives us some support for the possibility of a difference between the two groups, it is impossible to say that there absolutely is a difference between all extraverts and introverts.

Descriptive vs. Inferential Statistics

These two different types of research questions help to illustrate the two types of statistics we will examine in this book: descriptive statistics and inferential statistics.

Descriptive statistics refer to statistics that are used to describe a group of scores.  Both of the previous examples included descriptive statistics.  The average high temperature takes a group of scores (e.g., the high-temperature measurements for a particular day for the last one hundred years) and then describes all of those scores with one score, the average high temperature. Likewise, the group of extraverts’ and introverts’ scores on the test were taken and reduced to an average score.  Descriptive statistics will be the focus of Chapters 2 and 3.

Inferential statistics refer to statistics that are used to make inferences about the results of a research study.  The word “infer” means to draw conclusions from the evidence. For example, the phrase, “where there is smoke; there is fire,” is an example of inference. In many inferences, we are drawing a “big” conclusion from a “small” amount of data. For example, in our study comparing extraverts and introverts, we found that the extraverts performed better in groups than the introverts. But we also discussed that this result might have been due to the specific set of people we used in our study, and may not necessarily represent any true differences between extraverts and introverts. In fact, the word “infer” also means “to make a guess.”

To explore this bigger question of trying to make guesses about the “truth” from our research data, statisticians have created inferential statistics to help them gauge how well our specific results are likely to be due to a true effect. To do this, inferential statistics use different theories involving probability and sampling in order to infer the meaning of the results. As you might guess, this is a bit of a more complicated process and is the focus of the material after Chapter 3.

It is worth noting that when most researchers refer to “statistics,” they are mainly referring to inferential statistics and their procedures.