# The Essential Role of Statistics

Modern psychology couldn't get by without statistics. Some of these simply describe research data and stop there. An example is correlation, which yields a single number that indicates the extent to which two variables are “related.” Another example is the set of often-complex statistical computations that help researchers decide whether the results of their experiments are likely to be “real.”

A variable is literally anything in the environment or about a person that can be modified and have an influence on his or her particular thoughts, reactions, or behaviors. The amount of light or noise in a room is a variable — it differs from one room to the next. Height and weight are variables, as are intelligence, personality characteristics, and a host of observable behaviors, because these differ from one person to the next.

## Correlation

In correlation, the resulting number can range from 0 to +1.00 or 0 to –1.00. Where it falls indicates the strength of the correlation. The sign of the correlation indicates its direction. A correlation of 0 is nonexistent; a correlation of either +1.00 or –1.00 is perfect.

For example, to assess the correlation between height and weight, a researcher would measure the height and weight of each of a group of individuals and then plug the numbers into a mathematical formula. This correlation will usually turn out to be noticeable, perhaps about +.63. The “.63” tells us that it is a relatively strong correlation, and the “+” tells us that height and weight tend to vary in the same direction — taller people tend to weigh more, shorter people less. But the correlation is far from perfect and there are many exceptions.

What the correlations you encounter in this book mean vary somewhat according to the application, but here's a rule of thumb: A correlation between 0 and about +.20 (or 0 and –.20) is weak, one between +.20 and +.60 (or –.20 and –.60) is moderate, and one between +.60 and +1.00 (or –.60 and –1.00) is strong.

As another example, a researcher might assess the extent to which people's blood alcohol content (BAC) is related to their ability to drive. The participants might be asked to drink and then attempt to operate a driving simulator. Their BACs would then be compared with their scores on the simulator, and the researcher might find a correlation of –.68. This is again a relatively strong correlation, but the “–” tells us that BAC and driving ability vary in an opposite direction — the higher the BAC, the lower the driving ability.

## Inferential Statistics

For descriptive statistics such as correlation, the “mean,” or average, and some others that will be considered in context later in the book, the purpose is to describe or summarize aspects of behavior to understand them better. Inferential statistics start with descriptive ones and go further in allowing researchers to draw meaningful conclusions — especially in experiments. These procedures are beyond the scope of this book, but the basic logic is helpful in understanding how psychologists know what they know.

Again recalling Bandura's experiment of observational learning of aggression, consider just the model-punished and model-rewarded groups. It was stated that the former children imitated few behaviors and the latter significantly more. What this really means is that, based on statistical analysis, the difference between the two groups was large enough and consistent enough to be unlikely to have occurred simply by “chance.” That is, it would have been a long shot to obtain the observed difference if what happened to the model wasn't a factor. Thus, Bandura and colleagues discounted the possibility of chance alone and concluded that what the children saw happen to the model was the cause of the difference in their behavior.

This logic may seem puzzling to you, and it isn't important that you grasp it to understand the many experiments that are noted throughout this book. Indeed, it isn't mentioned again. The point of mentioning it at all is to underscore that people are far less predictable than chemical reactions and the like, and therefore have to be studied somewhat differently — usually without formulas.

Psychologists study what people tend to do in a given situation, recognizing that not all people will behave as predicted — just as the children in the model-rewarded group did not all imitate all the behaviors. In a nutshell, the question is simply whether a tendency is strong enough — as assessed by statistics — to warrant a conclusion about cause and effect.