Understanding Psychology (10th Ed)

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Statistics, the branch of mathematics concerned with collecting, organizing, analyz-
ing, and drawing conclusions from numerical data, is a part of all of our lives. For 
instance, we are all familiar with the claims and counterclaims regarding the effects 
of smoking. The U.S. government requires cigarette manufacturers to include a warn-
ing that smoking is dangerous to people’s health on every package of cigarettes and 
in their advertisements; the government’s data show clear statistical links between 
smoking and disease. At the same time, the tobacco industry has long minimized the 
negative effects of smoking.
Statistics is also at the heart of a considerable number of debates in the fi eld of 
psychology. How do we determine the nature and strength of the effects of heredity 
on behavior? What is the relationship between learning and schedules of reinforce-
ment? How do we know if the “double standard” regarding male and female sexual 
practices has shifted over time? These questions and most others of interest to psy-
chologists cannot be answered without using statistics. 
In this set of modules, we consider the basic approaches to statistical measure-
ment. We fi rst discuss approaches to summarizing data that allow us to describe sets 
of observations. Next, we consider techniques for deciding how different one set of 
scores is from another. Finally, we examine approaches to measuring the relationship 
between two sets of scores. 
Suppose as an instructor of college psychology you wanted to evaluate your 
class’s performance on its initial exam. Where might you begin? 
You would probably start by using descriptive statistics, the branch of statistics 
that provides a means of summarizing data and presenting it in a usable and con-
venient form. For instance, you might fi rst simply list the scores the pupils had 
received on the test:
72 78 78 92 69 73 85 49 
86 86 72 59 58 85 89 
80 83 69 78 90 90 96 83 
Viewed this way, the scores are a jumble of numbers of which 
it is diffi cult to make any sense. However, there are several meth-
ods by which you could begin to organize the scores in a more 
meaningful way. For example, you might sort them in order of 
highest score to lowest score, as in Figure 1. By indicating the 
number of people who obtained each score, you would have pro-
duced what is called a frequency distribution, an arrangement of 
scores from a sample that indicates how often a particular score 
is present.
Another way of summarizing the scores is to consider them 
visually. For example, you could construct the histogram, or bar 
graph, shown in Figure 2. In this histogram, the number of people 
obtaining a given score is represented pictorially. The scores are 
ordered along one dimension of the graph and the number of peo-
ple obtaining each score along the other dimension.