In Chapter 6, we discuss descriptive methods. At their most basic, descriptive methods may involve measuring a single variable. Thus, the key is to accurately measure your variable(s) using a good sample. Some methods, such as giving a psychological test to a large random sample of participants, make it relatively easy to accurately measure your variable(s) in a good sample. Archival methods may be good for getting large samples and for avoiding subject bias (participants faking their responses), but may use measures that don't quite fit the construct you want to measure. Observation may provide data about what most individuals actually do-- if observers can be objective and if you can observe a large enough sample. The tradeoffs among these methods are summarized in Table 6-3 (p. 157).
Regardless of the method used, researchers usually want to do more than measure a single variable. They want to see the relationships between variables. Because they often use correlation coefficients to see how variables are related, descriptive methods are also called correlational methods. Note that correlational methods allow you to find out that there is a relationship, but they don't tell you why the relationship exists. That is, they don't tell you which variable is influencing which. Figure 6-1 (page 144) shows you why correlational methods don't allow you to make causal conclusions. (If you want to know more about why it is so difficult to determine what causes what, see Chapter 8).
Not surprisingly, the results of correlational studies can often be summarized using correlation coefficients. If both variables are interval, you can use the Pearson r (If they aren't see, table 6-4, p. 162). Positive correlations mean that if a participant scores high on one variable, the participant will tend to score high on the other variable. Negative correlations, on the other hand, mean that if a participant scores high on one variable, the participant will tend to score low on the other variable. (To visualize this, see page 160--or better yet, go to this chapter's main page and download "The Correlator" program).
Some relationships are stronger than others. That is, in some cases, knowing a person's score on one variable (their height as a 21-year-old) is a very good predictor of their score on another variable (their height as a 22-year-old). In other cases, a relationship may be relatively weak (SAT scores and college grade-point average) and so that knowing one variable doesn't predict the other very well. As you would expect, you can tell from the correlation coefficient whether the relationship is strong or weak. However, you can't tell by looking at the sign of the correlation coefficient! The sign of the correlation coefficient has nothing to do with its strength. A -.6 correlation is just as strong as a +.6; a -.7 correlation is stronger than a +.6. Instead, you look at the strength of the relationship by seeing how far the correlation coefficient is from zero--the farther, the stronger. Or, you could square the correlation coefficient to get the coefficient of determination. The bigger the coefficient of determination, the stronger the relationship. Thus, you could say that a -.5 correlation was stronger than a +.4 correlation because .25 (-.5 X -.5) is bigger than .16 (.4 X.4).
If you find a correlation between two variables in your random sample, does that mean the two variables are really related? No, because it could just be due to random error. For example, if you had taken a different sample, you might have found no relationship or even the opposite relationship.
To find out whether the correlation you found in your sample means that there is a relationship in the population, you need to do a significance test. You can do a t test (if you divide your participants into two groups), an F test, or a test to see if the correlation is statistically different from zero. If you only have two groups (men and women), then all three tests will give you essentially the same results (see for yourself by looking at Box 6-1, p. 170). However, using thet test orF test can sometimes lead to two problems.
First, some people think that since they saw t tests being used to show that a treatment caused an effect, that since a t -test is being used, they can make cause-effect conclusions. What they are overlooking is that they were able to make causal statements because they collected their data using an experiment, not because of the statistical test they used.
Second, what do you do if you don't have two groups? For example, suppose you have a bunch of individuals who all scored differently on an introversion-extroversion test. You could arbitrarily categorize half of them as introverts and the other half as extroverts, and then do a t test. Note, however, that you have (as far as the t test analysis is concerned) thrown away each participant's individual score and just lumped him or her into a group of participants who have somewhat similar scores. Because you have essentially thrown away so much information about each individual's score, you lose power. By using the t test rather than testing to see if the correlation was significantly different from zero, you may fail to find a significant relationship.
Unfortunately, improper analyses are not the only reason you may obtain null results. You may fail because you didn't have enough participants, because you had an insensitive measure, because your test was looking for a linear relationship but the actual relationship was not linear, and because of restriction of range (see p. 175 for an explanation of restriction of range).