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a list of all the registered voters in a city (the population), randomly select 100 of them from the list (the sample), and ask those 100 whom they intended to vote for. Unfortunately, random sampling is difficult or impossible in most psychological research because the populations are less clearly defined than the registered voters in a city. How could a researcher give all American teenagers or all children with autism an equal chance of being selected for a sample? The most common alternative to random sampling is convenience sampling, in which the sample consists of individuals who happen to be nearby and willing to participate (such as introductory psychology students). The obvious problem with convenience sampling is that the sample might not be representative of the population. Once the sample is selected, researchers need to measure the variables they are interested in. This requires an operational definition—a definition of the variable in terms of precisely how it is to be measured. Most variables can be operationally defined in many different ways. For example, depression can be operationally defined as people’s scores on a paper-and-pencil depression scale, the number of depressive symptoms they are experiencing, or whether they have been diagnosed with major depressive disorder. When a variable has been measured for a particular individual, the result is called a score, and a set of scores is called data. Note that datais plural—the singular datumis rarely used—so it is grammatically correct to say, “Those are interesting data” (and incorrect to say, “That is interesting data”). 2.1.3 Statistical Relationships Between Variables Available under Creative Commons-NonCommercial-ShareAlike 4.0 International License (http:// creativecommons.org/licenses/by-nc-sa/4.0/). Some research questions in psychology are about one variable. How accurate are children’s memories for being touched? How talkative are American college students? How common is it for people to be diagnosed with major depressive disorder? Answering such questions requires operationally defining the variable, measuring it for a sample, analyzing the results, and drawing conclusions about the population. Chapter 2 19 For a quantitative variable, this would typically involve computing the mean and standard deviation of the scores. For a categorical variable, it would typically involve computing the percentage of scores at each level of the variable. However, research questions in psychology are more likely to be about statistical relationships between variables. There is a statistical relationship between two variables when the average score on one differs systematically across the levels of the other. Studying statistical relationships is important because instead of telling us about behaviors and psychological characteristics in isolation, it tells us about the causes, consequences, development, and organization of those behaviors and characteristics. There are two basic forms of statistical relationship: differences between groups and correlations between quantitative variables. Although both are consistent with the general definition of a statistical relationship—the average score on one variable differs across levels of the other—they are usually described and analyzed somewhat differently. For this reason it is important to distinguish them clearly. 2.1.3.1 Differences Between Groups Available under Creative Commons-NonCommercial-ShareAlike 4.0 International License (http:// creativecommons.org/licenses/by-nc-sa/4.0/). One basic form of statistical relationship is a difference between the mean scores of two groups on some variable of interest. A wide variety of research questions in psychology take this form. Are women more talkative than men? Do children using human figure drawings recall more touch information than children not using human figure drawings? Do people talking on a cell phone have poorer driving abilities than people not talking on a cell phone? Do people receiving Psychotherapy A tend to have fewer depressive symptoms than people receiving Psychotherapy B? Later we will also see that such relationships can involve more than two groups and
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