Given a thimbleful of facts, we rush to make generalizations as large as a tub.
—Gordon Allport (1954, p. 8)
A general critical thinking skill related to sampling from populations is con-sidering the size of the sample, or the number of participants in the study.
(FIGURE 2.11). As consumers of research, we need to understand which stud-ies provide strong evidence and which are junk science, and the number of participants in a sample is one critical difference between the two types of study.The importance of sample size can be difficult to understand when you think about it one way but easy to understand when you think about it a dif-ferent way. First, read the following information and answer the questions:
A certain town is served by two hospitals. In the larger hospital, about 45 babies are born each day, and in the smaller hospital, about 15 babies are born each day. As you know, about 50% of all babies are boys. The exact percentage of baby boys, however, varies from day to day. Sometimes it may be higher than 50% and sometimes lower.
1. For a period of 1 year, each hospital recorded the days on which more than 60% of the babies born were boys. Which hospital do you think recorded more such days?
a. the larger hospital b. the smaller hospital
c. they would each record approximately the same number of days on which more than 60% of the babies born were boys.
2. Which hospital do you think is more likely to find on any one day that more than 60% of babies born were boys.
a. the larger hospital b. the smaller hospital
c. the probability of having more than 60% of babies born being boys on any day is the same for both hospitals
(Sedlmeier & Gigerenzer, 1997, p. 34; original problem posed by Kahneman & Tversky, 1972)
Look carefully at both questions and the way you answered them. The first question is about the number of days you would expect 60 percent or more of the births to be boys, and the second is about what you would expect on one specific day. If you answered like most people, you selected option C for the first question and B for the second question. Both ques-tions are about sample sizes, however, and the answer to both quesques-tions is B.
The smaller hospital has fewer births and therefore a smaller sample size, and small samples are more variable, as you will see below. It may help to think about a similar situation that you are more familiar with: tossing a coin.
Suppose you want to know if a coin is fair—that is, heads will appear as often on the “up” side as tails when it is flipped. To demonstrate that the coin is fair, you would toss it a few times to show that heads and tails each come up about half the time. Suppose you flip it 4 times. Might you get 3 heads and 1 tail in 4 flips of a fair coin, when there is an equal chance of getting a head or tail on each flip? It is not hard to see how heads and tails might not appear equally if you flip a coin a few times. Now suppose you flip the same coin 100 times.You probably would not get exactly 50 heads and 50 tails, but just by chance you would get close to 50 for each. With only 4 flips, it is quite possible that 75 percent of the flips could be all heads or all tails just by chance.With 100 flips, that same 75 percent is very unlikely.
Can you see how this is the same problem as in the hospital scenario? The smaller hospital is more likely to have some days when the percentage of boys (or girls) is higher than 60 percent, even when the true number of girl and boy babies in the population is approximately equal. It is easier to understand this principle when thinking about any single day (question 2) than about the
FIGURE 2.11 Think Critically:Large Samples Are More Accurate Than Small Samples If you wanted to compare how many women like going to the beach and how many men do, but you only considered this small inset sample of seven people, you might think that only women go to the beach! But looking at the big picture, you can see that is clearly not the case.
number of days (question 1), although the reasoning is the same.Variability is discussed in more detail later in this chapter, but for now, you need to under-stand that small samples are more variable than large samples.
The law of large numbers states that you get more accurate estimates of a population from a large sample than from a small one.To apply this law in an everyday context, suppose you are deciding which of two universi-ties to attend.To help make this decision, you spend one day at each uni-versity and attend one class at each.You like the professor you meet at one of the universities much better than the professor you meet at the other.
Should this small sample of classes and professors influence your decision about which university to attend? Can you see how results from such a small sample could be very misleading? In planning a research project, as in deciding how you feel about a place, you must consider the size of the sample you are generalizing from.
➤
S U M M I N G U PWhat Are the Types of Studies in Psychological Research?
There are three main types of studies in psychological research: descriptive, corre-lational, and experimental. In descriptive and correlational designs, researchers exam-ine behaviour as it naturally occurs. These types of studies are useful for describing and predicting behaviour, but they do not allow researchers to assess causality.
Correlational designs have limitations, including directionality problems (knowing whether variable A caused variable B or the reverse) and the third variable prob-lem (the possibility that a third variable is responsible for variables A and B). In an experiment, a researcher manipulates the independent variable to study how it affects the dependent variable. An experiment allows a researcher to establish a causal relationship between the independent and dependent variables and to avoid the direc-tionality problem when trying to understand how one variable might affect another. An experiment gives the researcher the greatest control, so that the only thing that changes is the independent variable. If the goal is to conclude that changes in one variable caused changes in another variable, the researcher must assign participants at random to different groups to make the groups as equal as possible (on aver-age) on all variables except the one being studied. The researcher wants to know about a population, but because it is usually impossible for everyone in the popu-lation to be a research participant, the researcher uses a representative sample of the population and then generalizes the findings to the population. Random sam-pling, in which everyone in the population has an equal chance of being a research participant, is the best way to sample, but since this is usually not possible, most researchers use a convenience sample. Among the most important factors in whether the results from a particular sample can be generalized back to the population is sample size. In general, large samples provide more accurate results than small ones.
M E A S U R I N G U P
1. The main reason researchers randomly assign participants to different groups in an experiment is that ________________________________.
a. it is easier to assign participants to different conditions than it is to find people who naturally fit into different conditions
b. random assignment controls for any intuitions the participants may have at the start of the experiment
➤
➤
L E A R N I N G O B J E C T I V E S Provide examples of data collection methods that are appropriate for different research questions.Identify ethical issues and explain their importance.