Chapter 3: Probability and Sampling

identify both the (1)population of interest and the (2)sampling technique used: 1. University administrators want to determine the frequency of underage drinking at their school. They randomly select students from the registration records to send an anonymous survey to, with the percentages of men and women in the sample equal to the percentage of men and women at that university.

(1) The population is college students at that particular school. (2) A stratified random sample was used to make sure the proportion of men and women was that of the entire school.

identify both the (1)population of interest and the (2) sampling technique used: 2. A researcher is interested in mimicking behaviors that affect cooperation in a task. Psychology students from the participant pool are recruited to answer questions in the presence of a confederate (a researcher pretending to be a participant) who mimics the participants' body postures during the questioning. Then the participants are asked to work with the confederate to complete a task that requires that they work together. The amount of time taken to complete the task is measured.

(1)The population is adults, but a (2) volunteer sample of psychology students is used.

stratified random sampling

A form of probability sampling; a random sampling technique in which the researcher identifies particular demographic categories of interest and then randomly selects individuals within each category. Example: #1: Registered voters are randomly selected from lists of Democrats and Republicans to equal the proportion of registered Democrats and Republicans in the United States. #2: Suppose you wanted to survey students at your university or college on their use of social media to connect with their friends. If you do not want differences across gender to influence the study results, you could use a stratified random sample to select the same percentage of men and women for your sample as exists in your student population (e.g., 40% men, 60% women). Advantages: Reduces bias due to an identified characteristic of the population by equating proportions in the sample and the population for that characteristic to better represent the population Disadvantages: Similar to simple random sampling- can be difficult to ensure equal probability of being chosen from a large population

Make a frequency distribution graph of your roll outcomes using any of the procedures discussed in Chapter 2. Does the distribution of scores appear to be symmetrical or skewed? Explain your answer.

Answers will vary, but the distribution is more likely to be symmetrical because the middle scores are most common and the low and high scores should be equally but less common.

Roll the dice 20 times and record the total score on each roll. Was the most common outcome your most frequent outcome? Why do you think this result occurred?

Answers will vary, but the most common scores should be near the middle of the range (i.e., 5 to 7).

3.5 Imagine you are designing a study to test whether people with more money are happier than people with less money. Identify the population of interest for your study and describe how you would select a sample from this population.

Answers will vary. I would probably narrow the scope to adults in the United States. I would then set salary requirements for each group ("people with more money" and "people with less money"). Either through census data or a survey, I would create equal-sized pools of people to poll. I would use a cluster sample to make sure there are the same amount of people in each group.

cluster sampling

Clusters of individuals are identified and then a subset of clusters is randomly chosen to sample from. Example: Doctors who work at hospitals are chosen for a sample by identifying all hospital sin different areas of the United States and then randomly choosing 10 hospitals in each area of the United Sates to sample from. Advantages: Makes it easier to choose members randomly from smaller clusters to better represent the population Disadvantages: Can ignore segments of the population that are not in the clusters chosen for the sample.

convenince sampling

Members of population are chosen based on convenience and on who volunteers Example: Sample is chosen from students who volunteer to complete an extra credit assignment in their psychology course Advantages: Easier to obtain than probability samples Disadvantages: May not represent the population properly due to selection bias because random sampling was not used. Convenience samples are much easier to obtain than probability samples but can sacrifice some internal validity of the study due to an increase in sampling error. The more biased the sample (i.e., different from the overall population), the more sampling error there is. The more sampling error there is, the harder it is for a researcher to test their hypothesis.

How many different outcomes are there for a roll of a pair of dice? If you add together the values on each die, what is the most common value outcome from a roll of the two dice? What is the probability of obtaining the most common value on a roll?

Thirty-six outcomes. Value of 7. Probability: 1/6.

True/False: making sure that the sample is chosen so that the population is represented well in the sample (e.g., has similar demographics) can be difficult with large samples. Thus, researchers often attempt to balance the desire to reduce sampling error and select a representative sample with the practical limits of selecting individuals from very large populations.

True

probability sample

a sample chosen such that individuals are chosen with a specific probability

simple random sample

sample chosen randomly from the population such that all individuals have an equal chance of being selected Example: Students are chosen randomly from a list of all students at a university. Advantages: Reduces sampling error by choosing from all members of the population to best represent the population Disadvantages: Difficult to ensure that each member of a large population can be chosen in a sample. Simple random samples use the random selection process to create a representative sample, but this requires that a researcher first identify all the individuals in the population in order to randomly select some of them. This may be a difficult process for some very large populations. Opinion surveys, such as the one on global warming described at the beginning of Chapter 2, typically identify individuals in the population through their phone numbers and select them by randomly dialing a phone number to call the individuals selected. This allows everyone with a phone in the population an equal chance of being selected. However, this process might still provide a sample that is biased in some way with more individuals from a certain geographic area, racial or ethnic group, gender, or income bracket. Thus, there are other types of probability samples that can be used to attempt to reduce these sources of bias in the sample.

Convenience/Purposive Sample

sample chosen such that the probability of an individual being chosen cannot be determined convenience samples are much easier to select and are often used in cases where researchers want to learn about a very large population (e.g., all adults, all children of ages 5 and 6, etc.). This means that sampling error will typically be smaller with probability samples. However, for some behaviors of interest that may not differ much across individuals (e.g., some types of biological or cognitive behaviors), sampling error can be small with either type of sample, meaning that convenience samples can be used without too much concern that the sample is not representative.

quota sample

sample: a sample chosen from the population such that available individuals are chosen with equivalent proportions of individuals for a specific characteristic in the population and sample similar to stratified random sample, but without the random selection

distribution of sample means

the distribution of all possible sample means for all possible samples of a particular size from a population