When participants have an equal chance of being selected into the sample is A?

How would you go about figuring out the average salary of your city? Would you go door to door? Would you ask five people and assume that their salaries are a good representation of the whole city? Well, random sampling helps answer these questions for you!

• What is random sampling?
• Why is random sampling important?
• How is random sampling used in research?
• What are variables used in random sampling?

Random Sampling in Psychology

Random sampling is used in many psychological experiments that study populations. A population is a group of people that has characteristics that the researcher wants to study. A sample is drawn from the population that you want to study.

A population is defined as a group of people in which a researcher is interested in studying. This can be a group of college students, everyone who lives in a specific area code, or even an entire country!

Say you wanted to study depression in college women. It wouldn't be possible to create a study using every single woman in college. So, we would need to use a sample. You would only need to study a portion of the population you are interested in (say, 1,000 college women) selected at random.

The Importance of Random Sampling

Let's say I want to create a study. My hypothesis is that people at the mall have more money than people in the park. So I create a study design: I will go to the mall and ask 100 people how much money they have, and then I will go to the park and ask 100 people how much money they have. I will then compare the two averages.

I go to the mall and I pick 100 people shopping in a high-end watch store. After I'm done at the mall, I go to the park and pick 100 people who are having picnics. Just by my sampling, this study is already inherently flawed. I chose to pick people shopping in a high-end watch store, so it is likely that these people would have more money. My sample does not accurately reflect the mall's population as a whole.

With this kind of sampling, I can't really answer the question of whether the people in the mall have higher incomes. I didn’t really sample the mall's population. Random sampling helps fix this problem.

When doing a research study, there are different ways you can recruit participants. If your participants are chosen at random, this means that all members of the population had the same chance (or probability) of getting chosen to participate in the study. This type of sampling method is considered to be an unbiased sampling method, which is helpful in research because it helps limit outcomes which don’t truly reflect the population.

A hypothesis is an educated guess created before the initiation of a study.

An example of a hypothesis: we think people treated with medications respond better than those who are not medicated.

Unbiased sampling is the idea that choosing our population should not be affected by selection bias.

An example of sampling bias is reaching out to your friend group to complete a survey then assuming your results apply to all people your age.

Simple random sampling would line everyone up in a mall and choose participants at random. However, this may be costly, because in order to have a robust study you need to make sure your sampling really reflects the whole population. Using stratified sampling, you can group participants by stores.

You could do six groups representing six mall stores: A shoe store, a farmer's market, a soap store, a watch store, a high-end jewelry store, and a budget clothes store. After we characterize and group our population based on the stores, we can then sample participants from each group. This will allow us to more accurately sample the general population without recruiting a large number of participants.

Random Sampling in Research

There are different types of random sampling: Simple random sampling, systematic sampling, stratified sampling, and clustered sampling.

Random sampling is the process of selecting participants for a research study randomly. The goal of random sampling is to eliminate selection bias.

Simple Random Sampling

Simple random sampling is a method where each item or person in a population has an equal probability of being selected.

An example of simple random sampling is a researcher assigning 1000 people a unique number and then using a random number generator to select 100 people. In this example, all 1000 participants have an equal chance of being selected.

Systematic Sampling

Systematic sampling is a method that uses intervals in the selection process. If you have a population of 100 people who are in alphabetical order, then you may select every 10th person.

One example of a systematic random sample is a group of 10 participants that were selected from a phone book, such that every 100th person was selected.

Stratified Sampling

In stratified sampling the population is split up into groups based on distinct characteristics. Subsequently, the researcher randomly selects participants in each group.

Stratified sampling is a method of random sampling that involves splitting up a population into separate groups based on common characteristics, then picking participants from each of the separate groups.

One example of stratified random sampling is a researcher taking 1000 college students and splitting them up into groups based on their major. The researcher then selects 10 participants from each major, allowing for a more accurate sample of the population.

Clustered Sampling

Clustered random sampling uses clusters. It is similar to stratified random sampling; however, the population is split into many subgroups. These subgroups are known as clusters.

An example of clustered sampling is a researcher breaking down a population of customers into the time of day in which they came to a store, then selecting all the people who shopped during certain times.

Understanding the difference between stratified sampling and clustered sampling may be difficult. The way you can tell these two types of random sampling apart is that the methods are different after the population is split into groups. in stratified sampling, the researcher will select people at random from the group. In clustered sampling, the researcher will select the whole cluster for the sample!

Usually in random sampling, if someone is selected they do not enter the population again. People cannot be selected twice. There are certain studies in which a participant can be selected twice; this is called replacement. If there are 100 people and only 1 is chosen at random, the next population will be 99 and not 100, as the chosen person is not replaced. This ensures that one person will not be chosen twice and potentially skew the data.

Let’s look at the mall example again. Let’s say we use random sampling and choose 1 person out of 200. That 1 person happens to be a billionaire. He may be an outlier in our population, but random sampling ensures that he will only be counted once in our study. If we decided to replace him with a different participant, it is possible he would be selected again, further skewing our data.

An outlier is a data point that is very different (either much higher or much lower) from the other data points.

Sample size also matters. Choosing a small sample from a large population with or without replacement isn’t likely to change outcomes. Either way, it's unlikely that the same individual will be selected multiple times if the sampling is truly random.

Stratified Random Sampling

Stratified random sampling is a specific type of random sampling. In stratified random sampling, the population is first separated (or stratified) into different groups. These groups are called strata, and they are usually created based on shared characteristics.

Strata is the term for the smaller groups created from the larger population by the researcher.

Think of a small group of 100 people, put together from a population because they share the same hair color.

Stratified random sampling is helpful in heterogeneous populations because it helps ensure that all characteristics of the population are represented. This type of sampling can't be used with populations that don’t have distinguishing characteristics.

Heterogenous populations are populations with many different groups present within the population.

The population of New York City is an example of a heterogeneous population in regard to ethnicity.

Compared to simple random sampling, stratified random sampling is usually less strong. This is especially true when a population cannot be properly categorized. Since stratified random sampling relies on the characteristics of the groups, it allows a smaller sample of the population to accurately reflect the larger population. In these cases, stratified sampling allows for more precision than simple random sampling.

Variables in Random Sampling

There are a number of things to be considered when we do a random sample. What are the variable factors?

Discrete Random Variables

Discrete random variables, also known as categorical variables, are random variables that are not continuous. They all have a small number of values with no decimals.

An example of a discrete random variable may be the number of kids a person can have. This number can only be 1, 2, 3, 4. It cannot be 2.3 or 3.7.

Continuous Random Variable

Continuous random variables are variables that can be any real number. They can be a number with infinite numbers after the decimal point.

An example of a continuous random variable is the temperature outside on a given day. Even if two days report a temperature of 89 degrees, the exact temperature can be anywhere from 89.0 to 89.1, with infinite values in between.

Some important definitions to keep in mind:

• The independent variable is the variable that the researcher manipulates.
• The dependent variable is the measured behavior that determines the effect of the independent variable.
• A confounding variable is a variable that can influence a cause-and-effect relationship.
• The control group is the group that the researcher does not include in the treatment or experiment. The control group provides a measure of what to expect if no "treatment" (or other intervention) had taken place.

Mixed Random Variables

Mixed random variables are a mix of discrete and continuous variables. Essentially, a mixed random variable will have a discrete part and a continuous part.

Random Sampling Variability

Random sampling variability refers to the idea that different samples may have different means. If you want to reduce the variability, using a large sample group is helpful.

Variability in random sampling is the idea that different samples, even though chosen randomly, may have different statistical outcomes.

Let's say we want to study a population of 1,000,000. We sample 100 people out of the population and weigh each person. When we average their weights, the average is 150 lbs. Another research study with a similar method used the same criteria as us, and they got a mean of 155 lbs. This is random sampling variability.

After creating a sample and performing a study based on that sample, we can then draw inferences on the population as a whole, without actually testing the whole population.

Drawing an inference means that we are able to make an assumption about the whole population by just studying a small portion of it.

Suppose we selected 1000 college women at random, and found that those who participated in clubs and extracurricular activities were less likely to show symptoms of depression. We could then say, despite the fact that we only looked at 1000 college women out of the entire population of college women right now (measuring in the millions), that college women who were involved in clubs and extracurricular activities were less likely to have symptoms of depression.

When participants have an equal chance of being selected that is?

What is an equal chance to be included in the sample?

In which research method would a participant have an equal chance of being selected?

What is the process of selecting sample with equal chances from a population?