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# Statistics Dictionary

## Uses of Stratified Random Sampling

❶If you want to be able to talk about subgroups, this may be the only way to effectively assure you'll be able to. National polling organizations that use random digit dialing in conducting interviewer based polls are very careful to match the number of landline versus cell phones to the population they are trying to survey.

## Some Definitions

Sampling and types of sampling methods commonly used in quantitative research are discussed in the following module. Researchers commonly examine traits or characteristics parameters of populations in their studies. A population is a group of individual units with some commonality.

For example, a researcher may want to study characteristics of female smokers in the United States. This would be the population being analyzed in the study, but it would be impossible to collect information from all female smokers in the U. Therefore, the researcher would select individuals from which to collect the data. This is called sampling.

The group from which the data is drawn is a representative sample of the population the results of the study can be generalized to the population as a whole. The sample will be representative of the population if the researcher uses a random selection procedure to choose participants. The group of units or individuals who have a legitimate chance of being selected are sometimes referred to as the sampling frame.

If a researcher studied developmental milestones of preschool children and target licensed preschools to collect the data, the sampling frame would be all preschool aged children in those preschools. Students in those preschools could then be selected at random through a systematic method to participate in the study. This does, however, lead to a discussion of biases in research.

For example, low-income children may be less likely to be enrolled in preschool and therefore, may be excluded from the study. Extra care has to be taken to control biases when determining sampling techniques. There are two main types of sampling: The difference between the two types is whether or not the sampling selection involves randomization. Randomization occurs when all members of the sampling frame have an equal opportunity of being selected for the study. Following is a discussion of probability and non-probability sampling and the different types of each.

Probability Sampling — Uses randomization and takes steps to ensure all members of a population have a chance of being selected. There are several variations on this type of sampling and following is a list of ways probability sampling may occur:.

Non-probability Sampling — Does not rely on the use of randomization techniques to select members. This is typically done in studies where randomization is not possible in order to obtain a representative sample. There are several major reasons why you might prefer stratified sampling over simple random sampling. First, it assures that you will be able to represent not only the overall population, but also key subgroups of the population, especially small minority groups.

If you want to be able to talk about subgroups, this may be the only way to effectively assure you'll be able to. If the subgroup is extremely small, you can use different sampling fractions f within the different strata to randomly over-sample the small group although you'll then have to weight the within-group estimates using the sampling fraction whenever you want overall population estimates.

When we use the same sampling fraction within strata we are conducting proportionate stratified random sampling. When we use different sampling fractions in the strata, we call this disproportionate stratified random sampling. Second, stratified random sampling will generally have more statistical precision than simple random sampling.

This will only be true if the strata or groups are homogeneous. If they are, we expect that the variability within-groups is lower than the variability for the population as a whole. Stratified sampling capitalizes on that fact. For example, let's say that the population of clients for our agency can be divided into three groups: Caucasian, African-American and Hispanic-American. And, by chance, we could get fewer than that! If we stratify, we can do better.

First, let's determine how many people we want to have in each group. Let's say we still want to take a sample of from the population of clients over the past year. But we think that in order to say anything about subgroups we will need at least 25 cases in each group. Finally, by subtraction we know that there are Caucasian clients.

Because the groups are more homogeneous within-group than across the population as a whole, we can expect greater statistical precision less variance. And, because we stratified, we know we will have enough cases from each group to make meaningful subgroup inferences. Here are the steps you need to follow in order to achieve a systematic random sample:. All of this will be much clearer with an example. To use systematic sampling, the population must be listed in a random order.

Now, select a random integer from 1 to 5. In our example, imagine that you chose 4. You would be sampling units 4, 9, 14, 19, and so on to and you would wind up with 20 units in your sample. For this to work, it is essential that the units in the population are randomly ordered, at least with respect to the characteristics you are measuring.

Why would you ever want to use systematic random sampling? For one thing, it is fairly easy to do. You only have to select a single random number to start things off. It may also be more precise than simple random sampling. Finally, in some situations there is simply no easier way to do random sampling. For instance, I once had to do a study that involved sampling from all the books in a library. Once selected, I would have to go to the shelf, locate the book, and record when it last circulated.

I knew that I had a fairly good sampling frame in the form of the shelf list which is a card catalog where the entries are arranged in the order they occur on the shelf. To do a simple random sample, I could have estimated the total number of books and generated random numbers to draw the sample; but how would I find book 74, easily if that is the number I selected? I couldn't very well count the cards until I came to 74,! Stratifying wouldn't solve that problem either.

For instance, I could have stratified by card catalog drawer and drawn a simple random sample within each drawer. But I'd still be stuck counting cards. Instead, I did a systematic random sample. I estimated the number of books in the entire collection.

Let's imagine it was , Then I selected a random integer between 1 and Let's say I got Next I did a little side study to determine how thick a thousand cards are in the card catalog taking into account the varying ages of the cards.

Let's say that on average I found that two cards that were separated by cards were about. That information gave me everything I needed to draw the sample. I counted to the 57th by hand and recorded the book information. Then, I took a compass. Remember those from your high-school math class?

They're the funny little metal instruments with a sharp pin on one end and a pencil on the other that you used to draw circles in geometry class.

Then I set the compass at. In this way, I approximated selecting the th, th, th, and so on. I was able to accomplish the entire selection procedure in very little time using this systematic random sampling approach. I'd probably still be there counting cards if I'd tried another random sampling method.

Okay, so I have no life. I got compensated nicely, I don't mind saying, for coming up with this scheme. The problem with random sampling methods when we have to sample a population that's disbursed across a wide geographic region is that you will have to cover a lot of ground geographically in order to get to each of the units you sampled. Imagine taking a simple random sample of all the residents of New York State in order to conduct personal interviews.

By the luck of the draw you will wind up with respondents who come from all over the state. Your interviewers are going to have a lot of traveling to do. It is for precisely this problem that cluster or area random sampling was invented. For instance, in the figure we see a map of the counties in New York State.

Let's say that we have to do a survey of town governments that will require us going to the towns personally.

## Main Topics

Cluster sampling (also known as one-stage cluster sampling) is a technique in which clusters of participants that represent the population are identified and included in the sample. Cluster sampling involves identification of cluster of participants representing the population and their inclusion in .

### Privacy FAQs

Sampling Methods. Sampling and types of sampling methods commonly used in quantitative research are discussed in the following module. Learning Objectives: Define sampling and randomization. Explain probability and non-probability sampling and describes the different types of each.