Stats 1.4 sampling

City block example page 33

...

Example: a mall parking lot, each subsection of the lot could be a cluster

...

Summary illustrated on page 36!

...

Steps in systematic sampling

1. If possible, approximate the population size,N. 2. Determine the sample size desired, n. 3. Compute N/n and round down to the nearest integer. This value is k. 4. Randomly select a number between 1 and k. Call this number p. 5. The sample will consist of the following individuals: p, p+k, p+2k, ...., p + (n-1)k

Census bureau for the current population survey requires 5 stages of sampling

1. Stratified sample 2. Cluster sample 3. Stratified sample 4. Cluster sample 5. Systematic sample This survey obtains demographic estimates of the United States in no census years.

K selection example to represent the population adequately

20,325/100 = 203.25 so k = 203. Then we randomly select a number between 1 and 203 and select every 203rd individual thereafter. So if we select 90, we'd survey 90, 293rd, 496th, .... , 20,187th individuals.

Cluster sample definition

A cluster sample is obtained by selecting all individuals within a randomly selected collection or group of individuals.

Convenience sampling definition

A sample in which individuals are easily obtained and not based on randomness. Most popular being ones in which individuals in the sample are self-selected (voluntary response samples).

Cluster sampling troubleshoot

If the clusters have homogeneous individuals it's better to have more clusters with fewer individuals in each cluster If the cluster is heterogeneous then the cluster likely resembles the heterogeneity of the population. So each cluster is a scaled-down representation of the overall population. Thus, when a cluster is heterogeneous, fewer clusters with more individuals in each cluster are appropriate.

Different between stratified and cluster samples

In a stratified sample, we divide the population into two or more homogeneous groups. Then we obtain a simple random sample from each group. In a cluster sample, we divide the population into groups, obtain a simple random sample of some of the groups, and survey all individuals in the selected groups. Emphasis on all.

Cost is a general sense

Includes monetary outlays, time, and other resources.

Self-selected def.

Individuals themselves decide to participate in a survey These are also called voluntary responses Example is a phone-in survey Both samples are poor design because the individuals who decide to be in the sample usually have strong opinions about the topic.

Stratified sampling provides more ___ about the population for __ __ cost than simple random sampling.

Information, less cost

Systemic sampling is easier to employ so there's less likelihood of __ ___ ___

Interviewer error occurring

Systematic sample definition

Is obtained by selecting every kth individual from the population. The first individual selected corresponds to a random number between 1 and k.

Stratified sample definition

Is obtained by separating the population into nonoverlapping groups called strata and then obtaining a simple random sample from each stratum. The individuals from each stratum should be homogeneous in some way.

Multistage sampling

Most large-scale surveys obtain samples using a combination of the techniques presented.

Systematic sampling is a useful technique when you can't ______

Obtain a list of the individuals in the population

Example if k = 8

Randomly select a number between 1 and 8, such as 5. We survey the 5th, 5 + 8 = 13th, 13 +8 = 21st, 21 + 8 = 29th and so on, individuals until we reach the desired sample size.

Example: school administrator wants to learn the characteristics of students enrolled in online classes ...

Rather than obtaining a simple random sample based on the frame of all students enrolled in online classes, the administrator could treat each online class as a cluster and then obtain a simple random sample of these clusters. The admin would then survey all the students in the selected clusters.

Sample size considerations

Researchers need to know how many individuals they must survey to draw conclusions about the population within some predetermined margin of error. They must find a balance between the reliability of the results and the cost of obtaining these results. The more time and money researchers have, the more confidence they will place on the conclusions, and the more accurate the results of the statistical inference.

To obtain the stratified sample conduct a __ __ __ within each group

Simple random sample Use a different seed for each stratum

To determine the value of k when the size of the population, N, is known

Suppose N = 20,325 and we desire a sample of size n = 100. To guarantee individuals are selected evenly from both the beginning and end of the population (such as early and late grocery shoppers) we compute N/n and round down to the nearest integer.

A sampling technique that doesn't require a frame is __ __

Systematic sampling

Advantage of stratified sampling over random sampling

The researcher can determine the characteristics within each stratum, this allows an analysis to be performed on each stratum to see if any significant differences among them exist.

Problems with selecting k

The value of k must be small enough to achieve our desired sample size, and large enough to obtain a sample that is representative of the population. An estimate of the size of the population would help determine an appropriate value for k.

Goal of sampling

To obtain as much information as possible about the population at the least cost