LECTURE 4

EPSY 640

Texas A&M University

Multistage sampling

• 1-stratify for one variable

• 2-sample based on those strata,

• 3-then stratify again based on the selected strata samples and once again sample

Multistage sampling

• EXAMPLE

• sample states in the U.S. based on their populations

• then within each state sample individuals based on county

• finally contact a sample within the selected counties.

Multistage sampling

• Cluster sampling- if several strata occur together naturally, it will be cheaper to sample them in one geographic location than to travel widely to sample members of each stratum

• define clusters of strata

• then sample from the identified clusters

Cluster sampling

• Example: Texas Grade 3 students

• Define clusters: Amarillo, Austin, Dallas, El Paso, Fort Worth, Houston, Lubbock, McAllen, Midland-Odessa, San Antonio, San Angelo

• Each cluster has all counties around city

Cluster sampling

• Procedure

• 1. Sample cities (say 5)

• Sample counties around selected cities (2 @) = 10 counties + counties with 5 cities = 15 counties

• 2. List all school districts in the 15 counties

• 3. Sample school districts according to size

Cluster sampling

• 3. Sample school districts according to size:– 2 rural districts from each cluster (< 500

students)– 2 small districts from each cluster (501-1000)– 2 medium districts from each cluster (1001-

5000)– 2 large districts from each cluster (5000-10000)– all very large districts in the cluster (>10000)

Systematic Sampling

• use an Accessible Population in some preexisting form rather than enumerate all the cases and then randomly sample

• Example- telephone directory or mailing lists

Sample 770 persons from a telephone directory:

.Determine # of pages in the directory: example, 223.5

.Sample the pages to determine the number of names per page (note: in theory, from Table 4.2 we would need 142 pages to accurately determine this number, but this defeats our purpose in systematic sampling). Seven pages are sampled randomly, with the following count of names, including businesses: 210, 227, 245, 241, 210, 250, 222 AVG = 227

Total # names estimated = 223.5 x 227 = 50735

.Ndesired = 770

.Nper page = 770/223.5 = 3.4451901566since this is a fractional number, but double is close to the integer 7,plan to take 7 names per two pages. The total column inches of names is 90 per page (4 columns of about 23cm each, the last one less), or 180 per two pages.180/7 = 25.71428571429

Thus, we take the name closest to the marks at 25.7cm, 51.4cm, 77.1cm, 102.8cm, 128.5cm, 154.2cm, and 179.9cm. In practice we can set up a transparent page template with marks at the correct locations. This will facilitate selecting the names: Sample for first page:

Table 4.4: Procedure for systematic sampling an ordered population

Figure 4.3: Sample template for Systematic Seletion of Names from a Directory

Convenience sampling

• Self-selection, or volunteer samples, constitute the most common kind of convenience sample.

• Another common situation occurs when researchers must include all persons in a group constituted for other purposes, such as a school classroom, an intact group

Selection threat to causality

• “Backward selection doesn’t work: surveying Nobel laureates to find out what they like does not imply we can produce more by teaching those likes

investigating radio and chemistry

Nobel laureates (or good scientists)

Hierarchical Models

• Levels: comparable units (eg. Students)

• Units: elements for a particular level (eg. classrooms, schools, districts)

• 1st Level: (example, student)

• 2nd Level: (example, classroom or teacher)

• 3rd Level: (example, school)