Probability Sampling
Probability Sampling
A probability sampling method is any method of sampling that utilizes some form of random selection. In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen.
The sampling fraction
Sample/Population (n/N)
Systematic random sampling
It is slightly more accurate than simple random sampling. Arrangement of elements in the list can result in a biased sample.
Cluster (Area) random sampling
Divide population into clusters Randomly sample clusters Measure all units within sampled clusters Administratively useful, especially when you have a wide geographic area to cover Example: Randomly sample from city blocks and measure all homes in selected blocks
Types of probability sampling methods
Simple random sampling Stratified random sampling Systematic random sampling Cluster (area) random sampling Multistage sampling
Multi-stage sampling
Simple, stratified, systematic and cluster -- are the simplest random sampling strategies. In most real applied social research, we would use sampling methods that are considerably more complex than these simple variations. The most important principle here is that we can combine the simple methods described earlier in a variety of useful ways that help us address our sampling needs in the most efficient and effective manner possible. When we combine sampling methods, we call this multi-stage sampling. It involves repetition of two basic steps: listing and sampling It is highly efficient and less accurate.
Disproportionate stratified random sampling
When we use different sampling fractions in the strata, we call this disproportionate stratified random sampling. Unequal sampling fraction in each stratum.
Proportionate stratified random sampling
When we use the same sampling fraction within strata we are conducting proportionate stratified random sampling. Sampling fraction is equal for each stratum.
Stratified random sampling
It is sometimes called proportional or quota random sampling. It involves dividing your population into homogeneous subgroups and then taking a simple random sample in each subgroup. 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. (Precision will incrase if strata are homogeneous.) 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. It results in a greater degree of representativeness by decreasing the probable sampling error. It insures representation of each strata, oversample smaller population groups.
Stratification
Knowledge of the process allows you to group things so that you get the most information from your data collection for the effort expended. This is called stratification. Examples of possible strata are: Day of Week Sector Zip code Sex Age Weight African-American Hispanic-American
Steps to achieve systematic random sampling
Number units in population from 1 to N Decide on the n that you want or need N/n=k the interval size Randomly select a number from 1 to k Take every kth unit Example: We have a population that only has N=100 people in it and that you want to take a sample of n=20. To use systematic sampling, the population must be listed in a random order. The sampling fraction would be f = 20/100 = 20%. in this case, the interval size, k, is equal to N/n = 100/20 = 5. Now, select a random integer from 1 to 5. In our example, imagine that you chose 4. Now, to select the sample, start with the 4th unit in the list and take every k-th unit (every 5th, because k=5). You would be sampling units 4, 9, 14, 19, and so on to 100 and you would wind up with 20 units in your sample.
Simple random sampling
Objective: Select n units out of N such that every NCn has an equal chance Procedure: Use table of random numbers, computer random number generator or mechanical device. It is feasible only with the simplest sampling frame It can sample with or without replacement It is not the most accurate method available. Because You may, just because of the luck of the draw, not get good representation of subgroups in a population. To deal with these issues, we have to turn to other sampling methods.
Interval size
Population/Sample (N/n)
