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# Types of Probability Sampling Techniques

Simple Random, Systematic, Stratified, and Cluster Sampling
by

## Gerald John Velasquez

on 20 September 2012

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#### Transcript of Types of Probability Sampling Techniques

Objective: To select n units out of N such that each NCn has an equal chance of being selected.

Procedure: Use a table of random numbers, a computer random number generator, or a mechanical device to select the sample. 2 3 Assume that we are doing some research with a small service agency that wishes to assess client's views of quality of service over the past year - let's say you want to select 100 clients to survey and that there were 1000 clients over the past 12 months - Then, the sampling fraction is f = n/N = 100/1000 = .10 or 10% - Draw the sample by: a. print off the list of 1000 clients, tear into separate strips, put strips in a hat, mix and pull out the first 100 or b. ball machine used in lotteries or the best and less tedious way, using the c. EXCEL spreadsheet, in the column right next to it paste the function =RAND() which is EXCEL's way of putting a random number between 0 and 1 in the cells. This rearranges the list in random order from the lowest to the highest random number. Then take the first hundred names 4 Here are the steps you need to follow in order to achieve a systematic random sample:

- number the units in the population from 1 to N
- decide on the n (sample size) that you want or need
- k = N/n = the interval size
- randomly select an integer between 1 to k
then take every kth unit 2 3 EX. We have a population that only has N=100 people in it and that you want to take a sample of n=20.
- the population must be listed in a random order
- sampling fraction would be f = 20/100 = 20%
- the interval size, k, is equal to N/n = 100/20 = 5
- select a random integer from 1 to 5
- If you chose 4
- 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
- then, you would wind up with 20 units in your sample 4 Again, we took every third person in the sampling frame Where the population of distinct categories, the frame can be organized by these categories into separate "strata." Each stratum is then sampled as an independent sub-population, out of which individual elements can be randomly selected There are several potential benefits to stratified sampling.
First, dividing the population into strata enable researchers to draw inferences about specific subgroups that may be lost in a more generalized random sample.
Second, utilizing a stratified sampling method can lead to more efficient statistical estimates
Third, it is sometimes the case that data are more readily available for individual A B C D Potential drawbacks in using stratified sampling.
First, identifying strata and implementing can increase the cost and complexity of sample selection
Second, when examining multiple criteria, stratifying variables may be related to some, but not to others, further complicating the design
Third, in some cases (such as designs with a large number of strata, or those with a specified minimum sample size per group), stratified sampling can potentially require a larger sample than would other methods E F

1. Focuses on important subpopulations and ignores irrelevant ones.
2. Allows use of different sampling techniques for different subpopulations.
3. Improves the accuracy/efficiency of estimation.
4. Permits greater balancing of statistical power of tests of differences between strata by sampling equal numbers from strata varying widely in size.

1. Requires selection of relevant stratification variables which can be difficult.
2. Is not useful when there are no homogeneous subgroups.
3. Can be expensive to implement. G Also sometimes called proportional or quota random sampling, involves dividing your population into homogeneous subgroups and then taking a simple random sample in each subgroup H Objective: Divide the population into non-overlapping groups (i.e., strata) N1, N2, N3, ... Ni, such that N1 + N2 + N3 + ... + Ni = N. Then do a simple random sample of f = n/N in each strata. A Sampling is often clustered by geography, or by time periods B Clustering can reduce travel and administrative costs (cost effective) C Does not need a sampling frame listing D Requires a larger sample than SRS to achieve the same level of accuracy E Implemented as multistage sampling. First stage consists of constructing the clusters that will be used to sample from. Second stage, a sample of primary units is randomly selected from each cluster. Third stage, all ultimate units (individuals) selected at the last step of this procedure are then surveyed F Multistage sampling can substantially reduce sampling costs, where the complete population list would need to be constructed Cluster sampling is useful when it would be impossible or impractical to identify every person in the sample. Rather than randomly sample 10% of students from each class, randomly sampling every student in 10% of the classes would be easier.

By randomly selecting the classes, you have a greater probability of capturing a representative sample of the population. G In cluster sampling, we follow these steps:

- divide population into clusters (usually along geographic boundaries)
- randomly sample clusters
- measure all units within sampled clusters H 5 5 I J K I RESEARCH 1
DR. CAROLINA PANGANIBAN
GERALD JOHN S. VELASQUEZ RESEARCH 1
DR. CAROLINA PANGANIBAN
GERALD JOHN S. VELASQUEZ
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