Simple Random, Systematic, Stratified & Cluster Types Of Probability Sampling Techniques SIMPLE RANDOM Before I explain the various probability methods we have to define some basic terms. These are: N = the number of cases in the sampling frame n = the number of cases in the sample NCn = the number of combinations (subsets) of n from N f = n/N = the sampling fraction Each element of the frame has an equal probability of selection (EPS) Frame is not subdivided or partitioned Minimises bias and simplifies analysis of results SRS can be vulnerable to sampling error because the randomness of the selection may result in a sample that doesn't reflect the makeup of the population Line up our population into a nice and neat sampling frame and selected every 3rd member SYSTEMATIC STRATIFIED CLUSTER Sampling Strategies and their Advantages and Disadvantages Type : Simple Random When to use it : Population members are similar to one another on important variables Advantages : Ensures a high degree of representativeness Disadvantages : Time consuming and tedious 1 2 3 4 Type : Systematic When to use it : When the population members are similar to one another on important variables Advantages : Ensures a high degree of representativeness, and no need to use a table of random numbers Disadvantages : Less random than simple random sampling Type: Stratified Random When to use it : When the population is heterogeneous and contains several different groups, some of which are related to the topic of the study Advantages : Ensures a high degree of representativeness of all the strata or layers in the population Disadvantages : Time consuming and tedious Type : Cluster When to use it : When the population consists of units rather than individuals Advantages : Easy and convenient Disadvantages : Possibly, members of units are different from one another, decreasing the techniques effectiveness 1. Relies on arranging the target population according to some ordering scheme and then selecting elements at regular intervals through that ordered list 2. Involves a random start and then proceeds with the selection of every kth element from then onwards. In this case, k=(population size/sample size) 3. Starting point is not automatically the first in the list, instead randomly chosen from within the first to the kth element in the list 4. Select every 10th name, also referred to as 'sampling with a skip of 10, Every 10th' sampling is especially useful for efficient sampling from databases 5. Selecting (e.g.) every 10th street number along the street ensures that the sample is spread evenly along the length of the street, representing all of these districts 6. Vulnerable to periodicities. If present and the period is a multiple or factor of the interval used, the sample is unrepresentative of the overall population 7. The sample is especially likely to be unrepresentative of the overall population 8. One drawback is its difficult to quantify accurately its theoretical properties SRS may also be tedious when sampling from an unusually large target population SRS does not provide subsamples of the population Simplest form of random sampling 1

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

Advantages over other sampling methods

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.

Disadvantages

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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# Types of Probability Sampling Techniques

Simple Random, Systematic, Stratified, and Cluster Sampling

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