Department of Agricultural Education, Communications and Leadership 
R7
MODULES: R  7: Sampling
SAMPLING
Randomization
Random sampling as suggested by Van Dalen (1979) often means chance or a haphazard method of assignment to many people, but in reality it is a carefully controlled process. Randomization is used to eliminate bias, both conscious and unconscious, that researchers might introduce while selecting a sample. Kerlinger (1986) described randomization as the assignment of objects (subjects, treatments, groups, etc.) of a population to subsets (sample) of the population in such a way that, for any given assignment to a subset (sample), every member of the population has an equal probability of being chosen for that assignment. Randomization is essential for probability samples which are the only samples that can generalize results back to the population. Kerlinger (1986) reported that random sampling is important because it is required by inferential statistics. If the researcher desires to make inferences about populations based on the behavior of samples, then random sampling must be used.
Stratification
Stratified sampling is a procedure for selecting a sample that includes identified subgroups from the population in the proportion that they exist in the population. This method can be used to select equal numbers from each of the identified subgroups if comparisons between subgroups is important. A good example of stratified sampling would be to divide the population into men and women. The different strata to use for each study would be determined in part by the review of literature of previous research. The purpose of stratified sampling is to guarantee the desired distribution among the selected subgroups of the population.
Proportional
Proportional sampling (Van Dalen, 1979) provides the researcher a way to achieve even greater representativeness in the sample of the population. This is accomplished by selecting individuals at random from the subgroup in proportion to the actual size of the group in the total population. Proportional sampling is used in combination with stratified and cluster sampling.
Clusters
The most used method in educational research according to Kerlinger (1986) is cluster sampling. Groups of elements (clusters) instead of individuals from the population are used for the sample. Cluster sampling often is more convenient when the population is very large. It often isn’t possible to randomly select from the entire population but is more manageable when using clusters because of time, expense, and convenience. A cluster sampling is using schools as clusters and randomly selecting from the list of schools instead of randomly selecting individuals from a list that includes all schools. This can help the researcher cut down on travel expense, time, etc. One problem with cluster sampling is that it usually produces a larger sampling error than a simple random sample of the same size because the clusters tend to be more similar within the cluster, reducing the representativeness of the sample (Van Dalen, 1979).
Systematic
In some cases when the population of a study is available as a list, a sample is drawn from certain intervals on the list. The starting point is randomly chosen and then every so many numbers another individual is chosen from the list and added to the sample. This method can be equal to random selection only if the names were randomized at the beginning. Van Dalen (1979) cautions us to be wary of departure from randomness of the list because of structure, some trend, or cyclical fluctuation.
Purposive
Kerlinger (1986) explained purposive sampling as another type of nonprobability sampling, which is characterized by the use of judgment and a deliberate effort to obtain representative samples by including typical areas or groups in the sample. In other words, the researcher attempts to do what proportional clustering with randomization accomplishes by using human judgment and logic. As a result, there are many opportunities for error. In addition, nonprobability samples do not use random sampling which makes them unacceptable for generalizing back to the population.
In random sampling each object has an equal and independent opportunity of being chosen. Stratified sampling involves the identification of the variable and subgroups (strata) for which you want to guarantee appropriate representation (either proportional or equal). To use cluster sampling, you must list and identify all clusters that comprise the population and estimate the average number of population members per cluster to determine the number of clusters needed for the sample. Proportional sampling determines the ratio of individuals in subgroups for which you want proportional representation. Once the strata, cluster, or ratio has been determined, individual objects, clusters, or individuals in a subgroup are randomly selected. Systematic sampling takes every nth name (n=size of population divided by desired sample size) on a list of the population until the desired sample size is reached.
Determination of Sample Size
The first thing that is needed is to identify or define the population. Jaccard (1983) defined population as the aggregate of all cases to which one wishes to generalize. At this time, it is necessary to determine if your research requires the identification of subgroups and if so define the subgroups within the population. To have a sample that is of use it needs to be as close as possible to being representative of the complete population. Popham and Sirotnik (1973) contend that in order to draw legitimate inferences about populations from samples that the sample has to be representative of the population and randomly selected.
Van Dalen (1979) lists three factors that he considers to determine the size of an adequate sample as (l) the nature of the population, (2) the type of investigation, and (3) the degree of precision desired. The formula for estimating the sample size and a table for determining the sample size based on confidence level needed from a given population was provided by Krejcie and Morgan (1970).
where
S = required sample size
N = the given population size
P = population proportion that for table construction has been assumed to be .50, as this magnitude yields the maximum possible sample size required
d = the degree of accuracy as reflected by the amount of error that can be tolerated in the fluctuation of a sample proportion p about the population proportion P  the value for d being .05 in the calculations for entries in the table, a quantity equal to
X2 = table value of chi square for one degree of freedom relative to the desired level of confidence, which was 3.841 for the .95 confidence level represented by entries in the table
TABLE FOR DETERMINING NEEDED SIZE S OF A RANDOMLY CHOSEN SAMPLE FROM A GIVEN FINITE POPULATION OF N CASES SUCH THAT THE SAMPLE PROPORTION p WILL BE WITHIN ± .05 OF THE POPULATION PROPORTION P WITH A 95 PERCENT LEVEL OF CONFIDENCE
Population Size 
Sample Size 
Population Size 
Sample Size 
Population Size 
Sample Size 
10  10  220  140  1200  291 
15  14  230  144  1300  297 
20  19  240  148  1400  302 
25  24  250  152  1500  306 
30  28  260  155  1600  310 
35  32  270  159  1700  313 
40  36  280  162  1800  317 
45  40  290  165  1900  320 
50  44  300  169  2000  322 
55  48  320  175  2200  327 
60  52  340  181  2400  331 
65  56  360  186  2600  335 
70  59  380  191  2800  338 
75  63  400  196  3000  341 
80  66  420  201  3500  346 
85  70  440  205  4000  351 
90  73  460  210  4500  354 
95  76  480  214  5000  357 
100  80  500  217  6000  361 
110  86  550  226  7000  364 
120  92  600  234  8000  367 
130  97  650  242  9000  368 
140  103  700  248  10000  370 
150  108  750  254  15000  375 
160  113  800  260  20000  377 
170  118  850  265  30000  379 
180  123  900  269  40000  380 
190  127  950  274  50000  381 
200  132  1000  278  75000  382 
210  136  1100  285  100000  384 
Survey Design Notes by Dr. Don Dillman;
A Survey Can: "Provide the distribution of a characteristic in a population by collecting information from only a few of its members."
Rules of Thumb:





Measurement Error:



Sampling Error
Occurs because only a subset of the population is surveyed.
n  Precision 
97  +/ 10% 
385  +/ 5% 
1068  +/ 3% 
2175  +/ 2% 
Coverage Error



Nonresponse Error



For a survey to be accurate, each of the four sources of data collection error must be attended to .







Perspective for Improving Response





This is a social exchange, not and economic exchange.
Requirements for Maximizing Mail Survey Response











Why Mail Surveys Usually Fail





How to Improve Responce

A List



B List

SELF ASSESSMENT
1. Define.
Sample
Population
2. Describe the sampling approach of randomization.
3. Define stratification as related to sampling.
4. Explain clusters regarding a sample.
5. Describe proportional in relation to sampling.
6. Define and explain systematic sampling.
7. Explain the use of purposive sampling.
8. Explain how to determine the sample size needed to give the most representative sample.
9. Describe the type of sampling method that would be used for your research and explain why this would be the best choice.