5. Sampling DesignCensus and Sampling:• Census inquiry-includes all cases (100 %).

Highest accuracy is possible.• 100 % population survey is not practical in

all cases.• Therefore, reasonable representatives

among the population is considered practical and selected representatives are called sample.

Sampling: It is a technique of data collection in which some samples are taken for the study which represents the whole population.

Sample: A sample is a small proportion of

population , selected for observation /analysis.

Population or Universe A population is any group of individuals that have

one or more characteristics in common, which are of interest of the research fellow.

Universe is the boundary, within which the study is confined.

-finite universe-population of a city, number of workers in factory, are some examples of finite universe.-infinite universe-number of stars in the sky, listeners of a specific radio program, are some of the examples of infinite universe

Characteristics of a sample

• Sample should be as correct as possible, • It should represent the whole population,• Quality of sample is important than

quantity,• Sample should not be biased,• Sample should fulfill the purpose of the

study,

Sample Design

In sample design, following three points has to be considered;a. Sampling frame (List of population),b. Selection of sampling item

(Method of sampling)c. Size of sampling (Larger the sample size,

more accurate it is)

Sampling Methods: The methods by which units of

observation are selected, are broadly classified as;

i. Probably Sampling and,ii. Non-probability Sampling

i. Probability SamplingProbability sampling believes that each element in the universe has equal chance of selection.The implications of simple random sampling are: (a) equal probability of getting into the sample, (b) all choices are independent of one another, (c) gives each possible sample combination an equal probability of being chosen.

Probability Sampling is further classified as;

a. Simple Randomb. Systematic Randomc. Stratified Random and,d. Cluster or Multi-stage Random

a. Simple Random Sampling

This is very simple and basic methods of sampling. In this method, any item may be selected from the mass.

Example: Any 50 student from the college.

Probability of selection = n/N where, n = sample size, and N = population size.

b. Systematic Random sampling• Every Kth element in the population is sampled,

beginning with random start of an element in the range of 1 to k.

• Skip internal (or kth element), k = N/n, where N is population size and n is sample size.

• Advantages :It is simple and flexible. No need of random numbers table. Easy to instruct field workers to choose sample unit. To draw systematic sample, do following: (a) identify, list , and number the elements in the population, (b) identify skip interval, K, (c ) identify the random start, (d) draw a sample by choosing every kth entry.

c. Stratified Random Sampling • The process by which the sample is constrained to include

elements from each of the segments is called stratified random sampling.

• If population characteristics are heterogeneous, then simple random sampling does not serve as a good design so as to represent the sample units from each characteristics.

• In this condition, entire population is divided/sub-divided into homogenous groups or class called strata.

• For example-university students can be divided by their class level, major, gender, etc.

• After a population is divided into the appropriate strata, a simple random sample process can be taken within each stratum.

d. Cluster or Multi-stage Sampling

Cluster sampling is a plan that involves dividing the population into subgroups and then draws a sample from each subgroup.

This is a multistage sampling related to the geographical region.

* Example: If we have to study about the conditions of schools in Lalitpur district, we can take sample as:

- Select 4 schools from municipality and 12 schools from VDCs

- Take 4 schools from each constituency among 12- Take 1 secondary school, 1 lower secondary school and

2 primary schools.

Differences between stratified sampling and cluster sampling

• Division of the population into a few sub groups (each subgroups has many elements in it) in case of Stratified Sampling, but in case of Cluster Sampling, division of population into many subgroups (each subgroup has few elements in it).

• We try to secure homogeneity within subgroup in case of Stratified Sampling, but try to secure heterogeneity within subgroups in case of Cluster Sampling.

• Try to secure heterogeneity between subgroups in case of Stratified Sampling, but try to secure homogeneity between subgroups in case of Cluster Sampling.

• Randomly chose elements from within subgroups in Stratified Sampling but in Cluster Sampling, randomly chose several subgroups to study in depth.

ii. Non-probability Sampling

This method does not believe in equal chance. Some elements have more chance of being selected . This depends upon • Convenience sampling• Judgment or purposive sampling•Quota sampling (male and female for

example)• Snowball sampling (in case of network or

interconnectedness studies).

a. Convenience Sampling

In this method, the selection of sample depends upon the convenience of the researcher.

Example: Taking interviews with the drivers, pasangers or pedestrians in the street.

b. Judgment or purposive sampling

• In this method samples are taken at the judgment of the researcher as that fulfils his purpose.

Example: Taking views of 10 doctors about the eradication of T.B.

C. Quota sampling• This is better method of non-probability

sampling. In this method some quota are divided to each group of items and required samples are selected. (more priority to the small nos.)

Example:Subject No. of Student Quota (25 nos.)

Civil 100 12Computer 50 8Electronics 25 5

d. Snowball Sampling

This method is used where it is difficult to identify respondents. The respondents are located through referral network.

In the beginning, individuals are discovered and this group is then used to locate others who possesses similar characteristics and who, in turn, identify others.

Advantages/Merits of sampling• Speed or less time• Economy (reduced cost of the study).• Administrative convenience (complete census study requires

very huge administrative setup including human resources)• Reliability• Greater scope (more practical than census study with

reference to time, money, and man hours)• For infinite of too large population, sampling is only the way• For destructive testing, sampling is more economic than

census study.(source: S.C. Gupta, page 1048-1049)

Disadvantages/limitations of Sampling

• If not properly planned, the results obtained will not be reliable.

• Efficient sampling requires the services of qualified, skilled, and experienced person.

• If the sample size is the large proportion of the population size, it may require more time and money.

• In case we want to have information about each and every unit of the population, sampling is useless.

Sampling error• There would naturally be a certain amount of inaccuracy

in the information collected. Such inaccuracy may be termed as sampling error or error variance.

• Differently, sampling errors are those errors which arise on account of sampling and they generally happen to be random variations (in case of random sampling) in the sample estimates around the true population value.

• Sampling error = frame error + chance error + Response error.

• Sampling error can be reduced by increasing sample size.• (Source: Kothari, 2011, page 153-154)

Size of the Sample

• Size of sample-is the number of items to be selected from the universe.

- Sample size should neither be excessively large nor too small. It should be optimum.

- Optimum sample fulfills the requirement of efficiency, representatives, reliability, and flexibility.

- Decide the level of confidence or significance level (precision of study).

- Size of population and costs for research also need to be considered.

Approximate Sample Size • One principle of sample sizes is, the smaller the

population, the bigger the sampling ratio.• For example, for small populations (under 1,000), a large

sampling ratio (about 30 %) is recommended. • For moderately large populations (10,000), a smaller

sampling ratio (about 10 %) is recommended.• For large populations (over 150,000), smaller sampling

ratio (about 1 %) is recommended.• For very large populations (over 10 million), tiny

sampling ration (about 0.025 %) is adequate (source: w. Lawrence Neuman, page 220-221)Cohen J (1988 or latest). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum Associates. It provides tables for determining sample size.