 # Sample Design.

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Sample Design

Population and Universe
Population or Universe is any complete group of people, companies, hospitals, stores, college students or like that who share some set of characteristics. Population and universe can also be distinguished as: If complete set of element is finite it is known as Population. If complete set of element is infinite it is known as Universe.

Elements All those primary units which constitute universe or population, consisting some common set of characteristics are know as elements. In a survey when elements are human being we call them respondents.

Sampling It is a process of using small portion of the population or universe to make conclusions about the whole population.

Sample Population A subset or part of population capable of representing almost in same ratio the characteristics which are present in the population or universe Sample

Census An investigation of all the individual elements making up a population. It should be noticed that universe cannot be studied through census method.

Census Vs Sample Enumeration
A complete enumeration of all items in the ‘population’ is known as a census inquiry. A Sample survey is a sub group of population.

When a Census is appropriate
If the size of population is small Researcher is interested in gathering the information from every individual.

When Sample is appropriate
When the size of population is large. When time and cost are the main consideration in research If population is homogenous Sampling reduces the labour requirements and gathers vital information. Reduces non sampling errors

Essentials of a sample A sample must have following things which are very essential for drawing valid conclusions: It should be representative It should be independent It should be homogenous It should be adequate

Objectives of sampling
To obtain reliable information about the population. To arrive at the characteristics of the parent population. To test the reliability of difference between the sample estimates and population parameters. To test the validity

The Sampling Process Plan procedure for selecting sampling units 4
Determine if a probability or non-probability sampling method will be chosen Determine sample size 3 5 Select actual sampling units Select a Sampling Frame 2 6 Define the Target population Conduct fieldwork 1 7

Defining the target population
The specific, complete group relevant to the research project. Who has the information/data you need? How do you define your target population? Geography Demographics Use Awareness Reason: To define a proper source from which the data are to be collected.

Defining the target population
The target group should be clearly delineated. Thus, population is defined as: Elements Sampling unit Extent Time

The Sampling Frame A sampling frame is the list of elements from which the sample may be drawn. Sampling frame is also known as working population. Examples of sampling frames are a student telephone directory, the list of companies on the stock exchange, the yellow pages (for businesses).

The Sampling Frame Generally, it is not feasible to compile a list that includes the entire population, leading to sampling frame error. Sampling frame error - Error that occurs when certain sample elements are not listed or available and are not represented in the sampling frame

CLASSIFICATION OF Sampling METHODS
Sampling Technique Probability sampling Simple Random Sampling Complex Random Sampling Non-Probability sampling

Probability and Non-Probability Sampling
A Probability Sampling is one in which every unit in the population has an equal chance or a non zero probability of being selected in the sample. A Non-Probability Sampling is one in which units of the sample are chosen on the basis of personal judgment or convenience

Simple random sampling
Purest form of probability sampling It is a process in which every item of the population has an equal probability of being chosen. Applicable when population is small, homogeneous & readily available. A table of random number or lottery system is used to determine which units are to be selected.

Method of selecting random sample
It involves writing the name of each element of a finite population on a slip of paper and putting them into a box or a bag. After this, mix them thoroughly and then the required number of slips for the sample shall be picked one after the other without replacement. While doing this, it has to be ensured that in successive drawings each of the remaining elements of the population has the same chance of being selected

Complex random sampling
Also known as mixed sampling design. Under restricted sampling techniques, the probability sampling may result in complex random sampling designs. such designs may represent a combination of probability and non-probability sampling procedures in selecting a sample.

Sampling with probability proportional to size
Complex Random Sampling Systematic sampling Stratified Sampling Cluster Sampling Area sampling Multi stage Sampling Sequential Sampling Sampling with probability proportional to size

Systematic Sampling A sampling procedure in which an initial starting point is selected by a random process and then every nth number on the list is selected.

This method is an improvement over a simple random sample. Easier and less costlier method Can be conveniently used even in case of large populations. Problem of Systematic Sampling is Periodicity.

Stratified sampling A procedure in which simple random subsamples are drawn from within different strata that are more or less equal on some characteristics.

Stratified sampling Reasons for stratified sampling:
If population does not constitute a homogeneous group. To have more efficient sampling Reducing random sampling error Assuring that sample would correctly reflect the population

Stratified sampling Under stratified sampling the population is divided into several sub-populations that are individually more homogeneous than the total population. Then items are selected from each stratum to constitute a sample. Since each stratum is more homogeneous than the total population, research is able to get more precise estimates for each stratum and by estimating more accurately each of the component parts. Stratified sampling results yield more reliable and detailed information.

Cluster sampling Reason:
When the total area of research interest is large Process: Firstly, population is divided into a number of smaller non-overlapping areas, which are clusters of homogeneous units Secondly, few clusters are selected by using a simple random sampling method. Finally, all the units in the selected clusters are studied.

Low cost/high frequency of use Requires list of all clusters, but only of individuals within chosen clusters Can estimate characteristics of both cluster and population Disadvantages Larger error for comparable size than other probability methods Multistage very expensive and validity depends on other methods used

Multistage sampling Sampling that involves using a combination of two or more probability sampling techniques. Complex form of cluster sampling in which two or more levels of units are embedded one in the other. Process: First stage, random number of districts chosen in all states. Followed by random number of talukas, villages. Then third stage units will be houses. All ultimate units (houses, for instance) selected at last step are surveyed.

Sampling with probability proportional to size
In case the cluster sampling units do not have the same number or approximately the same number of elements, it is considered appropriate to use a random selection process where the probability of each cluster being included in the sample is proportional to the size of the cluster. The actual numbers selected in this way do not refer to individual elements, but indicate which clusters and how many from the cluster are to be selected by simple random sampling or by systematic sampling.

Sequential sampling A complex sample design
The ultimate size of the sample is not fixed in advance When the number of samples is more than two but it is neither certain nor decided in advance, this type of system is often referred to as sequential sampling.

Non probability sampling techniques
Convenience Sampling Judgement Sampling Quota Sampling Snowball Sampling

Types of Non probability sampling techniques
Convenience Sampling: The sampling procedure of obtaining those people or units that are most conveniently available. Judgement Sampling: A technique in which an experienced individual selects the sample based on personal judgement about some appropriate characteristic of the sample member.

Types of Non probability sampling techniques
Quota Sampling: This procedure ensures that various sub groups of a population will be represented on pertinent characteristics to the exact extent that the investigator desires. Snowball Sampling: A sampling procedure in which initial respondents are selected by probability methods and additional respondents are obtained from information provided by the initial respondents.

Sampling Error In a sample survey, since only a small portion of the population is studied and its results are bounded to differ from census results and thus having a certain amount of error. In Statistics, the word error is used to denote the difference between the true value and the estimated or approximated value. Sampling error is the gap between the sample mean and population mean.

Non Sampling Error Sampling Frame Error: A sampling frame is a specific list of population units, from which the sample for a study being chosen. Non Response Error: This occurs because the planned sample and final sample vary significantly.

Graphical Depiction of Sampling Errors
Respondents (actual sample) Planned Sample Sampling Frame Non-Response Error Sampling Frame Error Random Sampling Error Total Population

How to reduce errors Errors in sampling can be reduced if the size of sample is increased. Avoid leading questions Pre-test the questionnaire Train the interviewer to establish good rapport with the respondents.

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