Unit 4: Sampling Theory and Design of Sample Surveys

Course Code: ECODSC 253 (Statistics for Economics)

This unit provides a necessary bridge between probability theory and statistical inference by introducing techniques used to collect and analyze survey data.

1. Population and Sample Concepts
2. Census versus Sampling
3. Types and Methods of Sampling
4. Principal Steps and Laws of Sampling
5. Errors, Standard Error, and Limitations

1. Population and Sample Concepts

Before designing a survey, it is critical to distinguish between the group being studied and the portion being measured.

Population: The entire group of individuals or items that are the objects of a statistical investigation.
Sample: A finite subset of the population selected for study to derive conclusions about the population as a whole.
Parameter: A numerical value that describes a characteristic of the entire population (e.g., population mean).
Statistic: A numerical value calculated from sample data used to estimate a population parameter (e.g., sample mean).

2. Census versus Sampling

Investigators must choose between studying every member of a population or just a representative part.

Feature	Census Method	Sampling Method
Scope	Covers every unit of the population.	Covers only a representative fraction.
Accuracy	High, as every unit is examined.	Subject to sampling errors but can be very reliable if designed well.
Cost & Time	Expensive and time-consuming.	Economical and faster.
Feasibility	Not possible if testing involves destruction of items.	Ideal for large populations or destructive testing.

3. Types and Methods of Sampling

Methods of selecting a sample are broadly categorized into random and non-random techniques.

Random Sampling

Also known as probability sampling, where every unit has a known, non-zero chance of being selected.

Simple Random Sampling: Units are chosen such that every possible sample of a given size has an equal chance of selection.
With Replacement (WR): A unit is selected, recorded, and returned to the population before the next draw.
Without Replacement (WOR): A selected unit is not returned, meaning it cannot be selected twice.

Non-Random Sampling

Also known as non-probability sampling, where selection is based on convenience or judgment rather than chance.

4. Principal Steps and Laws of Sampling

A systematic survey involves several predefined stages and follows specific statistical laws.

Principal Steps in a Sample Survey:

Statement of the objectives.
Definition of the population to be sampled.
Determination of the sampling frame and units.
Selection of the sampling design/method.
Preparation of the questionnaire or schedule.
Data collection and analysis.

Laws of Sampling:

Law of Statistical Regularity: A moderately large number of items chosen at random from a large group are almost sure on average to possess the characteristics of the large group.
Law of Inertia of Large Numbers: Larger samples are more stable and less prone to fluctuations than smaller ones.

5. Errors, Standard Error, and Limitations

Sampling vs. Non-Sampling Errors

Sampling Error: The difference between the sample statistic and the population parameter arising because only a part of the population was studied.
Non-Sampling Error: Errors arising from faulty planning, data collection, or processing (e.g., non-response, measurement error).

Standard Error

The Standard Error (SE) is the standard deviation of a sampling distribution. It measures the extent to which a sample statistic is likely to differ from the population parameter.

Limitations of Sampling

Requires expert knowledge to design correctly.
Possibility of bias if the sample is not truly representative.
Conclusions are probabilistic, not absolute.

Exam Tip: Remember that increasing the sample size reduces Sampling Error but may increase Non-Sampling Error due to the difficulty of managing a larger operation.