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.
Table of Contents
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.