I have all the relevant content from the textbook. The block10 "SAMPLING" section is about water sampling (Appendix II) - not statistics. The main statistical sampling content is entirely in block12. Let me now compile the full answer.
Random Sampling Techniques - Park's Textbook of Preventive and Social Medicine
(Source: Park's PSM, 27th Edition - Biostatistics Chapter, pp. 954 onwards)
What is Sampling?
When a large proportion of individuals, items, or units have to be studied, a sample is taken. It is easier and more economical to study the sample than the whole population (universe). Great care must be taken to ensure that the group included in the sample is representative of the whole population.
The Sampling Frame
Before drawing a sample, a sampling frame must be prepared.
"A sampling frame is a listing of the members of the universe from which the sample is to be drawn."
The accuracy and completeness of the sampling frame directly influences the quality of the sample drawn from it.
Sampling Methods
Park's describes three main methods of random sampling:
1. Simple Random Sample
- Every unit in the sampling frame is assigned a number.
- A table of random numbers is then used to decide which units are included.
- Random numbers are a haphazard collection of numbers arranged to eliminate personal selection or unconscious bias.
- Each unit has an equal chance of being drawn.
- This technique provides the greatest number of possible samples.
Key feature: Equal probability for every unit; uses random number tables.
2. Systematic Random Sample
- Every 5th or 10th unit is picked at regular intervals.
- Example: To carry out a filaria survey in a town with a 10% sample -
- Houses are numbered first.
- A number is selected at random between 1 and 10 (say 4).
- Then every 10th number is selected from that point: 4, 14, 24, 34... and so on.
- Each unit in the sampling frame has the same chance of being selected.
- However, the number of possible samples is greatly reduced compared to simple random sampling.
Key feature: Picks every nth unit after a random start; practical and quick.
3. Stratified Random Sample
- The sample is deliberately drawn so that each portion of the sample represents a corresponding stratum of the universe.
- Particularly useful when one wants to analyze data by a specific characteristic of the population (e.g., Hindus, Christians, Muslims; age groups, etc.) - because these groups are not equally distributed in the population.
- Ensures proportional representation of all subgroups.
Key feature: Population divided into strata first, then random sampling within each stratum.
Sampling Errors
If repeated samples are taken from the same population, results will differ from one sample to another - this is called sampling error.
Factors influencing sampling error:
- Size of the sample - larger sample = smaller error
- Natural variability of individual readings - more variability = more error between samples
"As the size of the sample increases, sampling error will decrease."
Non-Sampling Errors
Errors may also arise from:
- Inadequately calibrated instruments
- Observer variation
- Incomplete coverage of selected subjects
- Conceptual errors
These are often more important than sampling errors.
Standard Error
- If random samples (n) are repeatedly taken from a population, each sample has a different mean (x̄).
- The distribution of all sample means follows a normal distribution, centred around the true population mean (μ).
- The standard error (SE) = σ/√n - it measures how reliable a sample mean is.
- 95% of sample means will lie within μ ± 2 (σ/√n) of the true population mean.
SE enables us to judge whether the mean of a given sample is within the set confidence limits.
Notation convention (Park):
- Greek letters (μ, σ) = population parameters
- Roman letters (x̄, s) = sample characteristics
Quick Summary Table
| Method | How it works | Key advantage | Limitation |
|---|
| Simple Random | Random number table assigns each unit equal chance | Unbiased; maximum possible samples | Time-consuming for large populations |
| Systematic Random | Every nth unit selected after a random start | Practical, quick | Fewer possible samples; risk of hidden periodicity |
| Stratified Random | Population divided into strata; random sample from each | Ensures representation of subgroups | Requires knowledge of population structure |
Source: Park's Textbook of Preventive and Social Medicine, 27th Edition - Biostatistics section, p. 954