Sampling Theory Quiz

Study Notes

Sampling Theory

Sampling: A process used to gather information about a population by collecting data from a subset of its members.
Census: A survey that includes all members of a population.
Sampling is preferred to a census for reasons such as cost-effectiveness, time efficiency, widening data scope, minimizing destructive research processes and feasibility when access to the entire population is impossible.
Reasons for conducting a census:
- Ensuring a representative sample: Eliminates the risk of a random sample not accurately reflecting the population.
- Addressing concerns about sampling: Satisfies those who may not be comfortable relying on data collected from a sample.
Population: The entire group of people, items, or units under investigation.
Sample: A subset of the population from which data is collected.
Frame: A list of elements from which the sample is selected.
Sampling frame: The specific list of individuals, institutions, or entities used for sample selection.

Parameters and Statistics

Parameter: A characteristic of the population. Examples include population mean, proportion, variance, and standard deviation.
Statistic: A characteristic of the sample. Examples include sample mean and proportion.
When mean, median, mode, and standard deviations describe a sample, they are called statistics. When they describe the population, they are called parameters.

Types of Sampling Methods

Random Sampling: Every unit in a population has an equal probability of being included in the sample.
- Advantages: Eliminates selection bias, ensures a fair representation of the population, and makes the sample suitable for statistical analysis.
- Also known as: Probability Sampling.
Non-Random Sampling: Every unit in the population does not have an equal probability of being included in the sample.
- Disadvantages: Introduces potential bias in the selection process and may not be appropriate for statistical analysis.
- Also known as: Non-Probability Sampling.

Random Sampling Techniques

Simple Random Sampling (SRS):
- Each unit in the population is assigned a number, and random numbers are used to select the sample.
- It is easier to implement with smaller populations.
- Advantages of SRS:
  - Requires minimal knowledge of the population.
  - Minimizes subjectivity and personal error. Provides relevant data.
  - Findings can be used for inferential purposes.
- Disadvantages of SRS:
  - Cannot guarantee a perfectly representative sample.
  - Doesn't utilize prior knowledge about the population.
  - Inferred accuracy depends on sample size.
Stratified Random Sampling (STRS):
- The population is divided into subgroups called strata, with similar characteristics within each stratum.
- A random sample is then drawn from each stratum.
- Potential for reducing sampling error compared to SRS.
- Types of STRS:
  - Proportionate: Sample sizes from each stratum are proportional to their representation in the population.
  - Disproportionate: The sample proportions differ from the population proportions.
  - Optimum Allocation: Used when the population is diverse. This method aims for a representative and comprehensive sample, making it more effective than other stratified samples.
Systematic Sampling:
- Selects every kth element from a sorted population list after randomly selecting the first element.
- Formula for k (sampling cycle): k = N/n, where N is the population size and n is the sample size.
- Advantages: Convenient and easy to administer.
Example of Systematic Sampling Application:
- A class has 110 students with numbers from 1 to 110.
- You need to choose a sample of 10 students.
- k = 110 / 10 = 11.
- Randomly select one number from the first 11 numbers.
- If the selected number is 6, the chosen sample would include students numbered 6, 17, 28, etc., until 107.

Description

Test your knowledge on Sampling Theory, including concepts such as sampling, census, population, and sample. This quiz will help you understand the advantages of sampling over a census and the importance of a representative sample.