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# Probability Sampling and Slovin's Formula

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@ColorfulBaltimore

### What is the traditional approach in Simple Random Sampling to determine individual samples?

Table of Random Numbers or lottery (fishbowl) method

### What is the key feature of Systematic Sampling?

Choosing every kth name on the list

### When is Stratified Sampling used?

To ensure fair representation of strata in the sample

### What is another name for Cluster Sampling?

<p>Area sampling</p> Signup and view all the answers

### Why is Systematic Sampling often preferred over Simple Random Sampling?

<p>It is easier and less trouble</p> Signup and view all the answers

### In what situations is Multi-stage Sampling typically used?

<p>When the selection of the sample is done in two or more steps</p> Signup and view all the answers

### What is the most commonly used formula in determining the sample size?

<p>Slovin’s formula</p> Signup and view all the answers

### In simple random sampling, why is it said that each member of the population has an equal chance of being selected?

<p>Because there is no bias that one person will be chosen rather than another.</p> Signup and view all the answers

### What does the value of 'z' represent in Lynch et.al.'s sample size formula?

<p>The value of the normal variable for a reliability level of 0.95.</p> Signup and view all the answers

### Why is simple random sampling considered independent?

<p>Because the choice of one person does not bias the researcher for or against the choice of another.</p> Signup and view all the answers

### What is the margin of error usually set at in the commonly used sample size formula?

<p>0.05</p> Signup and view all the answers

### What is the largest possible proportion, 'p', often set to in Lynch et.al.'s sample size formula?

<p>0.50</p> Signup and view all the answers

## Study Notes

### Simple Random Sampling

• Uses two methods: Table of Random Numbers (traditional approach) or the lottery (fishbowl) method
• Both methods are used to determine individual samples/respondents

### Systematic Sampling

• Choosing every kth name on the list
• kth stands for a number between 0 and the size of the sample that you want to select
• Often preferred due to ease and less trouble
• However, it is less precise and violates the assumption of each member having an equal chance to be selected

### Stratified Sampling

• Used to ensure fair representation of strata in the population
• Strata can be entities grouped accordingly, such as class sections, year levels, barangays, etc.

### Cluster Sampling

• Used when the population is large and spread over a large area
• Divides the population into segments, and then selects several segments at random
• Also known as area sampling, often applied on a geographical basis

### Multi-Stage Sampling

• Selection of the sample is done in two or more steps
• Population is divided into first-stage units, then a sample is drawn
• Further stages involve dividing the population into a hierarchy of sampling units

### Probability Sampling

• Requires determining the population size to compute the sufficient sample size
• The Slovin's formula is commonly used: n = 𝑁 / (1 + 𝑁𝑒2)
• Another formula is Lynch, et.al.'s: n = 𝑁𝑧2.𝑝(1−𝑝) / (𝑁𝑑2 + 𝑧2.𝑝(1−𝑝))
• The computed sample size is the minimum required, and the researcher may add more but not less

### Sample Size Formulae

• Slovin's formula: n = 𝑁 / (1 + 𝑁𝑒2)
• Lynch, et.al.'s formula: n = 𝑁𝑧2.𝑝(1−𝑝) / (𝑁𝑑2 + 𝑧2.𝑝(1−𝑝))

### Simple Random Sampling (Under Probability Sampling)

• Each member of the population has an equal and independent chance of being selected
• Equal chance due to no bias, and independent chance due to the choice of one person not affecting the choice of another
• Characteristics of the sample should be close to that of the population

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## Description

Learn about probability sampling and how to determine the minimum sample size needed in research using Slovin's formula. This formula helps researchers calculate the number of respondents or participants required for their study based on the population size.

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