Evidence-Based Approaches to Public Health: Biostatistics – Inferential Statistics: Sampling Methods and Sample Size Calculation
In this tutorial, we will explore two key concepts in inferential statistics: sampling methods and sample size calculation. Sampling refers to the process of selecting a subset of individuals from a population to represent the whole population, while sample size calculation ensures that the sample is large enough to draw valid and reliable conclusions.
By the end of this tutorial, you will understand different types of sampling methods, how to calculate the appropriate sample size, and why these steps are crucial in research design. Practice questions are included to help reinforce your knowledge.
Table of Contents:
- Introduction to Sampling and Sample Size
- Types of Sampling Methods
- Random Sampling
- Systematic Sampling
- Stratified Sampling
- Cluster Sampling
- Convenience Sampling
- Sample Size Calculation
- Importance of Sample Size
- Factors Influencing Sample Size
- Sample Size Formula
- Practice Questions
- Conclusion
1. Introduction to Sampling and Sample Size
Sampling is the process of selecting a subset (or sample) of individuals from a larger population to estimate population parameters and make inferences. Since it is often impractical to study an entire population, sampling allows researchers to make generalizations about a population based on a smaller, manageable group.
Sample size calculation determines the number of individuals needed in a sample to ensure that the results are statistically valid and reliable. If the sample size is too small, the study may lack the power to detect significant differences. If the sample is too large, resources may be wasted.
2. Types of Sampling Methods
There are several methods of sampling, each with its strengths and weaknesses. The choice of sampling method depends on the research design, the population, and the goals of the study.
2.1 Random Sampling
Random sampling (also called simple random sampling) is a method where each individual in the population has an equal chance of being selected for the sample. Random sampling helps minimize bias and ensures that the sample is representative of the population.
- Example: Drawing names from a hat or using a random number generator to select individuals from a population.
2.2 Systematic Sampling
Systematic sampling involves selecting individuals from a population at regular intervals (e.g., every 10th person on a list). While this method is easier to implement than random sampling, it can introduce bias if there is a pattern in the population list.
- Example: Selecting every 5th person from a list of attendees at a health screening event.
2.3 Stratified Sampling
Stratified sampling involves dividing the population into subgroups (or strata) based on characteristics such as age, gender, or income, and then selecting a random sample from each subgroup. This method ensures that all subgroups are represented in the sample.
- Example: Dividing a population by age group (e.g., 18-30, 31-50, 51+) and then randomly selecting individuals from each age group.
2.4 Cluster Sampling
Cluster sampling involves dividing the population into clusters (e.g., geographic areas or schools) and then randomly selecting entire clusters to include in the study. This method is often used in large, geographically dispersed populations, but it can introduce bias if clusters are not representative.
- Example: Selecting a random sample of schools and including all students from the selected schools in a study on childhood obesity.
2.5 Convenience Sampling
Convenience sampling involves selecting individuals who are readily available or easy to reach. While this method is inexpensive and easy to implement, it is prone to bias and may not be representative of the population.
- Example: Surveying individuals in a shopping mall who are willing to participate in a study on consumer behavior.
3. Sample Size Calculation
Sample size calculation is an important step in research design because it ensures that the sample is large enough to detect meaningful differences or associations. The calculation is based on several factors, including the desired level of precision, confidence level, and expected effect size.
3.1 Importance of Sample Size
Choosing the correct sample size is crucial for the validity of a study. If the sample size is too small, the study may not have enough power to detect significant differences or associations, leading to false-negative results. On the other hand, if the sample size is too large, the study may be unnecessarily expensive or time-consuming.
3.2 Factors Influencing Sample Size
Several factors influence the calculation of sample size:
- Desired confidence level: The confidence level reflects the degree of certainty that the sample accurately represents the population. Common confidence levels are 95% or 99%.
- Margin of error: The margin of error (or precision) represents how much error you are willing to accept. A smaller margin of error requires a larger sample size.
- Effect size: The effect size measures the magnitude of the difference or association you are trying to detect. Smaller effect sizes require larger sample sizes to detect.
- Population size: If the population is small, the sample size may be smaller, but for large populations, the sample size calculation is relatively independent of population size.
- Variability: The more variability there is in the population, the larger the sample size required to accurately estimate population parameters.
3.3 Sample Size Formula
The formula for calculating the sample size depends on whether the study is estimating a proportion or a mean. A basic formula for estimating sample size when proportions are involved is:
[math] n = \frac{Z^2 p(1-p)}{E^2} [/math]
Where:
- n: The required sample size.
- Z: The Z-score corresponding to the desired confidence level (e.g., Z = 1.96 for 95% confidence).
- p: The estimated proportion of the population with the characteristic of interest.
- E: The margin of error (precision).
For estimating the sample size for means, the formula is:
[math] n = \frac{Z^2 \sigma^2}{E^2} [/math]
Where:
- n: The required sample size.
- Z: The Z-score corresponding to the desired confidence level.
- σ: The population standard deviation.
- E: The margin of error.
4. Practice Questions
Test your understanding of sampling methods and sample size calculation with these practice questions. Try answering them before checking the solutions.
Question 1:
A researcher wants to study the prevalence of diabetes in different income groups. What type of sampling method should the researcher use?
Answer 1:
Answer, click to reveal
The researcher should use stratified sampling to ensure that all income groups are represented in the sample.
Question 2:
A study is conducted to evaluate the effectiveness of a new vaccine, and participants are selected by choosing every 10th person from a list of patients. What type of sampling method is this?
Answer 2:
Answer, click to reveal
This is an example of systematic sampling, where individuals are selected at regular intervals.
Question 3:
A public health study requires a 95% confidence level. The population has an estimated variance of 25, and the desired margin of error is 5. What is the minimum sample size required for the study?
Answer 3:
Answer, click to reveal
Using the formula for sample size when estimating the mean:
[math] n = \frac{Z^2 \sigma^2}{E^2} [/math]
For a 95% confidence level, Z = 1.96, σ² = 25, and E = 5:
[math] n = \frac{(1.96)^2 (25)}{5^2} = \frac{3.8416 \times 25}{25} = 3.8416 \times 1 = 3.8416 \approx 4 [/math]
Thus, a minimum sample size of 4 participants is required.
5. Conclusion
Sampling methods and sample size calculation are fundamental aspects of research design in public health. The choice of sampling method ensures that the sample is representative of the population, while sample size calculation ensures that the study is adequately powered to detect meaningful differences or associations.
Remember:
- Random sampling is ideal for reducing bias and ensuring a representative sample.
- Stratified sampling ensures that important subgroups of the population are included in the sample.
- Sample size calculation is influenced by factors such as confidence level, margin of error, and effect size.
Final Tip for the CPH Exam:
Make sure you understand how to choose the appropriate sampling method and how to calculate the required sample size for different types of studies. Practice identifying different sampling techniques mentioned in various studies, and practice calculating sample sizes.
Humanities Moment
The featured image for this CPH Focus is La Cène (1898) by Alexandre Falguière (French, 1831 – 1900). Falguière was a renowned French sculptor and painter, celebrated for works like Victor of the Cockfight, Joan of Arc, and The Dancer. A Prix de Rome winner and Officer of the Legion of Honor, he was also a prominent teacher and member of the Académie des Beaux-Arts, leaving behind a legacy of iconic sculptures and paintings now housed in major museums like the Musée d’Orsay.