Sample size determination is the process of calculating the optimal number of individuals or observations needed in a sample to ensure the study's results are reliable and statistically significant, based on the expected effect size, variability in data, significance level, and desired power of the study.
Sample
A subset of individuals or observations selected from a larger population for the purpose of studying the population.
Sampling
Sampling is a statistical method for selecting a subset of a population to make inferences about the whole.
There are two main types of sampling techniques: probability sampling and non-probability sampling.
1. Probability Sampling
Simple Random Sampling: Each member has an equal chance of selection.
Stratified Sampling: Population divided into strata, with random samples taken from each.
Systematic Sampling: Selecting every kth member from a randomly chosen starting point.
Cluster Sampling: Entire clusters are randomly selected, and all members within are surveyed.
2. Non-Probability Sampling
Convenience Sampling: Samples taken from easily accessible groups.
Judgmental or Purposive Sampling: Researcher selects participants based on judgment.
Quota Sampling: Population divided into subgroups, with a set number from each subgroup sampled.
Snowball Sampling: Existing subjects recruit future subjects.
The choice of technique depends on research goals, population nature, available resources, and desired accuracy. Probability sampling is ideal for generalizations, while non-probability sampling is used for specific insights or exploratory research.
Sample Size:
The number of individuals or observations included in a sample.
Several factors influence the sample size:
1. Effect Size:
This is the magnitude of the difference or association you expect to find between groups or variables.
A larger expected effect size allows for a smaller sample size, as larger effects are easier to detect.
2. Variability in the Data:
More variability (or higher standard deviation) in the population requires a larger sample size to distinguish the signal (effect) from the noise (variability).
3. Significance Level (α):
This is the probability of making a Type I error, which is rejecting a true null hypothesis. It is often set at 0.05 (5%).
A lower α requires a larger sample size to maintain the same power.
4. Power (1 - β):
Power is the probability of correctly rejecting a false null hypothesis, or the ability to detect an effect if one truly exists.
Higher power requires a larger sample size.
Formula
Sample size determination varies based on the type of outcome and the statistical test to be used.
Here are formulas and considerations for different types of outcomes:
1. Mean Difference (Two Independent Samples)
2. Proportion Difference (Two Independent Samples)
3. Correlation Coefficient
To calculate the sample size, these parameters must be estimated or assumed based on prior studies or pilot data. Statistical formulas or software can then be used to determine the appropriate number of participants.