Definition
A small sample refers to a sample size that is relatively small and may not provide as precise estimates of population parameters as a large sample.
Small samples typically require more careful statistical analysis and may rely on exact distributions rather than asymptotic approximations.
Characteristics
Distributional Assumptions: Analysis often requires assumptions about the underlying population distribution (e.g., normality) because the CLT does not apply as effectively.
Increased Variability: Estimates from small samples tend to be more variable and less reliable.
Use of t-Distribution: For small samples, especially when estimating means, the t-distribution is often used instead of the normal distribution to account for additional uncertainty.
Advantages
Cost and Time: Collecting data from a small sample is less expensive and time-consuming.
Feasibility: Small samples are easier to manage and analyze, especially when resources are limited.
Disadvantages
Less Precision: Estimates from small samples are less precise and more subject to random error.
Bias Risk: Small samples are more susceptible to bias, especially if the sample is not representative of the population.
Limited Generalizability: Results from small samples may not be as easily generalizable to the entire population.
Example
In a preliminary study to determine the effect of a new drug, a sample of 15 patients might be used.
Due to the small sample size, the researchers would need to use the t-distribution for statistical analysis and be cautious about the increased variability and potential for greater sampling error.