Definition
A large sample typically refers to a sample size that is sufficiently large to provide reliable estimates of population parameters and to use asymptotic approximations (such as the Central Limit Theorem).
There is no strict cutoff, but in many contexts, a sample size greater than 30 is considered large.
Characteristics
Central Limit Theorem (CLT): The CLT states that the sampling distribution of the sample mean approaches a normal distribution as the sample size becomes large, regardless of the population's distribution.
Precision: Larger samples tend to yield more precise estimates of population parameters.
Reduced Sampling Error: The variability due to sampling error decreases as the sample size increases.
Advantages
More Accurate Estimates: Large samples provide more accurate estimates of population parameters.
Robustness: Results from large samples are more robust and less influenced by outliers.
Use of Normal Approximation: Large samples allow for the use of normal approximation in many statistical tests, simplifying the analysis.
Disadvantages
Cost and Time: Collecting and analyzing large samples can be expensive and time-consuming.
Complexity: Managing and analyzing large datasets can be complex and require advanced statistical tools and expertise.
Example
In a study to determine the average height of adult men in a city, a sample of 500 men would be considered a large sample.
This allows the researchers to make reliable inferences about the population's average height.