The Central Limit Theorem is useful because it allows researchers to treat sample means as normally distributed even when the raw data come from an unknown or complex population. This eliminates the need to identify the parent distribution before performing inference, enabling the use of confidence intervals, t-tests, and ANOVA.
Conditions: The population distribution is unknown or not easily characterized.; The analysis focuses on sample means.; The sample size is sufficiently large for the CLT approximation to hold.
The Central Limit Theorem is useful because it allows researchers to treat sample means as normally distributed even when the raw data come from an unknown or complex population. This eliminates the need to identify the parent distribution before performing inference, enabling the use of confidence intervals, t-tests, and ANOVA.
Conditions: The population distribution is unknown or not easily characterized.; The analysis focuses on sample means.; The sample size is sufficiently large for the CLT approximation to hold.