lerreurtype

L'erreur-type, often written l'erreur-type or erreur-type, is a statistical term describing the precision of a sample statistic, most commonly the sample mean. It is defined as the standard deviation of the sampling distribution of that statistic, reflecting how much the statistic would vary if the study were repeated with different samples from the same population.

For the mean, the l'erreur-type of the mean (SEM) is calculated as s divided by the square root of the sample size n, where s is the sample standard deviation (or sigma for the population standard deviation). In notation: SEM = s/√n (or SEM = σ/√n with known population variance). This quantity indicates how close the observed sample mean is expected to be to the true population mean across repeated samples.

Interpretation and use: A smaller l'erreur-type implies greater precision in estimating the population mean. It is a key component in constructing confidence intervals: the interval around the sample mean is typically mean ± (critical value) × SEM, where the critical value is taken from the z or t distribution depending on sample size and variance knowledge.

Distinctions and cautions: The l'erreur-type measures the variability of the estimate of the mean, not the variability of individual data points. It decreases as sample size grows, but it does not describe the spread of the data itself. In reporting results, researchers may present the mean with either the l'erreur-type or the standard deviation, or provide confidence intervals to convey precision.

Other notes: Similar standard errors exist for other statistics (proportions, correlations, regression coefficients), each reflecting the sampling distribution of the respective estimator. The concept rests on assumptions such as random sampling and independence.