Question

What is a standard error?

What does it mean for an estimate to be "statistically significant"?

Answer 1

Standard error is the measure of variability in different samples from a population. For any given measure, standard error helps compare a sample and the population it represents. In case of the measure of mean it is called standard error of the mean (SEM). It represents sample mean dispersion around population mean.

Standard Error = \( s/\sqrt{n} \)s / √ (n)\( s / √ (n) \)

Where s = sample standard deviation and n= sample size.

 

In statistical hypothesis testing,  statistical significance of a finding implies it being the result of causal factor being tested rather than the finding arising by mere chance. A claim regarding a population is assessed by tests of significance based on collected sample data and the claim is supported or rejected. At a given significance level (usually α=0.05), a statistically  significant result means it is a real result and is not attributed to chance; the null hypothesis (H₀) is rejected in favour of alternate hypothesis (H_a).

 

Standard error is the measure of sample variability and helps compare sample and population measures. Statistical significance is a way of determining an estimate's reliability.