Statistics - Standard Error (SE)

1 - About

Standard Error is a measure of precision for a statistic (slope, intercept or custom calculations).

Standard error is an estimate of amount of sampling error as we typically don’t know the population parameters and that we are using a sample.

The standard error of an estimator reflects how it varies under repeated sampling (ie repeated training set).

Standard Error can be seen as the standard deviation of the error distribution. It determines the spread of the x's around the mean.

From two data set from the same population, we can get for the slope 0,5 or - 0.1 for instance. Standard Error permits to say how close is a coefficient to 0.

How much sampling error are we going to get, just due to chance. The standard error defines what you will just get due to chance.

Standard Error is the average amount of sampling error.

3 - Formulas

3.1 - Influence

Standard error and therefore sampling error are determined by:

3.2 - Bias

Standard error is biased by N as you can see in the formulas. Which means if N is increased:
  • standard error will go down.
  • the t-value will go way up
  • and the p-value will go down.

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