Standard Error (SE)
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Standard Error tells you how far a given sample parameter is from the population parameter.
I like to think of it as standard deviation, except for sampling distributions.
The below visual is from Statistics How To.
It shows that as you increase your sample size (the number of dice rolled), your sampling distribution gets closer to the population mean (and in turn, has less Standard Error (SE)).
With standard deviation held constant, the larger your sample size ⬆️, the smaller your standard error ⬇️ will be!
Your samples will be more closely representative of the population! There'll be less "error"!
Visualizing with the Empirical Rule
Scenario: Consider the population distribution of IQ scores, which is normal and has a mean (µ) of 100 and a standard deviation (σ) of 15.
σ = 15
n = 1
n = 1 because we're working with a population distribution of every individual data point in the population!
SE = 15 / √(1)
SE = 15 / (1)
SE = 15
The x-value ranges for our 68-95-99.7% groupings are separated by our Standard Error of 15!
Scenario: Consider the sampling distribution of IQ scores of sample size (n) 30. The population distribution for IQ scores is normal and has a mean (µ) of 100 and a standard deviation (σ) of 15.
σ = 15
n = 30
SE = 15 / √(30)
SE = 15 / (5.48)
SE = 2.74
The x-value ranges for our 68-95-99.7% groupings are separated by our Standard Error of 2.74!
When we increased our sample size, our standard error shrunk!
This resulted in our sampling distribution being more congregated around the population mean (since our standard error shrunk)!