Standard error: what it means and how to read it
In the report: se — The standard error of the estimate: how much it would vary from sample to sample.
How to read it
The precision of the difference: t is the difference divided by it, and the interval is built around it. Rarely reported on its own.
In plain words
A shop owner looked at 100 bills and found that the average was 40 dollars. She wondered how far another 100 bills could land from 40. She asked for se, the standard error, and got 2. Now she knows that her 40 is known to within about 2 dollars, so another 100 bills would usually average somewhere around 38 to 42. With 400 bills se would come out 1, so the average would be known twice as well. It is rarely written on its own, but the range around the average and the test of a difference are built on it.
Example
The cell with se is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- —
=STATS_PAIRED(Data!A1:T51, "before,after",0.95,"two-sided") - —
=STATS_INDEPENDENT(Data!A1:T51, "y,x1", "welch",0.95) - —
=STATS_ONE_SAMPLE(Data!A1:T51, "score", 5, 0.95,"two-sided")
Where you see it
STATS_PAIRED— Paired-samples t-test for two related measurements (e.g., pre vs post).STATS_INDEPENDENT— Independent-samples t-test for two groups: the two selected columns are the groups.STATS_ONE_SAMPLE— One-sample t-test against mu0.STATS_CI— Calculates the confidence interval of the mean for filtered columns (Student's t).STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Number of values — The number of values (rows) the result is computed on.
- Sum — The sum of the values; empty for a column without a single number (the sign . in a STATS_COMPUTE row where no item is answered), not 0.
- Mean — The arithmetic mean: the sum divided by n.
- Median — The middle of the sorted values; with an even n, the mean of the two middle ones.
- Minimum — The smallest value.
Get it in your sheet
One formula in a cell gives the whole report, Standard error included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)