Margin of error: what it means and how to read it
In the report: Margin of error (±) — Half the width of a two-sided interval: the t quantile times the standard error.
How to read it
The ± after the mean: "4.72 ± 0.69".
In plain words
A teacher asked 30 students how many minutes a day they spend on homework, and the average was 40 minutes. She could not tell how close that is to the average of every student in the school. The report showed the margin of error, 6.2, so the answer reads 40 minutes, plus or minus about 6. Now she can answer: the school's average is probably somewhere from 34 to 46 minutes, up to 6 minutes below or above her number. If the margin had been 1 minute, she could say about 40 minutes and trust it much more.
How it is computed
t(1 − (1 − level)/2; n − 1) · SE; one-sided: t(level; n − 1) · SEExample
The cell with Margin of error (±) is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — all columns starting with q
=STATS_CI(Data!A1:T51, "/^q/", 0.95, "two-sided")
Where you see it
STATS_CI— Calculates the confidence interval of the mean for filtered columns (Student's t).
Related values
- Width of the interval — Upper − Lower.
- Estimate within the interval — TRUE (1) when the slope of the data lies inside the interval.
- p-value — The probability of a result at least this extreme if there were no effect (if the null hypothesis held).
- Adjusted p of the pair — The p of the pair corrected for the number of comparisons by the posthoc method.
- Lower bound of the interval — The lower bound of the confidence interval, at the level in the label.
Get it in your sheet
One formula in a cell gives the whole report, Margin of error included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)