Statistics
Margin of error
The half width of the interval. The z score sets the confidence level.
The Formula
margin = z x SE
The half width of the interval. The z score sets the confidence level.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| E | Margin of error | same as data | Half the width of the interval. |
| z | Critical value | ratio | 1.645 for 90 percent, 1.96 for 95, 2.576 for 99. |
| SE | Standard error | same as data | Spread of the sample mean. |
What Each Symbol Means
Esame as data
Margin of error
Half the width of the interval.
zratio
Critical value
1.645 for 90 percent, 1.96 for 95, 2.576 for 99.
SEsame as data
Standard error
Spread of the sample mean.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a confidence interval page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Confidence Interval, filed under Math. Every number the guide produces comes from substituting into this one line.