Syntax
CONFIDENCE(alpha, standard_dev, size)
| Parameter | Description |
|---|---|
| alpha | Parameter of the CONFIDENCE function. |
| standard_dev | Parameter of the CONFIDENCE function. |
| size | Parameter of the CONFIDENCE function. |
Examples
95% confidence interval margin
Formula
=CONFIDENCE(0.05, 2.5, 50)
Returns 0.693 — with alpha=0.05 (95% confidence), std dev=2.5, and sample size=50, the margin of error is about 0.69 units.
Building the interval
Formula
=AVERAGE(B2:B51) + CONFIDENCE(0.05, STDEV(B2:B51), 50)
Adds the margin of error to the sample mean to get the upper bound of a 95% confidence interval.
Narrower interval with larger sample
Formula
=CONFIDENCE(0.05, 10, 400)
Returns 0.98. With 400 samples, the margin is small. Compare to CONFIDENCE(0.05, 10, 25) which returns 3.92 — larger samples give tighter intervals.
Common Errors
#NUM!
Alpha must be between 0 and 1 (exclusive), standard deviation must be positive, and sample size must be at least 1.
#VALUE!
Non-numeric arguments.
Tips
Alpha = 1 - confidence level
For a 95% confidence interval, alpha = 0.05. For 99%, alpha = 0.01. For 90%, alpha = 0.10.
Assumes known population std dev
CONFIDENCE uses the normal distribution, which assumes you know the population standard deviation. If you are estimating it from the sample, use CONFIDENCE.T instead.
Margin shrinks with sqrt(n)
To halve the margin of error, you need 4x the sample size. The margin is proportional to 1/SQRT(n).
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