Syntax
CONFIDENCE.T(alpha, standard_dev, size)
| Parameter | Description |
|---|---|
| alpha | Parameter of the CONFIDENCE.T function. |
| standard_dev | Parameter of the CONFIDENCE.T function. |
| size | Parameter of the CONFIDENCE.T function. |
Examples
Small sample CI
Formula
=CONFIDENCE.T(0.05, 3.2, 15)
Returns 1.77 — a wider margin than CONFIDENCE.NORM(0.05, 3.2, 15) which gives 1.62. The t-distribution accounts for extra uncertainty with only 15 samples.
Clinical trial
Formula
=CONFIDENCE.T(0.05, STDEV(B2:B26), 25)
Calculates the margin of error for a 25-patient trial using the sample standard deviation. Appropriate because n is small and sigma is estimated.
Converges to normal for large n
Formula
=CONFIDENCE.T(0.05, 5, 1000)
With n=1000, the result is nearly identical to CONFIDENCE.NORM because the t-distribution converges to the normal distribution for large samples.
Common Errors
#NUM!
Alpha not between 0 and 1, standard deviation not positive, or sample size less than 1.
#VALUE!
Non-numeric arguments.
Tips
Default choice for estimated std dev
If you compute the standard deviation from your sample (rather than knowing the population value), CONFIDENCE.T is technically correct even for large samples.
Wider than CONFIDENCE.NORM
CONFIDENCE.T always gives a larger margin than CONFIDENCE.NORM for the same inputs. The difference is substantial for small n but negligible for n > 100.
Degrees of freedom = n - 1
Internally, CONFIDENCE.T uses n-1 degrees of freedom. More degrees of freedom means the t-distribution is closer to the normal distribution.
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