5.1.2. Confidence Intervals
Confidence intervals for mean, median, geometric and harmonic means (t or Zintervals) and intervals for variance and standard deviation can be computed. Data input is in multisample format (see 5.0.1. Multisample Data Types).
By default, intervals for means are based on the tdistribution with a critical value of . It is possible to calculate intervals using the standard normal distribution with a critical value of . The confidence level 1 – α can be defined in Variable Selection Dialogue.
Mean:
Median: The methods used in computing the median and its confidence limits are reported in the header. These methods can be changed using the dialogues of the Quantiles (Percentiles) procedure (see sections 5.1.3.1. Quantile Methods and 5.1.3.2. Quantile Interval Methods).
Geometric Mean: Assuming Ln(X_{i}) i = 1,…, n are normally distributed, the limits are defined as:
where G is the geometric mean and the term a_{G} (which is not the standard error of geometric mean) is defined as:
Harmonic Mean: Assuming 1/X_{i} i = 1,…, n are normally distributed, the confidence interval is:
where H is the harmonic mean and the term a_{H} (which is not the standard error of harmonic mean) is defined as:
Variance: The 100(1 – α)% confidence interval for the variance is constructed using the chisquare distribution with n – 1 degrees of freedom:
where s^{2} is the sample variance.
Standard Deviation: The lower and upper limits are the square roots of corresponding limits for variance.
Example
Open ANOVA and select Statistics 1 → Descriptive Statistics → Confidence Intervals and from the Variable Selection Dialogue select AUC (C20) as [Variable] and Treatment (S19) as [Factor] and click [Finish].
Confidence Intervals
Data variable: AUC
Subsample selected by: Treatment = A
Number of Cases: 12

Value 
Lower 95% 
Upper 95% 
* Mean 
209.4167 
169.1754 
249.6580 
** Median 
200.5000 
154.0000 
290.0000 
* Geometric Mean 
199.8379 
161.9368 
246.6098 
* Harmonic Mean 
189.4269 
153.3584 
247.6786 
Variance 
4011.3561 
2012.9935 
11563.8961 
Standard Deviation 
63.3353 
44.8664 
107.5356 
* tinterval
** Quantile Method: Simple Average, Interval Method: Normal Approximation
Data variable: AUC
Subsample selected by: Treatment = B
Number of Cases: 12

Value 
Lower 95% 
Upper 95% 
* Mean 
167.1667 
137.7396 
196.5937 
** Median 
165.5000 
133.0000 
210.0000 
* Geometric Mean 
160.4173 
131.3584 
195.9047 
* Harmonic Mean 
152.6247 
123.7428 
199.0937 
Variance 
2145.0606 
1076.4422 
6183.7587 
Standard Deviation 
46.3148 
32.8092 
78.6369 
* tinterval
** Quantile Method: Simple Average, Interval Method: Normal Approximation
Go back to the Variable Selection Dialogue omit Treatment (S19) from the [Factor] list and select the Z interval option on the next dialogue.
Confidence Intervals
Data variable: AUC
Number of Cases: 24

Value 
Lower 95% 
Upper 95% 
* Mean 
188.2917 
164.9290 
211.6543 
** Median 
187.5000 
154.0000 
220.0000 
* Geometric Mean 
179.0460 
156.5802 
204.7352 
* Harmonic Mean 
169.0460 
146.8020 
199.2349 
Variance 
3410.0417 
2059.8730 
6710.0662 
Standard Deviation 
58.3956 
45.3858 
81.9150 
* Zinterval
** Quantile Method: Simple Average, Interval Method: Normal Approximation