The confidence interval is used to ensure accuracy of mean perception. It shows the interval of the mean value. The confidence interval calculates:
∆=t(n-1;0.05)sn,
where ∆ is the half-width of the confidence interval, n is the number of measurements, t(n-1;0.05) is the t-value for n-1 degrees of freedom at 0.05 significance level, s is the standard deviation (Johnson & Kuby, 2012).
The confidence interval is presented as Mean ± ∆. The percentage of the confidence interval refers to certainty of the mean: 95% confidence interval indicates that 95% of the population is within the interval, and 5% are out of the interval; 99% interval indicates that only 1% of the data is out of the interval. Therefore, 99% interval is wider that 95%.
The width of the confidence intervals for 99, 95, and 80% is illustrated on the pregnancy duration data found in Hand (1996). There were 1665 samples in the study, therefore n = 1665. The mean value was 39.1 week, and the standard deviation was 2.9 weeks. The calculations of the confidence interval are presented in Table 1.
Confidence intervals of pregnancy duration
As it is evident from the Table 1, the width of the confidence interval for 80% is 0.18, for 95% it is 0.28, and for 99% it is 0.36. This is because the 99% interval includes almost all values (except for 1%), while 80% interval includes only 80%. Therefore, the wider the confidence interval, the higher the accuracy.
References
Johnson, R. R., & Kuby, P. (2012). Elementary statistics. Boston, MA: Brooks/Cole Cengage Learning.
Hand, D. J. (1996). A handbook of small data sets. London [u.a.: Chapman & Hall.
