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Factors affecting the width of the CI include the sample size, the variability in the sample, and the confidence level. [4] All else being the same, a larger sample produces a narrower confidence interval, greater variability in the sample produces a wider confidence interval, and a higher confidence level produces a wider confidence interval. [5]
A confidence band is used in statistical analysis to represent the uncertainty in an estimate of a curve or function based on limited or noisy data. Similarly, a prediction band is used to represent the uncertainty about the value of a new data-point on the curve, but subject to noise.
If one makes the parametric assumption that the underlying distribution is a normal distribution, and has a sample set {X 1, ..., X n}, then confidence intervals and credible intervals may be used to estimate the population mean μ and population standard deviation σ of the underlying population, while prediction intervals may be used to estimate the value of the next sample variable, X n+1.
Confidence intervals are used to estimate the parameter of interest from a sampled data set, commonly the mean or standard deviation. A confidence interval states there is a 100γ% confidence that the parameter of interest is within a lower and upper bound.
The only difference between the confidence limits for simultaneous comparisons and those for a single comparison is the multiple of the estimated standard deviation. Also note that the sample sizes must be equal when using the studentized range approach.
The same applies for the meta-analysed measure of effect: if the points of the diamond overlap the line of no effect the overall meta-analysed result cannot be said to differ from no effect at the given level of confidence. Forest plots date back to at least the 1970s. One plot is shown in a 1985 book about meta-analysis.
An estimate of the standard deviation for N > 100 data taken to be approximately normal follows from the heuristic that 95% of the area under the normal curve lies roughly two standard deviations to either side of the mean, so that, with 95% probability the total range of values R represents four standard deviations so that s ≈ R/4.
Comparison of the rule of three to the exact binomial one-sided confidence interval with no positive samples. In statistical analysis, the rule of three states that if a certain event did not occur in a sample with n subjects, the interval from 0 to 3/ n is a 95% confidence interval for the rate of occurrences in the population.