Default confidence intervals
In most instances in Q, the lower and upper bounds of confidence intervals are computed using whichever is appropriate of:
- is the observed Average, %, Column %, Row %, Probability %, Total % or Coefficient,
- is the estimated or computed Standard Error which includes any computer and/or specified design effects,
- is the th quantile of student's t-distribution,
- is , and
- is the th quantile of the normal distribution.
Confidence intervals for percentages with unweighted samples
The Agresti-Coull interval is used to computed confidence intervals for categorical questions where there are no weights, except where Weights and significance in Statistical Assumptions has been set to Un-weighted sample size in tests or when Extra deff is not 1. The Agresti-Coull interval is given by:
Confidence intervals where Weights and significance has been set to Un-weighted sample size in tests
Where Weights and significance in Statistical Assumptions has been set to Un-weighted sample size in tests, confidence intervals are computed using:
- if represents a proportion,
- is the Standard Deviation,
- is Extra deff,
- is 1 if Bessel's correction is selected for Proportions in Statistical Assumptions and 0 otherwise.
- In most situations, the statistical tests computed by Q will not correspond to conclusions drawn if attempting to construct tests from the confidence intervals. There are many reasons for this, including:
- Multiple Comparison Corrections.
- Use of non-parametric tests in Q.
- The confidence intervals having statistical properties that make them sub-optimal from a testing perspective.
- To keep this page relatively short, is used in the formulas above where it is more conventional to use .
- Whereas the The Agresti-Coull interval is an improvement on the default formula for computing the confidence intervals, the formula used when Weights and significance in Statistical Assumptions has been set to Un-weighted sample size in tests, is generally inferior and is only included for the purposes of aiding comparison with results computed using this formula in other programs.