# Confidence Interval

From Q

## Contents |

## Default confidence intervals

In most instances in Q, the lower and upper bounds of confidence intervals are computed using whichever is appropriate of:

or

where:

- 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:

where:

## 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:

where:

- if represents a proportion,
- otherwise,
- is the Standard Deviation,
- is Extra deff,
- is 1 if
**Bessel's correction**is selected for**Proportions**in Statistical Assumptions and 0 otherwise.

## Notes

- 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.