Confidence Interval

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On SUMMARY tables, the Statisics - Cells menu contains options to show the Upper Confidence Interval and Lower Confidence Interval. On a crosstab, there are no built-in options, but you can use the following rules to add confidence intervals to the table:


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:

,
is Base n,
, and
is n.

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

  1. 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.
  2. To keep this page relatively short, is used in the formulas above where it is more conventional to use .
  3. 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.