Confidence Interval

From Q
Jump to navigation Jump to search

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:

x¯±tα/2,dfsx¯ or x¯±zα/2sx¯

where:

x¯ is the observed Average, %, Column %, Row %, Probability %, Total % or Coefficient,
sx¯ is the estimated or computed Standard Error which includes any computer and/or specified design effects,
tα/2,df is the α/2th quantile of student's t-distribution,
df is n1, and
zα/2 is the α/2th 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:

x¯~±zα/2x¯~(1x¯~)n~

where:

n~=n+zα/22,
n is Base n,
x¯~=x+zα/222n~, and
x 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:

x¯±tα/2,n1sx¯

where:

sx¯=deffx¯(1x¯)nb if x¯ represents a proportion,
sx¯=sxdeffn otherwise,
sx is the Standard Deviation,
deff is Extra deff,
b 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, s is used in the formulas above where it is more conventional to use σ.
  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.