Prerequisites
Effect estimates, standard errors, normal intervals, and covariance.
To compare two effects, estimate their difference directly. A significant estimate in one group and a nonsignificant estimate in another do not establish a significant difference. For independent estimates, variances of their difference add.
Worked example
Estimates 3 and 3 can receive different significance labels if their standard errors differ. The estimated contrast is still zero; the labels are not a test of that contrast.
Model and Assumptions
Fictional independent group-effect estimates on the same scale: A=4 with SE=1.5; B=3 with SE=2. A normal 95% interval is estimate +/- 1.96*SE. The abstract argues that the intervention works differently because only A's interval excludes zero.
Further inquiry
Reconstruct both separate intervals and the contrast interval. Then repeat the contrast calculation with covariance 1 and explain why neither nonsignificance nor an interval containing zero proves practical equivalence.
Review criteria
- Distinguish separate null tests from a contrast test.
- Use variance 4.25 when covariance is 1.
- State a substantive equivalence margin before making an equivalence claim.