Statistical tests of equivalence

Wellek (2003) illustrates the application of a series of familiar statistical tests corresponding to null and alternative statistical hypotheses of general form

H0: $$\theta \leq $$-t or $$\theta \geq$$ t and HA : -t $$ \leq \theta \leq$$ t

where $$\theta$$ is a function of parameters of interest (e.g. a difference between two group means) and t is the effect size of minimal interest (e.g. minimum difference in a pair of group means which is of clinical interest).

Equivalence tests are also known as reverse tests because they switch around the 'usual' hypotheses of form

H0: $$\theta$$ = t and HA: $$\theta \ne$$ t

and so the emphasis is on verifying rather than rejecting hypotheses such as equality of group means or zero correlations. Failing to reject a null hypothesis is not the same as showing it to be valid.

SAS and FORTRAN programs with help guides are available [http://zima04.zi-mannheim.de/wktsheq/ for free download] which run equivalence analyses for other statistical tests using methodology described in Wellek (2003). It is easier to run the SAS programs. After downloading change the file name from *.sas to *.sss before clicking on the icon. CBSUERS: If SAS is not on your PC it can be added on by one of our CBSU IT people.

• [:FAQ/mageq: Suggested effect sizes, t]
• [:FAQ/tequi: R code for equivalence test for (un)paired t-tests]
• [:FAQ/zequiv: R code for equivalence test for one sample z-test.]
• [:FAQ/bin2: R code for equivalence test for two unrelated proportions]

• [:FAQ/mcnequiv:R code for equivalence test using McNemar's test.]

• [:FAQ/oneweq: R code for equivalence test for one-way ANOVA.]

References

Lew MJ (2006) Principles: When there should be no difference - how to fail to reject the null hypothesis. Trends in Pharmacological Sciences 27(5) 274-278. [http://www.sciencedirect.com/science Available to CBSU users on ScienceDirect.]

Wellek S (2003) Testing of statistical hypotheses of equivalence. Chapman and Hall/CRC Press.