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 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.

• Suggested effect sizes, t

• R code for equivalence test for (un)paired t-tests

• R code for equivalence test for one sample z-test

• R code for equivalence test for two unrelated proportions

• R code for equivalence test using McNemar's test

• 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. Available to CBSU users on ScienceDirect.

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