6.1.2. Equivalence Test for Means
ttests are used to decide whether two means are significantly different from each other. If you wish to find out whether two means cannot be said to be different within predefined boundaries (lower and upper equivalence bounds), use this test. The null hypothesis tested is that the two means are not equivalent, i.e. difference between them is less than the lower equivalence bound or greater than the upper equivalence bound. If the alternative hypothesis is true, namely that the difference is between the two equivalence bounds, then the two means are said to be equivalent.
When the lower and upper equivalence bounds are 0, this test is equivalent to the standard ttest, except that here the confidence limits are reported at 1 – 2α level, rather than the usual 1 – α.
This is the parametric version of equivalence test for binomial proportions (see 6.4.3.5. Equivalence Test for Binomial Proportion).
Example
Open PARTESTS and select Statistics 1 → Parametric Tests → Equivalence Test for Means and select Before and After (C6 and C7) as [Variable]s and check all output options to obtain the following results:
Equivalence Test for Means
For Before and After
Lower Equivalence Margin = 
1.0000 
Lower Equivalence 
Difference 
Standard Error 
tStatistic 
Degrees of Freedom 
Pooled Variance 
6.6250 
4.5965 
1.2237 
30.0000 
Separate Variance 
6.6250 
4.5965 
1.2237 
29.7148 
Lower Equivalence 
1Tail Probability 
2Tail Probability 
Lower 90% 
Upper 90% 
Pooled Variance 
0.1153 

14.4265 

Separate Variance 
0.1153 

14.4289 

Upper Equivalence Margin = 
1.0000 
Upper Equivalence 
Difference 
Standard Error 
tStatistic 
Degrees of Freedom 
Pooled Variance 
6.6250 
4.5965 
1.2237 
30.0000 
Separate Variance 
6.6250 
4.5965 
1.2237 
29.7148 
Upper Equivalence 
1Tail Probability 
2Tail Probability 
Lower 90% 
Upper 90% 
Pooled Variance 
0.1153 


1.1765 
Separate Variance 
0.1153 


1.1789 
Overall 
1Tail Probability 
Lower 90% 
Upper 90% 
Pooled Variance 
0.1153 
14.4265 
1.1765 
Separate Variance 
0.1153 
14.4289 
1.1789 