Equivalence Test for 2x2 Crossover Design

Test

  

In addition to calculating the confidence interval (CI) for the difference (or ratio), Minitab also performs a hypothesis test. If you use the default method to calculate the CI, then both the test and the CI lead to the same conclusion about claiming equivalence.

The results for the hypothesis test include p-values for two separate null hypotheses:

·    The difference is less than or equal to your lower limit for equivalence.

·    The difference is greater than or equal to your upper limit for equivalence.

If both null hypotheses are rejected, then the difference falls within your equivalence interval and you can claim that the means for the treatments are equivalent.

Example Output

Test

 

Null hypothesis:         Difference ≤ -0.42503 or Difference ≥ 0.42503

Alternative hypothesis:  -0.42503 < Difference < 0.42503

α level:                 0.05

 

Null Hypothesis        DF  T-Value  P-Value

Difference ≤ -0.42503  15   1.7149    0.053

Difference ≥ 0.42503   15  -12.303    0.000

 

The greater of the two P-Values is 0.053. Cannot claim equivalence.

Interpretation

For the antacid data, the highest p-value is 0.053, which is greater than the a level of 0.05. These results indicate that the difference is not within your equivalence limits of -0.425 and 0.425. Thus you cannot conclude that the two antacids are equally effective at raising stomach pH.