Two-Sample Equivalence Test

Test

  

In addition to 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 products are equivalent.

Example Output

Test

 

Null hypothesis:         Difference ≤ -0.5 or Difference ≥ 0.5

Alternative hypothesis:  -0.5 < Difference < 0.5

α level:                 0.05

 

Null Hypothesis    DF  T-Value  P-Value

Difference ≤ -0.5  12   1.8637    0.044

Difference ≥ 0.5   12  -3.0566    0.005

 

The greater of the two P-Values is 0.044. Can claim equivalence.

Interpretation

For the cat food data, you can reject both null hypotheses because the p-values for both tests (0.044 and 0.005) are less than the a level of 0.05. These results indicate that the difference is within your equivalence limits of -0.5 and 0.5. Thus you can claim that amount of protein in the discount cat food is equivalent to the amount of protein in the original formulation.