Methods and formulas for common concepts used in Equivalence Test for a 2x2 Crossover Design

All of the calculations for the equivalence test for 2x2 crossover design assume that the treatment order for sequence 1 is the reference treatment followed by the test treatment, and that the order for sequence 2 is the test treatment followed by the reference treatment.

Let Y_ijk be the response for participant k during period j in sequence i, where i = 1, 2; j = 1, 2; k = 1 ... n_i .

If the response for either period is missing for a participant, then the data for that participant is omitted from the calculations.

Let d_1k and d_2k be defined as follows:

Let and S₁ represent the sample mean and the sample standard deviation of d_1k, k = 1, ..., n₁, given by the following:

Let and S₂ represent the sample mean and the sample standard deviation of d_2k, k = 1, ..., n₂ , given by the following:

Notation

Term	Description
	Sample mean of d1k, k = 1, ..., n1
S1	Sample standard deviation of d1k, k = 1, ..., n1
	Sample mean of d2k, k = 1, ..., n2
S2	Sample standard deviation of d2k, k = 1, ..., n2

Notation

Term	Description
ν	Degrees of freedom
n1	Number of participants in sequence 1
n2	Number of participants in sequence 2

Let k₁ be the lower limit that you specify andk₂ be the upper limit that you specify. By default, the lower equivalence limit, δ₁, is given by:

and the upper equivalence limit, δ₂, is given by:

However, if you select the option to multiply your limits by the reference mean, , then the limits are given by:

is the average of the average responses for the two reference periods.