Let “A” and “B” denote the two treatment values. Define the following notation:

So and are all observed at treatment level A, and and are all observed at treatment level B.

Define the *period difference* for an observation as the difference between period 1 and period 2 response values:

for and . Similarly, the *period ratio* is the ratio between period 1 and period 2 response values:

The *crossover difference* for an observation is the difference between treatment A and treatment B response values:

Similarly, the *crossover ratio* is the ratio between treatment A and treatment B response values:

In the absence of the IGNOREPERIOD option in the PROC TTEST statement, the data are split into two groups according to treatment sequence and analyzed as a two-independent-sample design. If DIST=NORMAL, then the analysis of the treatment effect is based on the half period differences , and the analysis for the period effect is based on the half crossover differences . The computations for the normal difference analysis are the same as in the section Normal Difference (DIST=NORMAL TEST=DIFF) for the two-independent-sample design. The normal ratio analysis without the IGNOREPERIOD option is not supported for the AB/BA crossover design. If DIST=LOGNORMAL, then the analysis of the treatment effect is based on the square root of the period ratios , and the analysis for the period effect is based on the square root of the crossover ratios . The computations are the same as in the section Lognormal Ratio (DIST=LOGNORMAL TEST=RATIO) for the two-independent-sample design.

If the IGNOREPERIOD option is specified, then the treatment effect is analyzed as a paired analysis on the (treatment A, treatment B) response value pairs, regardless of treatment sequence. So the set of pairs is taken to be the concatenation of and . The computations are the same as in the section Paired Design.

See Senn (2002, Chapter 3) for a more detailed discussion of the AB/BA crossover design.