Not sure which test to use

Hello everyone,

Does someone know which test i need to use to compare the means (multiple) of two groups when there is a research where there are 2 groups undergoing 2 interventions, since it's a crossover desgin, every particpant will do both of the interventions. The means that need to be compared are mutiple bloodmarkers.

"The crucial variable for analysis is the within-subject difference in outcome between the two study periods. In order to assess the difference between treatment effects, a statistically valid test for independent samples has to be carried out with the values obtained for this variable.

The assumption that the washout phase was long enough to rule out a carryover effect should be checked in a preliminary test. To this end, the sum of the values measured in the two periods is calculated for each subject and compared across the two sequence groups by means of another test for independent samples. If this test yields a statistically significant result, the usual test for differences between the effects of the two treatments should not be applied."

Or maybe some useful material can be found here.

With kind regards