# Advice needed with hypothesis testing of experiment with crossover design

I have conducted a randomized, single-blinded experiment, stimulation vs sham, two-session, within-subject, cross-over design.

In each of the experimental sessions, participants alternately received either real stimulation or sham stimulation. In each session two measurements are recorded:

heart rate - one-dimensional (frequency), average of two separate measurements made during each session (a baseline measurement without stimulation, nor sham stimulation, and a measurement with stimulation or sham stimulation). Averages are calculated for baseline and stimulation and for each condition.

1. brain activity
• three-dimensional (three different brain waves), measured once each session. Averages are calculated for each brain wave in each condition.

For example, average baseline HRV in session 1 (stimulation condition) was 128. When receiving stimulation it was 167. Brain wave 1 had an average of 67 in this session, brain wave 2 an average of 50, and brain wave 3 an average of 80. In the second session (sham condition) baseline HRV was 132 and 133 when receiving sham stimulation. Brain wave 1 had an average of 90 in this session, brain wave 2 an average of 80, and brain wave 3 an average of 100.

It is hypothesized that in the active stimulation condition, two of three brain waves is increased (brainwave 1 and 3). These brainwaves are not going to be compared to each other, but between conditions (active vs sham). E.g. brain wave 1 in session 1 vs. brain wave 1 in session 2.

The heart (HRV) is thought to increase in the active condition, and this should be compared with baseline (in the beginning of the session, without stimulation) and sham stimulation. Since the stimulation is thought to active afferent (central) brain pathways, it is possible that both parameters (Brain activity and HRV) are stimulated and covariate. Though, seeing changes in HRV is a lot less plausible based on previous research, so I guess I want to analyse them as separate measures, and if both show significant changes, maybe a covariance analysis is in place...

Question: How do I optimally calculate if there are significant differences between the conditions?

Is this just done by paired t-tests? What further steps can I take? I would also like to know if there's a correlation between each brain wave and HRV.