# Statistics for Neuroscience experiment - mean and its power?

I have the following situation. In the explorative study, I had run several EEG experiments using Neurosky Mindwave (single-electrode EEG set). The device outputs real-time calculated "attention" values once per second in the range 0-100.

I had 8 participants and 4 consecutive sessions in 4 days (a session per day). The session lasted approx. 20min and for each session the participant had to complete 6 tasks (approx. 2minutes) whilst his attention has been measured using Mindwave and also the time to complete it. The hypothesis is that attention value will be increased comparing the first and the last day and secondary the time to complete the tasks will be decreased.

My question now is how to measure a possible increase of the attention correctly? The simplest is to take the mean and check if it increases and the time decreases. However, my concern is that is not powerful enough and also the time to complete the task varies among the subjects and sessions.

On the sample, the distribution of attention values look like this:

Average

SD

Do you have any suggestions how to properly check the hypothesis (i.e. that measured attention of a subject has increased comparing the first and the last day)?

attention ~ session + (1|participant) + (1|session)

This models participant and session with random intercepts to account for the non-independence of measurements caused by repeated measurements on a participant within a session. It also models session as a fixed effect. As long as you treat session as continuous here, a negative slope for session would indicate a decrease in attention or task_time over the four days.