23 patients suffering from bruxism (grinding of teeth) have been given a treatment. Their baseline bruxism has been measured for three nights, then they were treated for 23 nights, then again the "post" baseline was measured for three nights.
The raw data looks like this:
patient night score duration minutes of sleep
1 1 20 25 480
1 2 28 67 480
The values are:
- patient = patient number
- night = night (1 to 26)
- score = total number of bruxism attacks during that night
- duration = total seconds of bruxism (sum over all attacks) for that night
- minutes of sleep = the observed timespan (rounded to a quarter hour)
In all, there are 598 datasets, 26 consecutive nights for 23 different patients.
The interesting variables have been defined as:
nph = number of bruxism attacks per hour (score * 60 / minutes of sleep) sph = duration of bruxism in seconds per hour (duration * 60 / minutes of sleep)
The nightly means over all patients are:
nph <- c(8.808858, 8.364923, 11.932373, 9.108704, 8.135258, 6.886013, 6.379688, 6.034062, 5.731728, 5.823831, 5.128421, 4.526408, 5.145101, 5.860569, 7.691637, 5.645240, 5.151750, 7.496109, 5.375605, 5.994595, 5.650951, 6.459269, 4.490204, 7.891916, 7.684742, 7.583042)
sph <- c(23.528665, 16.382689, 29.492815, 23.752084, 19.966185, 16.104159, 15.135596, 13.218658, 11.626881, 11.321739, 13.418337, 8.391212, 9.062977, 10.665424, 9.535756, 9.925929, 9.040313, 14.635182, 8.549451, 10.346057, 9.742318, 16.437902, 7.443140, 14.204343, 12.648306, 13.401150)
These are mean number of bruxism attacks per hour (nph) and total duration of bruxism in seconds per hour (sph), over 26 nights, with treatment from night 4 to 23.
A plot of these two variables shows that their progress over the 26 nights is roughly "parallel", indicating that both react in roughly the same way to the treatment.
The filled circles are the three nights pre and three nights post treatment. Due to the scaling the maximum value for both variables fall on the same point (third night).
My question is:
How can I analyse how "parallel" these two "curves" are?