statistical significance of the mean of a mean of a mean

Considering the picture below

each values X could be identified by the indeces `X_g_s_d_h`

g = group g=[1:5]
s = subject number (variable for each g)
d = day number (variable for each s)
h = hour h=[1:24]

so X_1_3_4_12 means that the value X is referred to the

12th hour
of 4th day
of 3rd subject
of group 1

First I calculate the mean (hour by hour) over all the days of each subject. Doing that the index d disappear and each subject is represented by a vector containing 24 values.

`X_g_s_h` will be the mean over the days of a subject.

Then I calculate the mean (subject by subject) of all the subjects belonging to the same group resulting in `X_g_h`. Each group is represented by 1 vector of 24 values

Then I calculate the mean over the hours for each group resulting in `X_g`. Each group now is represented by 1 single value

I would like to see if the means `X_g` are significantly different between the groups.

Can you tell me what is the proper way?


The number of subjects per group is different and it is also different the number of days for each subject. I have more than 2 groups