Cochran-Mantel-Haenszel test

Hello,

I have some satellite tag time-at-depth (TAD) frequency data that I
would like some help with.

The data was transmitted via satellite as percent time spent in each of
7 depth bins (0m, 0-1m, 1-10m, 10-50m etc.), binned over 6-hour
intervals.  I categorized each row of data corresponding to a date and
time into summer vs. winter, and day vs. night, and then summed and
averaged the given % for each depth bin.  My data looks like this (for
one individual, HG03):

HG03.dat
   Season  Time Depth    Sum       Avrg
1    summ   day     0   17.2  0.1702970
2    summ   day     1   23.9  0.2366337
3    summ   day    10  868.5  8.5990099
4    summ   day    50 2698.2 26.7148515
5    summ   day   100  419.7  4.1554455
6    summ   day   200  266.1  2.6346535
7    summ   day   300 1668.6 16.5207921
8    summ   day   500 4138.2 40.9722772
9    summ night     0  283.6  5.7877551
10   summ night     1  229.1  4.6755102
11   summ night    10  479.3  9.7816327
12   summ night    50  761.9 15.5489796
13   summ night   100  235.8  4.8122449
14   summ night   200   40.9  0.8346939
15   summ night   300  763.1 15.5734694
16   summ night   500 2106.1 42.9816327
17   wint   day     0    0.0  0.0000000
18   wint   day     1    0.0  0.0000000
19   wint   day    10    0.0  0.0000000
20   wint   day    50    0.0  0.0000000
21   wint   day   100    7.9  1.1285714
22   wint   day   200   92.1 13.1571429
23   wint   day   300    0.0  0.0000000
24   wint   day   500  600.0 85.7142857
25   wint night     0   43.9  1.7560000
26   wint night     1    0.3  0.0120000
27   wint night    10    0.3  0.0120000
28   wint night    50    0.8  0.0320000
29   wint night   100   10.5  0.4200000
30   wint night   200   51.6  2.0640000
31   wint night   300  411.4 16.4560000
32   wint night   500 1981.2 79.2480000

I wanted to test whether significant differences existed between depth
in summer vs. winter, and day vs. night, controlling first for season
and then for time of day.  I carried out a Cochran-Mantel-Haenszel test,
using Average Frequency (Avrg) as the dependent variable (2x2x8
contingency table).

ct<-xtabs(Avrg~Time+Depth+Season,data=HG03.dat)
mantelhaen.test(ct)

        Cochran-Mantel-Haenszel test

data:  ct
Cochran-Mantel-Haenszel M^2 = 28.4548, df = 7, p-value = 0.0001818

ct<-xtabs(Avrg~Season+Depth+Time,data=HG03.dat)
mantelhaen.test(ct)

        Cochran-Mantel-Haenszel test

data:  ct
Cochran-Mantel-Haenszel M^2 = 111.5986, df = 7, p-value < 2.2e-16

However, I'm not sure if these results are valid, since my raw data is
already in frequencies, not in counts.  When I used Sum as the dependent
variable, I obtained different results.

I am at a loss on how to proceed.  If anyone has any ideas, they would
be greatly appreciated.

Thanks!
Romney


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