test for decreasing response

Hi,

sorry for the bad subject line...

I was wondering if somebody can give me some statistical advice
on following problem?

Design:
-------

10 individuals were tested.

Each individual was tested 10 times sequentially (time between
measurements equidistant at 10s). The response variable X seems
to decrease as this simplified scatterplot illustrates (only 3
individuals and 6 time points are displayed):


r |
e | x
s | o
p | l x
o |
n | o o x
c | x x
e | l o x
| l l l o
X | o l
|
-----------------------------> time
1 2 3 4 5 6 ...


legend: x=individual1, o=individual2, l=individual3

Goal:
-----

The main purpose of the experiment is to show that the response
variable decreases with time. The plots clearly show this. Which
statistic procedure is best to support this hypothesis?


The data is neither normally distributed (Shapiro test) nor are
variances homogeneous (Bartlett test).

1.) Using parametric tests anyway:
----------------------------------

ANOVA followed by posthoc tests (ie TukeyHSD, Scheffe, etc).

Regression analysis?

2.) Using non parametric tests:
-------------------------------

Kruskal-Wallis rank sum test (H0 is rejected).

Regression analysis?

3.) Using Generalized linear model (GLM):
-----------------------------------------

Seems easiest, since normality and homogeneity of variances are
not a prerequisite.

There is however a limitation I have found:

,----[ http://tinyurl.com/c5gpn ]
| Limitations:
| 1. requirement of independence of the observations repeated
| measurements on the same subject or over time induce
| correlations which cannot adequately analyzed within the GLM
| frame.
`----


Further questions:
------------------
Would this design be considered a longitudinal study or maybe even a
time series?


If anybody can comment on or suggest a reasonable approach for this
kind of problem I would be very grateful.

TIA

Patrick
--
Linus: I'll throw the ball, see?
Then you go bounding after it and bring it back!
Snoopy: Maybe we should think about this a little more.

.

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