time changing distributions, what is significant ?

Dear fellow statisticians,
I am struggling with the task of quantifying the "statistical
significance" of changes in a discrete distribution over time. I am
not even sure whether this is a well-posed problem to begin with. If I
was to measure e.g. the age distribution of people entering a building
on a daily basis, I would naturally observe fluctuations in that
distribution. Clearly, small variations would be interpreted as
"sampling noise" whereas major shifts would indicate sth. more
substantial. How would I quantify this ?
Would a ChiSquare test be an appropriate test for testing overall
stationarity ? Or a two-way ANOVA decomposition ? Or should I look at
the variance of a multinomial distribution instead ?
Also, what if wanted to test specific days for significant deviation
from my Null model instead of overall ?

Thanking you!

Markus

.

Relevant Pages