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Standardised deviations test

F

forza_bologna

Member
Hi,


I have a question related to chapter 12, more exactly it refers to standardised deviations test.

I read in the Course Notes the following:
"If there is heterogeneity within the age groups or death are not independent, the variance will be (respectively) smaller or greater than we would expect if our underlying model were correct."

Why is that?

Many thanks,
 
Hi forza_bologna,

http://www.acted.co.uk/forums/showthread.php?t=9840

Take a look at this excellent thread, question posted and answered by MIliev - well done, MIliev!

My take on the heterogeneity is that the more there is of it, the less likely you are to come up with a rubbish estimate of qx for a particular age group just from the random chance of getting a bunch of high-risk or low-risk lives. With more heterogeneity, we are closer to a stratified sample of the entire population for that age group.

If deaths are not independent then there is more variance.
eg 10 independent lives # deaths ~ Bin(10,q)
Variance = 10q(1-q)
All 10 lives die together # deaths = 10* X where X~Bin(1,q)
Variance = 100q(1-q)

(10 times more risk!)

Good luck!
John
 
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