For an exercise, I have been given a measurement of mineral density at
two points of time. The task is to ascertain the rate of loss of
mineral density and estimate the change across the two points.
If the data were categorical, I would know how to calculate
incidence/risk rates, but I don't know how to obtain rates for
continous data. How would the rate of loss be ascertained in this
context? I am using SPSS.

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Request for Question Clarification by raisingmyhand-ga on 11 Dec 2003 18:41 PST

hi, 
It sounds like there are two parts to the exercise
1) Rate of density loss: To calculate the rate of loss of mineral
density, you will want to subtract density#2 from density#1 and then
divide by the time between the two time points.

2)You want to estimate the "change across the two points." Can you
clarify what you mean by this? It sounds like you are looking for a
statistical test here, and I'm not sure what hypothesis you would be
testing. Or did you just need to calculate the rate of loss?

Thanks, 
RMH

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Clarification of Question by gareth981-ga on 14 Dec 2003 09:18 PST

The null hypothesis would be that there is no different between the
measurements at time 1 and time 2, but I'm not sure if this is same as
the "rate". Is it possible to test the significance of a rate of loss?

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Request for Question Clarification by raisingmyhand-ga on 14 Dec 2003 23:53 PST

I think you can just run a paired t-test on the mean density at time 1
vs. the mean density at time 2. If the p-value is significant there
was a significant change.

It's a little strange to ask whether a rate of change is significant.
You could ask whether the rate of change is significantly different
from some other rate of change, but in this case the real question
seems to be, Was the rate of change different than zero, was there
really a change? So if you found a significant difference in the
density, I think you can say that the rate of change was
"significant."

A more natural way to summarize your findings would be to say that
there was a significant change, and the estimated rate of change was
xx ounces per year plus or minus your standard deviation.

Let me know if this helps. If not, maybe you could post your values
and the question as it appears in the exercise.

Regards,

RMH

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Clarification of Question by gareth981-ga on 15 Dec 2003 10:05 PST

That answers my question thanks, I'll do a t-test and get 95%
confidence limits for each timepoint.

I'm glad I was able to help with your question. A few related links follow: 

1) Here is a link to an SPSS tutorial demonstrating the paired t-test: 
SPSS Tutorial--How to do a paired samples t-test
http://academic.uofs.edu/department/psych/methods/cannon99/level2c.html

2) Some information on usage of the t-test: 
"The t-test gives the probability that the difference between the two
means is caused by chance."
SISA
http://home.clara.net/sisa/t-thlp.htm

3) A description of the Paired t-test: 
"The within subjects t-test is also known as the ?paired t-test?, the
?dependent t-test?, or the ?repeated measures t-test?.  The reason the
test has all of these names is because it is used in several different
situations:  the same person is in the study twice (longitudinal or
repeated measures design) or pairs of individuals are linked together
or ?yoked? (e.g., twins, or married couples) because they are
naturally linked or because the experimenter linked them as when they
are ?matched? on some score (e.g., matched on age)."
http://www.upa.pdx.edu/IOA/newsom/da1/ho_t-test.doc

Best wishes
RMH