[R] relation in aggregated data

[Joris Meys]

You examples are pretty extreme... Combining 120 data points in 4
points is off course never going to give a result. Try :

fac <- rep(1:8,each=15)
xprum <- tapply(x, fac, mean)
yprum <- tapply(y, fac, mean)
plot(xprum, yprum)

Relation is not obvious, but visible.

Yes, you lose information. Yes, your hypothesis changes. But in the
case you describe, averaging the x-values for every day (so you get an
average linked to 1 y value) seems like a possibility, given you take
that into account when formulating the hypothesis. Optimally, you
should take the standard error on the average into account for the
analysis, but this is complicated, often not done and in most cases
ignoring this issue is not influencing the results to that extent it
becomes important.

YMMV

Cheers

On Wed, Jul 7, 2010 at 4:24 PM, Petr PIKAL <petr.pikal at precheza.cz> wrote:
> Dear all
>
> My question is more on statistics than on R, however it can be
> demonstrated by R. It is about pros and cons trying to find a relationship
> by aggregated data. I can have two variables which can be related and I
> measure them regularly during some time (let say a year) but I can not
> measure them in a same time - (e.g. I can not measure x and respective
> value of y, usually I have 3 or more values of x and only one value of y
> per day).
>
> I can make a aggregated values (let say quarterly). My questions are:
>
> 1.      Is such approach sound? Can I use it?
> 2.      What could be the problems
> 3.      Is there any other method to inspect variables which can be
> related but you can not directly measure them in a same time?
>
> My opinion is, that it is not much sound to inspect aggregated values and
> there can be many traps especially if there are only few aggregated
> values. Below you can see my examples.
>
> If you have some opinion on this issue, please let me know.
>
> Best regards
> Petr
>
> Let us have a relation x/y
>
> set.seed(555)
> x <- rnorm(120)
> y <- 5*x+3+rnorm(120)
> plot(x, y)
>
> As you can see there is clear relation which can be seen from plot. Now I
> make a factor for aggregation.
>
> fac <- rep(1:4,each=30)
>
> xprum <- tapply(x, fac, mean)
> yprum <- tapply(y, fac, mean)
> plot(xprum, yprum)
>
> Relationship is completely gone. Now let us make other fake data
>
> xn <- runif(120)*rep(1:4, each=30)
> yn <- runif(120)*rep(1:4, each=30)
> plot(xn,yn)
>
> There is no visible relation, xn and yn are independent but related to
> aggregation factor.
>
> xprumn <- tapply(xn, fac, mean)
> yprumn <- tapply(yn, fac, mean)
> plot(xprumn, yprumn)
>
> Here you can see perfect relation which is only due to aggregation factor.
>
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>



-- 
Joris Meys
Statistical consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

tel : +32 9 264 59 87
Joris.Meys at Ugent.be
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