Post by Rich UlrichPost by Jinsong ZhaoHi there,
I have a experiment that have been run for more than 20 weeks. I got a
var1 var2 var3 var4 ...
0W 139.9 134.3 215.7 331.1 ...
1W 143.5 138.5 228.9 342.0 ...
2W 157.1 161.5 272.6 355.9 ...
3W 174.6 174.3 316.9 358.1 ...
6W 170.4 184.4 307.2 358.4 ...
9W 172.8 197.5 303.4 374.9 ...
12W 160.5 213.9 270.1 379.9 ...
15W 144.5 198.1 250.0 345.9 ...
18W 105.1 186.8 211.4 298.7 ...
21W 89.2 182.6 191.7 254.6 ...
according to the data, all variable change with time. I want to explore
1) if they change in a same pattern?
2) if they are not in same pattern, which are same and/or different?
3) if variables can transform to each other, is it possible to get the
quantitative relationship?
Now, to my knowledge, I don't find proper methods to solve the above
puzzles. What are your opinions?
Any suggestions or comments are really appreciated. Thanks in advance.
Computers are not yet successful at doing our thinking for us.
So far, it helps to have some intentions and expectations.
You might tell us what you are measuring, and why. Then -
WHY do they all change? What was your expectation?
What external factors are acting on them?
- Why do you have a 3-week interval, *except* you also
have 1W and 2W stuck in there? That upsets any analysis
that would want to assume equal intervals.
- You could drop the decimal place to make the numbers easier
to look at. Unless you are achieving some very high precision
of fit with something, the loss of precision will be invisible.
look pretty constant at 3W, 6W, 9W
are higher at 3 6 9 than at 0 1 2.
are lower at 18 21 than at 12 15.
So, grossly, they share a lot of shape.
A principle components analysis might show that there is
only one apparent factor among the 4 scores ... but I don't
know how reliable that indicator is, given that these are
each a time series. On the other hand, the content of a second
factor would suggest what difference is different.
If you look too hard, you will find too much. Apparently this
happened in biology in the late 19th century, with people fitting
high degree curves to few points. A Frenchman whose name I do
not recall stated, and here is the English translation,
If you give me four parameters, I can give you an
elephaant. With a fifth, also the trunk.
I do not know of any examples where it can be said that looking
at the data produced the model, rather than selecting among the
models which were already in the investigator's mind. Sometimes
ideas come into the mind which were not already there, like the
dancers in a circle which gave rise to Kekule's coming up with
the ring structure of benzene.
One should NEVER ask the statistician to make the assumptions
about the model, nor should one use a method of analysis because
someone else used it. But the statistician should ask YOU about
not only your assumptions, but also about the accuracy of your
data. Accuracy is not the right word, it is how much variation
you would expect if you could repeat the esperiment exactly.
I coclude by inserting my commandments.
I am often requested to repost my five commandments. These are
posted here without exegesis.
For the client:
1. Thou shalt know that thou must make assumptions.
2. Thou shalt not believe thy assumptions.
For the consultant:
3. Thou shalt not make thy client's assumptions for him.
4. Thou shalt inform thy client of the consequences
of his assumptions.
For the person who is both (e. g., a biostatistician or psychometrician):
5. Thou shalt keep thy roles distinct, lest thou violate
some of the other commandments.
The consultant is obligated to point out how their assumptions affect
their views of their domain; this is in the 4-th commandment. But the
consultant should be very careful in the assumption-making process not
to intrude beyond possibly pointing out that certain assumptions make
large differences, while others do not. A good example here is regression
analysis, where often normality has little effect, but the linearity of
the model is of great importance. Thus, it is very important for the
client to have to justify transformations.
There are, unfortunately, many fields in which much of the activity
consists of using statistical procedures without regard for any assumptions.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
***@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558