First of all, thank you all for your answer.
Since most of them didn't understand the situation well with my poor
question I'm explaining the background in detail before posting the
answer.
I'm analyzing the data which has done already by a
consulting company.
About 22,000 inlet located in Orange County, California need to be
cleaned every year by CalTrans(California Department of Transportation)
with a lot of budget.
CalTrans doesn't want to spend money to clean up every
inlet. So, they want to find which factor controls the solid
volume and clean up only part of inlet to reduce their budget.
Unlike usual ANOVA process the consulting company
where took care of this analysis determined factor and
level first from another similar study and found which inlet
corresponded with their study design.
I was wondering about their analysis and wanted to
analyze with different approach.
Another company cleaning all inlet in 97 and 98(Cleaning Program) have
some information. The information of data are not designed for some
statistical analysis.
However, I thought bigger data can give me a better result.
Cleaning Program data has, for example, where the
inlets are located, what the type of inlet is, and so
on. Let's talk about the first one in depth.
There're 8 levels in terms of location -freeway(16179), offramp(2912),
bridge(2505), auxiliary(231), marker(2815), street(1172),
transition(1698), onramp(2662).
Now you can see the difference the number of data in
parenthesis. There're five more categories like that.
Too many levels and too many difference of data among
levels.
All of them has significant p-value after running
ANOVA one factor at a time and I can't run ANOVA with
lacking of some combinations if I combine all factors and that's
why I tried with Factor or Cluster analysis.
I hope you understand my question better then before.
Thank you again for your reply and please let me know
if you have any advices on that.
POST(All or part?)
----------------------------------------------------------------------------
------------------------
I suggest the only reason for using part, rather than the whole, of
your
data would be if your software cannot cope with such a large sample.
But is 20000 so large these days?
It is certainly likely that many practically unimportant effects will
show
up as significant when you analyze a large sample. I guess you should
be looking at things like confidence intervals for differences between
levels.
You may find that many such differences are statistically significant,
but not practically significant. A related issue is to make sure that
you are considering appropriate sources of variation in your analysis.
I don't understand why you only want to analyze one factor at a time -
unless you mean you are considering enlarging the model one factor (or
interaction?) at a time in some stepwise manner.
A final suggestion: you might consider using criteria such as PRESS -
or related cross-valedictory criteria.
I agree with your general concern about this issue - the books are not
very clear about what to do when you have "too much" data, i.e. so much
that everything looks "statistically" significant.
I'll be interested to hear how you get on.
---------------------------------------------------------
What kind of data do you have ? I'm working on binary data and
especially on clustering binary Data. If you submitted your data to such
procedure and have the associated partition I would like to compare the
results with those generated by my program, if your data is binary of
course.
PS : Sorry, but my data is not a binary one like you see.
If you still interested in my data, however, please let me know.
----------------------------------------------------------------------------
------------------------
It seems to me that instead of merely testing for significance of
factors you may find it more profitable to construct a mathematical
model to quantify the relationship between your response variable
and the factors of interest. With so much data you should be
able to estimate parameters fairly precisely.
It is exceedingly difficult to give general advice when your
original posting is so imprecise as to the nature of the data
the number of factors of interest, what the purpose of the
investigation
is and so on.
----------------------------------------------------------------------------
------------------------
After running ANOVA every factor has significant p value.
Is it just because there are TOO many data?
No. You have to look at the absolute size of the effects. A factor that
increases your blood pressure significantly (coffee) may not be of any
real importance because the increase is about 1% and lasts only about
20 minutes.
With large samples you can identify very subtle relationships in your
data, but that's not the same as finding anything important.
---------------------------------------------------------
1) If you have enough data, you can detect almost anything. IF AND
ONLY IF, the data is truly random and independent in the other factors.
2) I question the wisdom of doing only 1 factor at a time.
3) If your intent is to discover which factors have a reasonable
(largest) effect on the response, then use 1 factor at a time to find
which ones to look at more closely. But do not consider the AoV results as
more than an indication.
4) Examine the correlations between the factors - do not get excited
about anything which has a high correlation with another factor.
'factor' = independent variable.
5) Never, never, forget the 'Hazards of happenstance data.' See
Box, Hunter & Hunter - they have a whole chapter of just that title.
I just finished an analysis of 41,254 lines of data, with many, many
columns of possible factors. You have my sympathy :)
Suggestion:
Do the 1-way AoV on each of the factors. If the factors are
continuous, do full blown regression instead. Linear should do it in most
cases.
Use graphics to confirm the numerical analysis. Always.
Check the distribution of data in the regressions - look for obvious
outliers, etc.
Select those factors which have the highest F ratios. Say, less than a
dozen of them.
Do a correlation matrix on the factors, all of them. Dump any with
correlation coefficients over 0.9.
Examine the correlation matrix for high cross-factor correlations.
Anything over about r=0.4 is suspect. Anything over 0.7 or so, remove it
from the selected high-effect factors. These coefficient values are
estimates - you may want to use different selection criteria.
Plot the remaining factors against the response(s), and suggest that
these are the ones to look at more closely.
If you can collect new data, you now know where to look. If you can't:
Select out subsets of data that fit an orthogonal design matrix, as in
a DoE design. You may not be able to get data for a complex design, so
go for 3 factors at a time, 2 levels, if need be. Leave continuous
factors as such, selecting groups that come close to the desired levels.
Analyze that data.
You may take a higher confidence in the results of this analysis than
the one you did with all the data - it's cleaner. Now make your
predictions.
Go back and collect the new data, based on the predictions you have
now.
If it fits the prediction, cheers! You won!
If it doesn't, best go back and look carefully at your work again.
Specifically, what exactly were you measuring, and with what sort of
precision. What are you _not_ measuring? I'm thinking of surveys & ratings
schemes, particularly. In fact, it would pay you to do this first, if
you can. But I assume you already have.
---------------------------------------------------------
---------------------------------------------------------
POST(Too many data...)
----------------------------------------------------------------------------
-----------------------
ANOVA or T-test. Does not matter. With large data you need not worry
about the distribution either. The outcome: significant difference.
What you are trying to do: not a good idea. (Why have a powerful test
based on many units of data, when you can have a lot of tests, each
with little power.)
Ignore the business of significance, and estimate the difference of the
two levels of the factor (with high precision).
----------------------------------------------------------------------------
-----------------------
The results should be identical. I'd use the t.
--------------------------------------------------------
~~~~~~~~~~~~~~~~~
Yongkyu Shin
Office Water Resource
CSUS Civil Eng.
~~~~~~~~~~~~~~~~~
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|