Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Which statistical method should be used?
Replies: 1   Last Post: May 30, 2013 7:54 PM

 Messages: [ Previous | Next ]
 Jinsong Zhao Posts: 22 Registered: 11/27/10
Which statistical method should be used?
Posted: May 30, 2013 6:21 AM

Hi there,

We design a experiment with 2 factors. One factor is SR, which has 3
levels, RS, WS, and CS. Another factor is WFPS, which has 2 levels, 50%
and 90%. The response variable is the concentration of nitrate, which
will be measured at 0, 1, 2, ..., 7, 9, 11, ..., 31 days (totally, 20
times).

The experiment could be performed with 4 different scenarios:

(1) The complete random design. Each treatment have 3 replications. So,
we have 3 * 2 * 3 (i.e., SR * WFPS * replications) experiment units. The
response variable is measured from the sub-samples obtained from each
unit at each sampling time.

(2) The same design as the above, but the number of experimental units
will be 3 * 2 * 3 * 20 (i.e., SR* WFPS * replications * sampling times).
At day 0, 3 * 2 * 3 units will be measured for the response variable,
and then discarded. At day 1, another 3 * 2 * 3 units will be measured
and discarded. And do the same thing until the experiment ends.

(3) The complete block design for the scenario (1). It means that there
is no replication. Each replication is a block. In each block, there are
3 * 2 (i.e., SR * WFPS) units.

(4) The complete block design for the scenario (2). It also means that
there is no replication. Each replication is a block. In each block,
there are 3 * 2 *20 (i.e., SR * WFPS * sampling times) units.

A typical experimental results (only for WFPS = 50%) is listed following:

Day RS WS CS
0 0.272 0.272 0.272
1 0.875 2.392 2.430
2 0.260 0.733 1.375
3 0.417 1.734 4.676
4 0.310 0.929 4.029
5 0.325 0.975 3.936
6 0.314 1.010 3.105
7 0.354 0.896 2.667
9 0.407 0.855 2.659
11 0.481 0.917 2.057
13 0.288 0.860 1.575
15 0.294 0.710 1.378
17 0.551 0.757 1.316
19 0.228 0.662 1.049
21 0.294 0.688 1.034
23 0.126 0.697 0.676
25 0.064 0.437 0.671
27 0.081 0.600 0.824
29 0.148 0.437 0.790
31 0.553 0.874 1.179

I have read some papers that are similar with our experiment. And
(non-)linear mixed effect model are commonly used. However, I don't know
whether this method is suitable in our situation, for the data is not
varied in monotonic way.

Another question is when choosing the statistical method for the 4
scenarios, what I should paid more attention.

The third question is which book covered this kind of experiment.

Thank you very much for your consideration on this post. And any
suggestions or comments will be really appreciated.

Regards,
Jinsong

Date Subject Author
5/30/13 Jinsong Zhao
5/30/13 Ray Koopman