randomization and nested designs

[MAM]

Q1 I have a question about randomization use with nested designs.

I have C nested within A and B ie C( A B) where A and B are crossed.

A and B are each at two levels so I have 4 treatment conditions. C also has two levels and there are two replicates.

I want to be sure I am not adding an additional step.


step 1. I want to randomize the nested variables numbered 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Because I have 2 replicates which use the same experimental unit I renumbered the variables as 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8

This will involve 4 randomizations one for each treatment condition.

The results of the randomizations for the 4 levels of A and B is

2 2 1 1 3 4 4 3 5 5 6 6 7 8 8 7

This is in randomized once.jpg file.



step 2. Should I randomize the 4 treatment conditions. seen in randomized once file?

This is not necessary is it? I am looking for a rule to follow.



Q2 It is not necessary to randomize blocks is it? This is a similar situation. I am not finding a rule about this in my textbooks.

Thank you.

Sincerely,
MM

 

[Miner]

Can you elaborate on the nesting? What causes factor C to be nested and how is it nested within multiple factors?

Q2: While there may be an exception, I would say no. You block to remove the effect of an undesired noise variable to make your test more powerful. You are not really interested in the effect of the block.

 

[MAM]

I am in class and need to be careful about what I submit online. The enclosed file is the design matrix for the nested design I am using. C is a fixed factor in my application. The columns represent u A B A*B C(A B).

I would not randomize factor levels A*B just the C(A B). To do so would add an unnecessary randomization. I am wondering about the interpretation however with A and B being randomized or not. This is a similar situation to Q2? It is not necessary to randomize blocks but it could be done?

I appreciate this discussion. Thank you.

Sincerely,
MM

 

[MAM]

You asked... Can you elaborate on the nesting? What causes factor C to be nested and how is it nested within multiple factors?
Please see the enclosed file for my questions. Thanks. MM

 

[MAM]

I noticed that another analysis I ran used 1,0 coding for the design matrix. I wonder if that could be the problem here? Nested designs require 1,0 coding?

MM

 

[Miner]

To be sure I understand, you are assigning 8 different pieces of equipment to the 4 combinations of A & B (2 pieces of equipment per combination) for the first replicate then reassigning the same 8 pieces of equipment to a different combination for a second replicate?

 

[MAM]

You got it correct. I went over my attached file and made it more generic changing to a discussion about cars and length and width. Pages 3 and 4 have my question clearly marked in red. I do things by hand and then check whether the software I am using gives the same results. Thank you.

 

[Miner]

Minitab does use Yates standard order. Your order is the reverse of Yates. I understand why as it makes organizational sense, but is not Yates.

 

[MAM]

I am now including a randomization scheme I developed for this problem. I am including the details as to how to randomize a nested factorial design of three factors with C nested under four combinations of A and B. I need to know if it is correct.

 

[Miner]

This looks good to me.