7
votes
adonis in vegan: order of variables or use of strata
As you've noted yourself, by running two adonis models with your fixed factors inverted you see that both the variance assigned to each factor, and the P-values differ each time. This occurs in ...
- 345
7
votes
Accepted
What is a Randomized Complete Block Design. How do we create one and analyze it?
There are a number of different designs that use the term "Randomised Complete Block Design", but they are all based on a very basic idea, that of blocking. A block is just another factor (a ...
- 65.8k
7
votes
Accepted
Randomized blocking design and Mixed Models
The smallest observational units in your experiment is the plots. There is indeed a random term associated with plots, that is the usual observational or residual variance. As that is is all models, ...
- 82.8k
6
votes
Accepted
How should I analyse this experiment with two blocking factors
Is this another type of Randomized Complete Block Design?
It is very closely related but this seems to be a Latin Square design, not a RCB design, though we could say that it's an extension of the ...
- 65.8k
4
votes
Accepted
Appropriate "semi-paired" t-test
In experimental design your batches of material is called blocks. Then the blocks/batches are modeled as a random effect, and the A/B-instrument comparison is done within blocks.
You can solve this ...
- 82.8k
4
votes
Accepted
Do I want a mixed model for fractional factorial designs?
I have heard some arguments, that a mixed model is not appropriate for this design, since there is no theoretically interesting variance at the lower level, since the treatment combinations are ...
- 65.8k
4
votes
Block design or completely randomized?
In your case, the "treatment" is the condition that you assign to the subjects at random. As Bruce explained, this is simply a randomized assignment of the treatment but not a blocking ...
4
votes
3 Treatment Agronomic Experiment: Latin Square or Randomized Complete Block Design with 4 replicates?
It is more natural to compare designs with equal number of observations, so I will compare a $3\times 3$ latin square (LSQ) with a thrice replicated RCBD. The LSQ leaves 2 df (defgrees of freedom) for ...
- 82.8k
4
votes
Accepted
Difference between blocking and split plot-design?
What is needed to understand is what split plot design does and how it is different from blocking.
Consider a factor $A$ with $p$ levels. If an RBD is constructed with, say, $r$ blocks, $p$ levels of $...
- 10.3k
4
votes
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Relationship between blocks, factors and treatments
I think your understanding is good as a start. I am no great fan of the Montgomery book (the other you mention I do not know), a useful supplement would be Box, Hunter & Hunter: Recommended books ...
- 82.8k
3
votes
Accepted
Restricting block size in a factorial experiment
This would be an incomplete block design. If you are conducting a 2^4 experiment, a complete block would need to have 16 observations in each block, but here you are restricted to 8 per block. ...
- 11.6k
3
votes
Is there an experimental design that tests three different factors?
If you need to test each device and combinations, you would need to test all $2^3$ combinations. To test this for each person would take 80 trials, not thirty. (The test plan you have would only ...
- 1,640
3
votes
How to generate a Randomized Complete Block Design?
The agricolae package is useful for this task. In your case:
...
- 11.6k
3
votes
Accepted
Experimental Design Problem with Goofy Constraints
First, the problem of maximizing $\sum B_{mf}$ is a knapsack problem, there does exist at least one R package for such problems, adagio. If $B_{mf}$ is undefined ...
- 82.8k
3
votes
Accepted
Block design or completely randomized?
If I understand your description, this is a completely randomized design. Of course, if you're sampling without replacement, the number of options on each draw
dwindles as you proceed. Finally, the ...
- 57.6k
3
votes
ANOVA with blocking question
What you have is a $2^2$ factorial design twice replicated. That means that the two factors, that you call blocks, are orthogonal. So if you compare brands by means of ratings, the comparison is ...
- 82.8k
3
votes
Does this design indeed raise concerns about pseudoreplication?
Seems to me that there are two questions that your experiment might be used to answer. The first is the most obvious: does the supplement affect the weight gains of cows. For that question you are ...
- 17.2k
2
votes
Is ANOVA always more powerful than a two-sample t-test when the data can be blocked?
Using terminology from design of experiments, you seem to have a randomized block experiment (assuming suitable randomization was done) where the blocks are defined by the operators, and you have two ...
- 82.8k
2
votes
Accepted
To keep or not to keep ... block effect when not significant?
You should analyze according to the design, which was blocked. So, keep the blocks in the model.
Doing otherwise, that is, removing blocks from the model, inflated the degrees of freedom, and tests do ...
- 82.8k
2
votes
Examples of connected designs in DOE
We can draw the block design as a graph, in the meaning of graph theory. I used the igraph package in R to draw: (this is your ...
- 82.8k
2
votes
Is it appropriate to consider the interactions between blocking and fixed factors
If you want account for the possibility that treatment effects differ between blocks, you should not specify this as a fixed interaction, but as a random slope. See http://www.bristol.ac.uk/cmm/...
- 8,699
2
votes
Is this a Blocked design ANOVA, two way anova, or ANCOVA
Looks like a two-way ANOVA without interaction to me:
"condition" is a factor with 4 levels
"subject" seems to be a factor with n levels.
Note that, depending on your exact protocol, a linear mixed ...
- 41
2
votes
Difference between one-way ANOVA with randomised blocks and nested ANOVA?
Here is my understanding of the difference. With a randomized block design, you have a characteristic of the units-of-analysis that you stratify (block) and then randomize into your treatment ...
- 1,838
2
votes
Accepted
When to use blocks?
One blocks the design and the analysis for added precision. This will in effect reduce standard errors, and increase the chances of obtaining a significant finding (provided the experiment does ...
- 64.8k
2
votes
Block-treatment interaction for Randomized Block Design (RCBD) and Generalized Random Block Design (GRBD)
I am surprised this is not answered on site so far (at least I cannot find it by search). We suppose balanced designs. First the unreplicated case, then the analysis is by a two-way anova. Let the ...
- 82.8k
2
votes
Determining standard error of the mean from a correlated, stationary time series using known autocorrelation without block averaging
Seems as if "effective sample size" is a suitable concept for you to look at,
in particular the formulae for $Var(\hat{\mu})$ and $n_{eff}$.
https://en.wikipedia.org/wiki/Effective_sample_size
A ...
- 336
2
votes
Accepted
Does RCBD tend to increase the F value compared to the one way ANOVA?
If the blocks are quite different, then using that information will reduce the estimate of error variance.
On the other hand, if the blocks barely differ, then it might even slightly increase the ...
- 290k
2
votes
Accepted
ANOVA complete block design, more units per block than treatments
The choice of a completely randomized design will lose efficiency. You also may not be able to identify some effects which would be very disappointing.
Your second choice, the CRBD, is better. While ...
- 1,648
2
votes
Accepted
The treatments are collectively not significant but one of the treatment is significant
From table 2, you can see that coefficients for Treatment 1 (T1) and Treatment 2,3 (T2, T3) have a different sign (negative and positive). This says that T1 has a negative effect on your dependent ...
- 156
2
votes
Accepted
Why is it acceptable to use the Sum of Squares of an Interaction as the Sum of Squares Error in a Randomized Complete Block Design?
Note that this is a Randomized Block Design, and the justification is in the word Randomized. If we have formally the same layout, but randomization was not done, then we cannot just assume that the ...
- 82.8k
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