Hi,
Need to clarify something,
If I have two factors, F1 (4 levels a, b, c, d) and F2 (i, ii, iii, iv) what statistical design will be the best suitable!. Let's suppose F1 is 4 levels of potash fertilizers and F2 includes 4 spiked Cd soil concentrations.
Can we randomize all 16 sets of treatments together and both designs are the same in sense of the physical arrangement of pots and statistical explanation?
Means ANOVA under CRD (2way)= ANOVA under Factorial (2-way interaction), as CRD is the physical arrangement of experimental sets while 2 way ANOVA under CRD (or Factorial ANOVA with 2 way interaction) is used to explain the statistical significance of data (of course data arrangement can differ).
Please give your valuable suggestions
Hello Muhammad,
The completely randomized design (CRD) is generally superior to a multi-factor design in which the researcher can not assign cases to individual cells. An example of the latter would be that of a randomized block design, in which cases are stratified on the basis of some attribute variable (e.g., sex), and are randomly assigned to treatment conditions only within that specific level of the blocking / nuisance / extraneous variable. One problem with any design having restrictions on randomization is that the interaction term might not be an accurate/unbiased estimate of reality.
So, if you have the luxury of randomizing cases to both F1 and F2 of your design, that is the preferred way to proceed. Functionally, it doesn't matter whether you conceptualize this as a two-way design, or as a single factor design having 16 combinations. Your ability to test for F1, or F2 as "main effects," or F1*F2 as an interaction is equal either way.
However, for balanced designs, the basic rules for computation of SS, df, and error terms are the same for a CRD or multi-factor design (with restriction/s on randomization), if that's what you're asking. For unbalanced designs, the choice of Type I, II, or III SS computations depends on the specific design, assumptions about the population, and research questions.
Good luck with your work.
Look at the linear model below.
yijk = μ + αi + βj + γij + εijk
i = 1, 2, 3, 4
j = 1, 2, 3, 4
k = 1, 2, 3, .... n
Abolfazl Ghoodjani The model you have mentioned itself seems to be multiple linear regression if i am not wrong. Basically, the confusion is the justification of difference between physical as well as statistical attribution of both designs (CRD 2 way and factorial with 2-way interaction)
Sorry but there are no 2-way CRDS so you are confused. You May mean a simple random block design of some sort. A CRD HAS ONLY ONE FACTOR AND IT'S STATISTICS ARE A ONE WAY ANOVA. see first attached screenshot for details of that.a
Just in case the factorial design which studies interaction
is added for completeness here. Best wishes, David Booth
This could be determined by the condition under which the experiment is proposed. If the conditions like access to heat, light, air under the greenhouse/laboratory is more re less homogeneous, then the suitable statistical design could be completely randomized one with the 16 pots randomly placed. Otherwise 2-way factorial design with a blocking factor is necessary to get rid of nuisance due to difference in the conditions. I think that is the difference. Best regards
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