1. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Types of Designs Completely Randomized Design (CRD): Completely Randomized Designs are used to study the effects of a single factor without considering any other variables. The experiment compares a response (dependent variable) to a factor (or different levels of that factor). In CRDs the levels of the factor are always randomly assigned to experimental units. The first example in calculating the F ratio was a CRD design: a 1 a 2 a 3 6813 8129 4911 5118 367 4812

2. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Types of Designs Completely Randomized Design (CRD): As another example, lets say we wish to examine the effect of 3 different levels of phosphorous in the diet on growth rate in small fish. We would also like to make sure that the experiment has some biological replication and that those replicates are randomly assigned How do we proceed? First determine 3 essential numbers. Most times you will set this up in your head but, when experiments get larger and more complicated, it’s best to write these out. For ACUC approval – they like to see your work. How many replications? n = 3 How many levels of the factor? L = 3 (for this example) How many factors? k = 1 (for this design)

3. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Types of Designs Completely Randomized Design (CRD): So: what is the total sample size we will need? N = n x k x L or 3 x 3 x 1 = 9 In the lab we are using tanks of fish for our experimental unit thus, we will need 9 tanks (with an appropriate number of fish to sample in them). But how do we assign levels to tanks? RANDOMLY (drawing lots or computer etc.) How many different way to run the experiment? 9! / (3! 3! 3!) = 362,880 / 216 = 1,680 Ways to uniquely order this experiment.

4. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Types of Designs Completely Randomized Design (CRD): A randomized experiment could look like this: high P = HP, Maintenance P = MP, and Low P = LP The data from this experiment could be summarized as: Factor Level ReplicateHPMPLP 123.321.217.8 221.421.819.8 320.920.719.9 This is evaluated using a one-way ANOVA LP MPMP HP LP MPMP HP MPMP

5. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Types of Designs Completely Randomized Block Design (CRBD): Why “Blocking”? Blocking is simply the arrangement of experimental units in groups that are similar. Blocking is used to address factors that are not of primary interest to the researcher. Time, sex, temperature, feeder… ALL EXPERIMENTS HAVE FACTORS THAT ARE NOT OF INTEREST BUT MAY EFFECT THE RESULT. Typically you will have to spend some time determining the factors which may effect your experiment and how much interest they are in the result. This important process is often overlooked and as a result - can be detrimental to the interpretation of the experimental result. Basically to block a “nuisance” factor you create homogeneous block where the nuisance factor is held constant but the factor of interest is variable. LP MPMP HP LP MPMP HP MPMP

6. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Types of Designs Completely Randomized Block Design (CRBD): Basically to block a “nuisance” factor you create homogeneous block(s) where the nuisance factor is held constant but the factor of interest is variable. Why? You are reducing within experimental error. “Block what you can, randomize what you cannot” For the phosphorous example, let’s say that we found out that P might be used differently between male and female fish – how would we block this then? LP MPMP HP LP MPMP HP MPMP

7. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Types of Designs Completely Randomized Block Design (CRBD): Why block to control for sex? Well now we’ve got two factors: phosphorous and sex Phosphorous has 3 levels and sex has two levels N = n x L 1 x L 2 => N = 3 x 3 x 2 = 18 tanks Two sets of tanks ? (i.e. 18 tanks – each with males and females separated) LP MPMP HP LP MPMP HP MPMP LP MPMP HP LP MPMP HP MPMP

8. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Types of Designs Completely Randomized Block Design (CRBD): All levels of both factors are accounted for. In this particular design can you test for the effect of sex? What about putting males and females in each tank and sampling equal numbers of each sex from each tank? LP MPMP HP LP MPMP HP MPMP LP MPMP HP LP MPMP HP MPMP LP MPMP HP LP MPMP HP MPMP

9. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Types of Designs Completely Randomized Block Design (CRBD): This is a 2-factor design We use ANOVA to test this and to test for differences associated with sex (if we think its important) This is a blocked design and we still test it with a one-way ANOVA. LP MPMP HP LP MPMP HP MPMP LP MPMP HP LP MPMP HP MPMP LP MPMP HP LP MPMP HP MPMP