What is: “Experimental Unit”, “Replicate”, “Total sample size”, “treatment size”?

Experimental unit: This is the (field plot/animal/gear/whatever) to which "treatments" are applied. Treatments can be directly applied (like a dose of insecticide to an insect) or they can be observational (sex, weather, disease). If you randomize, you typically randomize the experimental units. Note that there are some additional terms: subsample, techincal replicate, pseudoreplicate. These three are terms used when multiple samples are taken from a single experimental unit.

Replicate: A replicate is one experimental unit in one treatment. The number of replicates is the number of experimental units in a treatment.

Total sample size: My guess is that this is a count of the number of experimental units in all treatments. This is not very informative, and leads to trouble if the design is unballanced. Afterall, I could say that my total sample size was 100 in four treatments. Sounds good, unless I reveal that one treatment had 60 replicates, one treatment had 30 replicates and the other two had five each.

Treatment size: I am not sure, but I would guess that this is the number of experimental units in each treatment.

Recognize that a huge variety of people use statistics. They may not all use all of the same terminology in exactly the same way.

The problem with examples is that they can be aranged in a multitude of different ways. Methods sections often don't provide sufficient detail to replicate an experiment. In your example there is a treatment (herbicide) and a control (water). I want to evaluate herbicide resistance in 6 genotypes, 20 plants per genotype.

1) I place all of the plants in one box. I mix up a tank of herbicide, and spray half the box. Technically, this is one replicate, no matter how I process the plants.

2) I place 12 plants in a box. Half get sprayed. This is two plants from every genotype. I still made up a single tank, so this is one replicate.

3) I place 12 plants in a box, just like in 2. However, I mix up a new solution each time. If I am really good, I might use a different sprayer/nozzles. I will end with 10 replicates.

People often argue that I really don't care about the sprayer effect, nor the effect of the person using it. So I will go with plan 2 (above), and treat this as 10 replicates. This is great so long as you assume that the sprayer that you are using is typical, and no errors were made in mixing up the herbicide. With those untestable assumptions holding true, this is fine.

Replicates are composed of experimental units. In my experiment I used 100 experimental units, but I had 25 replicates. I can now figure out that I had 4 treatments, each with 25 replicates.

I could run the experiment by putting 20 plants from one genotype into the box, spraying half of them and then repeating for the other genotypes. With 6 genotypes, this design is 6 seperate experiments. You cannot compare genotypes.

Ok, so I have an experiment with 6 genotypes, and I am interested in how they respond to an herbicide. I will meanure root length, plant height, chlorophyll content, and survival. I care about the sprayer-user effect, but I do not want to measure these.

I go to the greenhouse and start 100 of each genotype. When they are at size I will select 20 out of each 100 for my experiment that are most similar. I will number all of the plants from 1 to 20 for each genotype, and I will use a random number generator to select a plant from each genotype. I will treat these. I will then use the random number generator to select another plant, and treat those. I will do this a total of ten times. The remaining plants are my controls. Depending on the research question, I might spray the controls with water, or a blank formulation. Mostly, this is how this type of experiment is done, though prople generally do not use a random number generator. Plants are chosen arbitrarily. It may be that plants are paired where I select a tall one to treat, then I select a tall one to use as a control. I select a short one to treat, and a short one for the control. And so forth.

That is the simple experiment. However, I am now interested in the sprayer-user effect and I want to measure these. I need more than 20 plants. I will have the following treatments:

1) herbicide versus control

2) Bob, Janice, Paul, Alice, Sam, and Nian.

3) Sprayer nozzles 8001, 8002, 8003, 8004, 8006. I have special equipment that allows me to measure the droplet size spectrum produced by each nozzle for the herbicide that I am applying.

In this case I have five nozzles. So for each nozzle I need a set of 20 plants from each genotype to run the original experiment. I will mix up my herbicide solution in small batches, treat one plant from each genotype, and then mix up another batch of herbicide. My assistants (Janice, Paul, Alice, Sam, and Nian) will do the same. All of us will have a different batch of plants and will conduct the entire experiment.

After thinking a bit more about the problem, Bob decides that he wants to know if the person effect is consistent. Bob is part of a multinational company, so he tells labs in Japan, India, England, South Africa, and Italy to run the same experiment using 6 people from their labs.

Your "situation A" versus "situation B" makes no difference in the experimental design. It may make some difference in how you analyze the numbers. I would start by disagreeing that all of the measurements in "situation A" are parametric. All the variables in situation A are continuous, while the situation B variable is discrete.

I would like to ask the same question since I want to clarify the answers above, and I ,also, have seen multiple approaches in papers.

We have four different petri dishes with seedlings inside. Each petri dish includes 6 seedlings (I cannot put more than 6 in the petri dish). Two out of the four petri dishes have the exact same treatment and the other two are controls.

The question here is: Do I have 12 biological replicates/treatment (see the two petri dishes as one whole treatment)? Or do I have 6 biological replicates/treatment (the one petri dish) and the other petri dish consists an independent repetition of the experiment?

Second part of my question is : In the latter case how do I present the results? I run the statistical analysis with the 6 plants and then an independent statistical analysis with the "independent repetition", aka the other 6 plants? Or do I perform statistical analysis between the plants of the same treatment as independent replicates, 6 versus 6, to see if they have a significance difference?

Thank you so much for your time.

An experimental unit is one particular element from the subject population under study. Each experimental unit will receive a certain treatment (specific combination of levels of each factor), and its response will be measured. The experimental units can be physical individuals (e.g. persons, animals, plants, seeds, etc.), samples of matter (e.g. solids, liquids, gases, etc.), individual events (e.g. attempts, lots, runs, etc.), or groups of individuals.

If the response variable measured is root length, the experimental unit is each seedling, as its root length can be measured individually. However, if the response variable is a probability of germination or the average root length, then the experimental unit must be a group of seeds (in a dish/plate/box).

Depending on how the experimental unit is defined, you determine the number of replicates for each each treatment in the design.

On the other hand, an independent experiment or repetition requires that no correlation exists between the measurements. If the experiments are done at the same time (or at least one external uncontrolled factor is exactly the same), those experiments will not be independent repetitions.

Eirini Evangelia Thomloudi: As long as you can guarantee that the treatments are identical for both petri dishes, then you have 12 biological replicates of the treatment. If the experiments are performed at the same time, they are not independent repetitions because there might be some correlation in the results. If some external uncontrolled factors are different (e.g. they were prepared by a different person), you should block your results by assigning a different category to each repetition. Then, you can analyze all the results by including the block category as a factor in order to see if its effect is significant or not.

Hi,

for clear definitions and comprehension of why distinguishing these terms is crucial, I do recommend the classical paper authored by Stuart H. Hurlbert: Pseudoreplication and the Design of Ecological Field Experiments. Ecological Monographs, Volume54, Issue2, June 1984, Pages 187-211.

Originally addressed to ecologists, it became a reference in experimental biology. You will also find other papers on pseudoreplication in other areas, all of them defining the concepts that you mention, both in practical and statistical terms.

All the best,

Claudio

Eirini Evangelia Thomloudi

An "experimental unit" is the smallest entity that you can treat randomly; in your case, each one of the Petri dishes can be submitted to a particular treatment established randomly. The six seeds inside each dish are "observations", because you cannot treat each of them independently of the other five. Your "n" is the number of experimental units = dishes. From a statistical point of view, having 1, 6 or 100 seeds inside dishes is strictly the same, each one is n=1. Yet, having many seeds ="observations" per dish, can you give a more precise idea about the value of your variable for every dish, because instead of recording just one seed, which could have particular individual characteristics, you have the mean reaction of a group, reducing individual variability. Biological and technical replicates are terms used for distinguishing true replicates (=biological) from the variability due to technical procedures. For instance, you can analyze gene expression in the RNA extracted from 4 individuals treated independently, performing 3 PCR for each of them. In this case, the individuals are equivalent to experimental units, and the 3 PCR per individual, the equivalent to 3 observations. Again, statistically speaking, your n= 4.

You need to find a reference book or article on design of experiment.