The most upvoted muddy point post of the week:

The most upvoted muddy point post of the week:

An experiment:

A biologist is interested in studying the effect of growth-enhancing nutrients and different salinity levels in water on the growth of shrimps. The biologist has ordered a large shipment of young tiger shrimps from a supply house for use in the study. The experiment is to be conducted in a laboratory where 10 tiger shrimps are placed randomly into each of 12 similar tanks in a controlled environment. The biologist is planning to use 3 different growth-enhancing nutrients (A, B, and C) and two different salinity concentration (low and high).

• Factors are categorical explanatory variables. There are two factors: nutrient type and salinity concentration.

• The values each factor can be are its levels.Nutrient type has three levels and salinity concentration has two levels.

Since nutrient type has three levels and salinity concentration has two levels, there are 3x2=6 treatment combinations.

• The experimental units are what the treatment is applied to.

• Here the treatment is applied to each tank.

• You could also look at the experimental units as the group of 10 shrimp in each tank.

• Either way there are 12 experimental units.

• And since there are 6 treatments, there are 2 replicates of each treatment.

• The experimental units are what the treatment is applied to.

• Here the treatment is applied to each tank.

• You could also look at the experimental units as the group of 10 shrimp in each tank.

• Either way there are 12 experimental units.

• And since there are 6 treatments, there are 2 replicates of each treatment.

Another key component of the design of this experiment is randomization. The experimenter should randomly assign the shrimp into the 10 groups, and then randomly assign the groups to the 12 tanks.

Suppose now that the room in which the tanks will be placed is laid out so that the experimenter can put 6 of the tanks along a wall beside a window and the other 6 tanks on a windowless wall.

How should we deal with this?

Window

No window

Nutrient C, low salinity

Nutrient B, low salinity

Nutrient A, low salinity

Nutrient A, high salinityNutrient B, high salinity

Nutrient C, high salinity

Nutrient C, low salinity

Nutrient B, low salinity

Nutrient A, low salinity

Nutrient A, high salinity

Nutrient B, high salinityNutrient C, high salinity

BLOCKS

TREATMENTS

Window

No window

Nutrient C, low salinity

Nutrient B, low salinity

Nutrient A, low salinity

Nutrient A, high salinityNutrient B, high salinity

Nutrient C, high salinity

Nutrient C, low salinity

Nutrient B, low salinity

Nutrient A, low salinity

Nutrient A, high salinityNutrient B, high salinity

Nutrient C, high salinity

BLOCKS

TREATMENTS A blocking variable is another factor that we typically don’t care about. We expect that the observed values of the outcome will be more similar within blocks than they are between blocks. We want to control for this source of variation (differences between levels of the blocking variable).

How? Assign (randomly) treatments to experimental units within blocks.

Correct answer: control