Contrast the three types of factorial designs.

6-1 (150 words and 1 reference)

Contrast the three types of factorial designs.

Contrast the three types of factorial designs.


Factorial designs are a way to test many different effects in one experiment. They can be used to test the effects of many variables, or they can be used to find out how combinations of factors affect individual outcomes. For example, you might want to know whether wearing a hat affects how much heat we lose from our head when exercising outside in hot weather, or whether having two sweaters instead of just one makes us feel more comfortable during cold-weather activities such as hiking or skiing down steep slopes.

A single factorial experiment.

A single factorial experiment is a way to test many different effects in one experiment. A single factorial design has two levels of one factor, which are not repeated and cannot be interchanged. The levels must be mutually exclusive (that is, one can only be on at any given time) and exhaustive (that is, there must always be an exact amount of each level).

A split-plot design with two levels.

In a split-plot design, each factor is replicated in two or more plots. The first level of replication is the split between the treatment and control groups; this is called the factorial design. In a split-plot design, there are four possible configurations:

  • A replicate with one treatment group and three replicates with one control group (i.e., 1:1).
  • A replicate with two treatments groups (i.e., 2:3)
  • Three replicates with two control groups (i.e., 3x3x2).

The last configuration may be referred to as an “interaction” because it shows how changes in one factor affect those other factors when they’re present at different levels within each plot.*

An AB design with two levels and one factor.

An AB design is the most common type of factorial design. An AB design is used to test two factors at two levels each. For example, if you want to test the effect of different types of peanuts on a woman’s cholesterol level and whether she has high blood pressure or not, an AB design would be ideal because you can measure each factor at two levels (peanuts are either “good” or “bad”) and determine whether there is a significant difference between these two groups based on their results.

You can create an AB design by choosing four cells in your data table and then adding another row for each cell combination by using Rows Per Column Formula option #2 under Solver tab in Excel. To do this:

Factorial designs are a way to test many different effects in one experiment.

Factorial designs are a way to test many different effects in one experiment. They are useful for testing interactions between factors, such as the effect of various temperature levels on the growth rate of bacteria.

In factorial design, each factor is tested with several values; if there’s no difference between two combinations of values or levels (e.g., 3 and 5), then this means that both factors were not important at that level. For example, you might want to know whether an increase in temperature affects how fast bacteria grow when they’re present at different temperatures: one experiment might look at how much faster bacteria grow when they’re kept warm vs cool; another may compare how much faster they grow inside a test tube versus outside it (without any heat).


Here are some tips for writing good factorial designs:

You should always include a factor that is the same across all your experiments. This ensures that you can run each one in isolation from one another, and it also helps ensure that the results of each experiment are meaningful. You can use a single factor for this if necessary, but make sure to keep track of how many different ways there are to set up this type of design! You should also be careful about over-reporting certain effects when designing experiments with multiple factors because it may lead readers astray or confuse them about what’s actually happening in nature; we recommend keeping your number of independent variables low so as not to overstate any particular result


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