# How many variables are there in the factorial research design of 2 * 3 * 2?

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technology and computing
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The investigator plans to use a

**factorial experimental design**. Each independent variable is a factor in the**design**. Because**there**are three factors and each factor has**two**levels, this is a**2**×**2**×**2**, or**2**,^{3}**factorial design**. This**design**will have**2**=8^{3}**different experimental**conditions.

Consequently, how many interactions can be studied in a 2 * 3 * 5 factorial design?

Similarly, a **2 ^{5} design** has five factors, each with two levels, and

**2**= 32

^{5}**experimental**conditions.

**Factorial**experiments

**can**involve factors with different numbers of levels. A

**2**

^{4}

**3 design**has five factors, four with two levels and one with three levels, and has 16 ×

**3**= 48

**experimental**conditions.

Notation.

A | B | |
---|---|---|

ab | + | + |

**2x2**= There are two IVS, the first IV has two levels, the second IV has 2 levels. There are a total of 4

**conditions**,

**2x2**= 4.

Similarly one may ask, how many factors are in a 2x3 factorial design?

three factors

The simplest of the two **level factorial** experiments is the **design** where two factors (say **factor** and **factor** ) are investigated at two **levels**. A single replicate of this **design** will require four runs ( ) The effects investigated by this **design** are the two main effects, and and the interaction effect .