A 2×2 factorial design is used to understand how two independent variables (each with two levels) affect one dependent variable.
A useful way to visualize the effects that the two independent variables have on the dependent variable is to create an interaction plot, which displays the mean value of the dependent variable at each level of the independent variables.
The following step-by-step example shows how to create and interpret an interaction plot in Excel.
Step 1: Enter the Data
Suppose we want to understand the effects of sunlight exposure (low vs. high) and watering frequency (daily vs. weekly) on the growth of a certain species of plant.
Suppose we collect data on 60 plants and calculate the mean plant growth at each level of sunlight exposure and watering frequency. Here’s how to enter these mean values into Excel:
This tell us that:
- The mean growth for plants that received high sunlight and daily watering was about 8.2 inches.
- The mean growth for plants that received high sunlight and weekly watering was about 9.6 inches.
- The mean growth for plants that received low sunlight and daily watering was about 5.3 inches.
- The mean growth for plants that received low sunlight and weekly watering was about 5.8 inches.
Step 2: Create the Interaction Plot
Next, we need to highlight the values in the cell range C4:E6 as follows:
Then click the Insert tab along the top ribbon in Excel, then click the first chart option within the Line Chart group:
This will automatically insert the following line chart:
Feel free to modify the title, axis labels and colors on the plot to make it more aesthetically pleasing:
Step 3: Interpret the Interaction Plot
Here’s how to interpret the lines in the plot:
Main Effect of Watering Frequency:
Since the two lines are mostly flat, this tells us that there is very little difference in plant growth between daily and weekly watering. This tells us that watering frequency probably doesn’t have a statistically significant effect on plant growth.
Main Effect of Sunlight:
Since the two lines are fairly far apart, this tells us that there is a noticeable difference between low sunlight and high sunlight.
For example, we can see that the average growth for plants that received low sunlight was around 5-6 inches. We can also see that the average growth for plants that received high sunlight was around 8-9 inches.
This tells us that sunlight probably has a statistically significant effect on plant growth.
Interaction Effect Between Watering Frequency & Sunlight
Since the two lines in the plot are mostly parallel, this tells us that there is no interaction effect between watering frequency and sunlight.
For example, the effect that sunlight exposure has on plant growth isn’t dependent on watering frequency. Similarly, the effect that watering frequency has on plant growth isn’t dependent on sunlight exposure.
If the two lines in the plot were not parallel (or if they crossed each other) then this would be an indication that there is an interaction effect between watering frequency and sunlight on plant growth.
A Complete Guide: The 2×2 Factorial Design
How to Create an Interaction Plot in R