Statistics Tip: In 2-Factor (2-Way) ANOVA, separated lines show that Factor A has an effect

​In this example, we are testing 2 Factors for their effect on the y Variable, Cleanliness. 

• Factor A is the Detergent type.  There are 2 "levels": Detergent #1 and Detergent #2. 
• Factor B is the Water Temperature. There are 3 levels: Cold, Warm, and Hot.

 
We see from the graph that -- for all three levels of Factor B, Detergent #1 cleans better than Detergent #2. The lines are substantially separated, indicating that the difference is Statistically Significant. (The ANOVA numbers will tell us for sure.) 
 
If Factor B did have an effect, the lines would be slanted. Again, separated lines tell us that Factor A has an effect. 

​If the lines were not separated, as below, then Factor A does not have an effect.