Statistical interaction can occur in a two-way ANOVA, where variables work independently within a study. When this happens, it is important to consider the interaction between the variables. A statistical interaction occurs when the combined effect of two variables causes a greater or lesser change than what would be expected if the variables were independent of each other. In other words, the variables are dependent on each other in some way.
To understand the effect of the variables on the data, it is necessary to know the levels of each variable. The independent variables have a greater impact on the dependent variable, while they do not directly affect each other. In a study on level of care in Hospice, researchers collected data from family members regarding three conditions: Hospice with LPC, hospital with LPC, and hospital without LPC. Family members reported no change in the level of care between the hospital with LPC and hospital without LPC comparison.
However, when comparing the hospice vs. hospital with LPC or hospice vs. hospital without LPC groups, there was a significant difference in the level of care, indicated by a p-value less than the chosen significance level (α). This suggests that there is an interaction between LPC and hospice, as well as between LPC and hospital.
In a broader context, interaction refers to the action that occurs when two or more objects influence each other. It is important to consider the concept of a two-way effect in interactions, as opposed to a one-way causal effect. The combination of many simple interactions can lead to emergent phenomena that may be surprising.
Interaction has different meanings tailored to various sciences, but the underlying principle is that all systems are interrelated and interdependent. Every action has a consequence, and this applies to statistics as well. In statistics, an interaction is a special property of three or more variables, where two or more variables interact in a non-additive manner to affect a third variable.
In other words, the effect of the two variables interacting is greater than the sum of their individual effects. To illustrate this concept, consider the example of two friends who are on different weight loss programs. The researchers evaluate two different diets and two different exercise programs. One program focuses on cardio, while the other focuses on weight training. The goal is to determine which combination results in greater weight loss.
The researchers randomly assign participants to either diet A or diet B, and to either the cardio or weight training regimen. After one month, they record the amount of weight lost by each participant. The analysis of the data will determine if there is an interaction between the type of diet and the type of exercise regimen, indicating whether the combined effect of the variables is greater than what would be expected if they were independent.
In conclusion, statistical interactions can occur in a two-way ANOVA when variables work independently within a study. Understanding the interaction between variables is crucial to comprehending the effect on the data. An interaction happens when two or more variables interact in a non-additive manner, resulting in an effect that is greater or lesser than the sum of their individual effects. This concept of interaction applies across various disciplines, emphasizing the interrelated and interdependent nature of all systems.
