There are 4 reasons why not do this:
- 1) Splitting the table hurts the accuracy of the estimates for parameters because we are essentially making two less-accurate instead of pooling all the evidence into one estimate.

- 2) To acquire probability statements about the variable used to split the data they need to be included in a model. Otherwise, we will have a weak statistical argument.

- 3) We may want to use a different model to compare data like information criteria. 

- 4) Multilevel models allow for borrowing of information which improves estimates in all categories. 


Splitting data into two data frames

Creating levels of African nations and Non-African nations for the continent variable, showed a new relationship when observing log(GDP) versus ruggedness of the terrain.

University of Virginia, Charlottesville

In experimental research, an interaction effect (or simply an interaction) exists when the influence of one independent variable on a measured outcome is fundamentally altered depending on the specific level of a second independent variable. This indicates that the variables do not operate in isolation; rather, they combine to produce complex effects that cannot be fully explained by analyzing them independently.

Interaction Effect

McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd ed.). Chapman and Hall/CRC.

Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd edition)

Example: Creating levels of an independent variable 

An intuitive research example of an interaction effect involves the relationship between psychotherapy and a patient's motivation. Generally, the positive impact of receiving psychotherapy is significantly stronger among individuals who are highly motivated to change compared to those who lack such motivation. This represents an interaction because the effectiveness of one independent variable (whether or not the person receives therapy) relies entirely on the specific level of a second independent variable (the individual's degree of motivation).

Interaction Between Psychotherapy and Motivation

Interaction effects can be easily understood through everyday scenarios where multiple factors combine to determine a unique outcome. For example, your decision to watch a movie might depend on both the film's genre and the specific friend accompanying you. While there might be a main effect for preferring a blockbuster movie, an interaction occurs if your choice completely changes based on who is coming along. Another practical illustration is a drug interaction, where two medications may each be independently beneficial, but taking them together produces dangerous or lethal results.

Everyday Examples of Interaction Effects

A simple effect analysis is a statistical method used to break down an interaction to understand precisely what is driving the results. Because an interaction indicates that the effect of one independent variable depends on the level of another, relying solely on main effects can be misleading. To clarify the relationship, researchers use simple effects analyses to examine the effect of each independent variable at each specific level of the other independent variable, rather than averaging across those levels.

Simple Effect

A study by Brown and colleagues illustrates an interaction effect by exploring memory recall differences based on an individual's level of hypochondriasis. The researchers hypothesized and found that participants high in hypochondriasis recalled negative health-related words more accurately than those with low hypochondriasis. However, both groups demonstrated similar recall rates for non-health-related words. This finding highlights a clear interaction, as the influence of the word type on memory recall is directly dependent on the participants' level of hypochondriasis.

Interaction Between Hypochondriasis and Word Type in Memory

In factorial research designs, the effect of one independent variable can depend on the specific level of another variable in several distinct ways. The two primary ways these complex relationships manifest are through spreading interactions, where an effect is present at one level but weak or absent at another, and cross-over interactions, where the independent variable produces opposite effects depending on the second variable's level.

Types of Interactions

Schnall and colleagues demonstrated an interaction effect by investigating the combined influence of disgust and private body consciousness on moral judgment. Rather than conducting separate studies for each independent variable, they examined them simultaneously in a single experiment. The results revealed an interaction: the impact of the disgust manipulation on moral judgment was not uniform, but instead depended fundamentally on whether participants exhibited high or low levels of private body consciousness.

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