Unraveling the Science of Causality
Understand the “logic of causality” for informed research methods selection
Researchers presume causality often without due contemplation
*This article is based on research done by the author — Lee & Lu (2023)
We commonly define “contributory” causality
Social scientific research aims to understand how different things are connected and how one thing can influence another. This is crucial for building theories and explaining how changes in one concept can cause changes in another. However, the idea of causality can be pretty tricky and has different interpretations among scholars and philosophers as it’s a complex concept.
Interestingly, many researchers tend to oversimplify causation. They say things like “X has an effect on Y” without really thinking deeply about how it all works. When researchers dive into causal statements, often unconsciously, they usually presume that there are probabilistic uncertainties in the relationship between cause and effect, saying, “X is likely to increase/decrease Y.” In other words, X might make it more likely for Y to happen or decrease the chances of Y occurring, but it doesn’t guarantee whether it will really happen or not. There could be other factors at play that also influence Y.
“The relationships between these factors and booking intention can go in the same or opposite direction. But because these relationships are “probabilistic,” it’s unlikely that any single factor can perfectly predict whether someone will book a place or not.”
So, in this more probabilistic view of causality, X is considered a “contributory” cause, which means it plays a part in causing Y, but it’s not the only thing responsible. And Y might still happen or not happen because of other factors as well. For example, in home-sharing research, many studies have looked at important factors that affect whether guests choose to book an Airbnb place. These factors include price, location, and details about the host like their profile, ratings, and how quickly they respond (Wu et al., 2017). The relationships between these factors and booking intention can go in the same or opposite direction. But because these relationships are “probabilistic,” it’s unlikely that any single factor can perfectly predict whether someone will book a place or not.
In social sciences, things can get a bit complicated when we try to figure out what causes what.
Way back, David Hume talked about causation, and since then, researchers in philosophy, math, and science have been linking it to sufficiency and necessity — which we’ve kinda forgotten about.
This post is about how these two concepts (i.e., sufficiency and necessity) are important when we want to understand and test causal relationships.
Sufficiency and necessity in causal logic
Causality is a big deal in science, and it can be pretty tricky to figure out sometimes.
Surprisingly, though, lots of researchers take the easy way out and just say, “X causes Y,” without really thinking it through. They use this “contributory” logic of causality, where X likely influences Y, but it’s not like X is absolutely necessary or sufficient for Y to happen. This contributory approach is more common in social sciences where things are complicated and something strictly deterministic is difficult to find.
But by doing this, we forget about two important ideas from Hume: sufficiency and necessity (Lewis, 1973). These views have been around for a long time, ever since Hume talked about causation in 1777. And they’re not just some philosophical mumbo-jumbo; they’re actually important in fields like math and science. The way we think about causality, how we explain it, and how we study it are all linked to (in)sufficiency and (un)necessity.
Sufficiency logic suggests that if a particular cause is present, it will guarantee the presence of a specific outcome. However, the absence of that cause doesn’t necessarily mean the absence of the outcome, as there might be other causes that can lead to the same outcome. For example, to find trees (Y), you can visit a mountain (X1) or a park (X2).
Necessity logic, on the other hand, states that a cause is essential for producing a certain outcome. Without that cause, the outcome never occurs. For instance, water (X) is necessary for the growth of trees (Y). Without water, trees cannot survive. While a boost in water supply doesn’t necessarily lead to an increase in tree growth, regardless of other (un)favorable conditions like fertile soil, the lack of water (i.e., absence of X) will inevitably result in the tree’s demise (i.e., absence of Y).
Sometimes, a cause can be both necessary and sufficient for an outcome. This means that the presence of the cause guarantees the presence of the outcome, and the absence of the cause ensures the absence of the outcome. For example, when a person reaches the voting age (X), he or she is eligible to vote (Y). Also, before reaching the required age, the person cannot vote.
Types of causes and causal assumptions
Following the sufficiency/necessity discussions above, four fundamental types of causes are:
- Sufficient cause
- Necessary cause
- Necessary-and-sufficient cause
- Contributory cause (unnecessary-and-insufficient cause)
I emphasize the significance of discerning between these causal types, as each entails distinct assumptions (such as additivity, probability, and symmetry) and demands different approaches to theory development and testing. Such differentiation is crucial for advancing our understanding of causality and its complexities.
The discussions are based on my recent article (Lee & Lu, 2023)
Determinism vs. Probability
The concepts of sufficient, necessary, and necessary-and-sufficient causes, as opposed to contributory causes, do not hinge on the assumption of probabilistic causation. In the probabilistic framework, causation is understood as a factor that increases the likelihood of the effect, as exemplified in contributory causation, where,
“X is likely to increase/decrease Y.”
In contrast, sufficiency and necessity logics adopt a deterministic perspective, positing that a cause guarantees or ensures the occurrence of the outcome, without relying on probability. In this regard, necessity logic asserts that,
“without X, there is absolutely no Y,”
while sufficiency logic maintains that,
“with X, there is always Y”
Symmetry vs. Asymmetry
Necessary and sufficient causes, as opposed to necessary-and-sufficient and contributory causes, involve a special type of causal relationship known as causal asymmetry. This means that changes in the cause and the outcome do not necessarily happen together in the same or opposite direction.
In simple terms, a sufficient cause is one that alone can produce a specific outcome, but the absence of that cause does not guarantee the absence of the outcome, thereby,
“X is sufficient but not necessary for Y.”
On the other hand, a necessary cause is one that must be present for a particular outcome to occur, but its presence alone doesn’t guarantee that the outcome will happen, thus,
“X is necessary but not sufficient for Y.”
In contrast, necessary-and-sufficient and contributory causes have symmetrical effects, meaning that changes in these causes will — always or likely, respectively — lead to subsequent changes in outcomes.
Additivity vs. Non-additivity
Unlike sufficient and contributory causes, necessary and necessary-and-sufficient causes do not involve a causal assumption of additivity. This means that each cause cannot be substituted, and does not have a separate effect on the outcome.
Sufficiency or contributory causes suggest that a single cause can lead to an outcome, and this cause can be substituted with other causes to produce the same result. Imagine it like building a house (Y), where each brick adds to the structure, but you can use different types of bricks (Xn) and still get the job done. This idea can be represented by an additive model in statistics, where each cause contributes independently to the final outcome — i.e., “Y = a + b1X1 + b2X2 + . . . + bnXn.”
On the other hand, necessary causes work differently. In this approach, each cause is essential and must be present to produce the outcome. It’s like the parts of a puzzle, where every piece is necessary to complete the picture, and you can’t substitute any of them (although having all parts does not automatically ensure the completion of the puzzle). This perspective doesn’t assume that each cause has a separate effect on the outcome; rather, all causes must be present for the result to happen.
The figure above well presents a visual representation of four causal types and their corresponding outcomes. Note:
- The horizontal axis (X) represents the causal factor
- The vertical axis (Y) represents the outcome
- No instances are expected in the lower-right quadrant, where there is an evident presence of sufficient X, but Y is absent.
- Similarly, the upper-left quadrant, characterized by the absence of necessary X but the presence of Y, is not anticipated to have any events.
- In the case of contributory X, observations may occur in all quadrants.
So what? — Causal Logic-Method Fit
I recommend providing a clear specification of the causal logic underlying the proposed relationship, including concepts of sufficiency and necessity, as well as assumptions of (non-)additivity, probability/determinism, and/or (a)symmetry. For typical “contributory” hypotheses (i.e., “X likely increases/decreases Y”), mean-based methods like t-tests, ANOVA, regression, and SEM are valid options, as they align with probabilistic, additive, and symmetric assumptions.
However, in cases where hypotheses explicitly propose the sufficiency logic of causality (i.e., “X always produces Y”), the conventional additive model may not provide valid insights. This is particularly true in complex social contexts, where each independent variable alone may not be sufficient to produce the outcome variable. In such instances, an alternative approach known as “conjunctural causation” (Fainshmidt et al., 2020) becomes relevant. Conjunctural causation views sufficiency as a combination of causally relevant factors that together generate the outcome.
In this regard, the outcome (Y) is the result of a combination of factors (X1, X2, X3, … Xn) acting concurrently, moving away from the additive view and acknowledging the combinatory roles of causes influencing the outcome (i.e., “a set of X1, X2, X3, … Xn together produces Y”). To test causal relationships based on conjunctural sufficiency logic, we recommend employing comparative configurational methods, such as qualitative comparative analysis (QCA). These methods can help identify combinations of factors that are causally linked to the outcome and are well-suited for studying complex causal relationships in social contexts.
In order to investigate “necessary” causal relationships which involve non-additive, deterministic, and asymmetrical perspectives of causality, it becomes essential to employ techniques that accurately capture these functions. One such approach is the utilization of necessary condition analysis (NCA) to examine causal factors based on necessity logic. NCA is an analytical method that focuses on scrutinizing hypotheses related to the necessary causal elements contributing to specific outcomes (Dul, 2016). Since its introduction in 2016, NCA has gained recognition as a valid and valuable option for analysis across diverse fields, including psychology, medicine, computer science, as well as various management subfields such as HRM, supply chain management, international business (Richter & Hauff, 2022), and marketing.
Author’s note:
I — Wangoo Lee — am a PhD behavioral researcher mainly studying tech-enabled service delivery and necessity causality/NCA.
