GENERAL HYPOTHESES (Scientific models)

General Hypotheses are explanatory models that apply to large categories of observations.

DEFINITION: General Hypotheses are tentative, specific explanations of phenomena that can be rejected by experimental data.

General Hypotheses take many different forms. Some General Hypotheses are relatively simple statements. For example, consider a General Hypothesis:

General Hypothesis (GH) 1: "Soda consumption is one cause of childhood obesity in the United States."

GH1 is tentative, because we are not sure that soda consumption contributes to obesity. GH1 is specific because it focuses on one factor (soda) out of many that could contribute to obesity. GH1 is part of an explanation of the phenomenon of childhood obesity (a current public health problem). It would be possible to demonstrate that soda consumption does not result in childhood obesity and reject GH1. Therefore, GH1 fits the definition of a General Hypothesis.

General Hypotheses typically apply to large categories of observations. For example, GH1 applies to the entire population of obese American children, a category that includes millions of people. Millions of children may seem like a large population, but General Hypotheses often have even wider scope. For example the General Hypothesis "The interaction of actin and myosin is the basis for muscle contraction" explains how muscle contracts not only for all humans on Earth, but also for all other animals that have ever lived on Earth (many millions of species). Therefore, general hypotheses can can have scopes that extend over wide ranges of entities, space, or time.

General Hypotheses express models of different types.

It is useful to think of General Hypotheses as models that explain aspects of the natural world (Giere, 2001). For example, engineers frequently use scale models to design cars, airplanes, buildings, and other physical structures. Engineering models may be physical models, constructed from materials such as wood or plastic. More recently, engineers frequently use computer models, which simulate material properties and physical laws to design structures (or evaluate existing structures).

Physical models are also used in some fields of science (Vogel, 1999). However, even physical models require mathematical relationships that enable scale models to make accurate predictions about the objects that the models represent. Moreover, constructing physical models is not feasible for many natural systems. Therefore scientists often express General Hypotheses as conceptual or mathematical models (Braaten and Windschitl, 2011). Conceptual models are typically simplified representations of natural systems. Conceptual models are similar to frameworks: structures of assumptions, facts, and rules that are connected using logical relationships. Similar to frameworks, it is often helpful to express conceptual models using pictures or graphical representations.

For example, the interaction of actin and myosin (or "sliding filament") hypothesis for muscle function can be thought of as a conceptual model of muscle structure at the molecular level. The sliding filament hypothesis is primarily a structural model of muscle based on microscopic visualization (Huxley and Hanson, 1954). However, even structural models can often lead to functional predictions (such as the trapezoidal relationship between muscle force and length; Morgan et al., 2002).

Other important models seek to predict function with very basic representation of structure. For example, Newton's Laws of Motion describe how objects behave mechanically. With Newton's second law:

F = m*a

we can predict how much an object will accelerate based on a force and the mass of the object. Similarly, Newton's law of gravitation

F = G * (M1 + M2) / r

allows us to predict gravitational forces between objects based on mass and distance. However, Newton's laws do not explain why objects behave like they do. Moreover, Newton's laws are limited to objects moving slowly relative to the speed of light (Einstein's model, "relativity," is necessary to describe the behavior of fast-moving objects). Nevertheless, Newton's laws are useful examples of conceptual and mathematical General Hypotheses that can predict the behavior of physical objects moving relatively slowly.

"General" does not mean "vague."

For writing, the distinction between "general" statements and "vague" statements is very important.

DEFINITION: "General" statements apply to a large range of people, places, or things; widespread.

DEFINITION: "Vague" statements are uncertain, indefinite, or of unclear character or meaning.

Clearly, "General" statements and "Vague" statements are very different things. However, many people mistake vague statements for general statements when writing hypotheses. For example, consider the statement:

GH2: "Desirable Difficulties affect test performance"

(Remember that "Desirable Difficulties" are study or practice strategies hypothesized to make study or practice more difficult, but are desirable because the difficulties contribute to learning).

Is GH2 a general statement, a vague statement, or both?

GH2 is definitely a general statement. GH2 implies that Desirable Difficulties affect test performance in ALL situations: for all people, for all tests, for all types of performance. GH2 is also a vague statement. In addition to not specifying types of tests or performance, we also do not know what types of study strategy GH2 refers to. Therefore, GH2 is a vague over-generalization.

A more specific statement would specify the aspect of study hypothesized to underlie a "Desirable Difficulty" compared to a specific type of study that does not involve Desirable Difficulties. For example, we could create a dichotomy to identify two potential sources of Desirable Difficulty:

Study involving Desirable Difficulties can be compared to "blocked study," where learners repetitively study a single subject for a block of time. Blocked study is both repetitive and predictable.

GH3: "Non-repetitive study results in lower performance during practice, but more learning, than blocked study of mathematics skills."

GH3 is general because it applies to all mathematics skills. However, GH3 also specifies the types of study strategies being compared (non-repetitive vs. blocked) and the outcome measures (performance during practice and learning). Therefore, we can envision testing GH3, provided that we more specifically define the category"mathematics skills" and the assessment of "performance," and "learning."

General Hypotheses are explanations based on deductive reasoning, inductive reasoning, and assumptions to fill a "gap" in knowledge.

How can we create General Hypotheses?

Creating General Hypotheses is challenging and requires extensive research and reasoning. The motivation for creating a General Hypothesis is most often to fill a "gap" in understanding. A "gap" in understanding is an area of inquiry that is (1) important; (2) NOT sufficiently understood, and (3) surrounded by areas that we do understand enough to create explanations that include the gap in understanding.

The purpose of a General Hypothesis is to provide one explanation that potentially fills the "gap" in understanding.

There are many ways to create General Hypotheses. However, at the broadest level, creating a General Hypothesis involves creating an explanatory scientific model using deductive reasoning (based on known principles) and inductive reasoning (previous observations). We also cannot avoid making some assumptions. Known assumptions can be stated in a forthright manner. The fact that we also make assumptions that are unknown to us can temper our confidence in hypotheses.

General Hypotheses do not need to be one sentence.

There is no reason that General Hypotheses must be expressed in a single sentence! If a General Hypothesis is more than a one sentence explanation, then it is acceptable to use as many sentences as necessary to express the General Hypothesis. For example, it might be clearer to express GH3 with two separate sentences that each express one idea:

GH4: "Non-repetitive practice results in lower performance during practice than blocked study of mathematics skills. However, non-repetitive practice results in more learning than blocked study of mathematics skills."

Explanations (or models) may involve multiple steps or separate elements that require many sentences to explain. For example, the sliding-filament hypothesis involves myosin, actin, binding sites, ATP, etc. Models may be expressed using mathematical relationships. Including or explaining a model can all be part of a General Hypothesis.

Testing General Hypotheses requires many studies.

Although General Hypotheses have many forms, General Hypotheses have one property in common: testing General Hypotheses nearly always requires many studies. Theoretically, it may be possible to use modus tollens to reject some General Hypothesis using a single experiment. However, in practice even rejecting General Hypotheses requires multiple experiments (Giere, 2006). No scientific model is perfect, but models may still be useful and widely explanatory even if some of their predictions are not accurate (McElreath, 2019). Moreover, experiments are not perfect, and depend on known and unknown assumptions. It is also difficult or impossible to design an experiment that completely isolates a single variable and definitively tests a hypothesis. Therefore, rejecting a General Hypothesis typically requires the "consilience" of MANY studies that consistently point to a single conclusion to reject the General Hypothesis.

MANY studies are also required to support General Hypotheses. Strong inference requires many studies to exclude many possible alternative hypotheses. Inductive reasoning involves considering evidence from many studies of different types to support or reject hypotheses. Even with many studies, scientists can never be 100% confident in conclusions about hypotheses. Science can therefore be seen as a continual quest to construct more useful (but always tentative to some degree) models of the universe.

"All models are wrong, but some are useful" -- George Box et al.

Therefore, many studies are needed to either reject or support General Hypotheses.

General Hypotheses are testable models that apply to large categories of observations. Strong General Hypotheses are NOT vague, but as specific as possible.