Frameworks can help to structure and simplify inductive reasoning.

There are many ways to reason using induction. Inductive arguments can be based on many types of observations, use different numbers of observations, and include different specific observations. Instead of being "valid" or "not valid," "sound" or "not sound," the persuasiveness of inductive arguments is a continuum: from weak to strong (Layman, 2005). Because of the "open ended" nature of Induction, it can be difficult to organize information into simple and compelling arguments. 

Structure is one key to clarity despite complexity.

Using a framework to structure inductive reasoning can be helpful. For example, frameworks for establishing causation can be generalized to help make inductive arguments (Mill, 1843).

Many people are familiar with the phrase "correlation does not imply causation." Simply because two events are correlated with each other does NOT mean that one event causes the other to happen. Concluding that a causal relationship exists solely from a correlation is an example of the logical fallacy Affirming the Consequent.

However, sometimes correlations DO reflect causal relationships! More generally, sometimes data are consistent with predictions because the predictions come from valid scientific models! How can predictions from valid models be separated from spurious coincidence?

One way to gain confidence in hypothesized causal relationships or scientific models is to repeatedly test predictions of the models and reject alternative models using Strong Inference. Another possibility is to inductively support validity. Inductive reasoning has limitations that constrain the strength of inductive conclusions. However, structuring inductive reasoning using different types, or categories, of evidence can strengthen inductive arguments. 

When evidence from different categories of investigation are all consistent with a hypothesis, we can be more confident in the hypothesis. 

One useful set of categories for evidence was explained by Bradford Hill, and are referred to as "Hill's Criteria" (Hill, 1965; Fedak et al., 2015). Although I have modified Hill's criteria from the original 9 to 8 and changed some terminology, the following categories are generally consistent with the original criteria.

Modified Hill's Criteria for testing General Hypotheses.

1) ReliabilityDo repeated studies all lead to the same conclusions?

For General Hypotheses to be useful, they must be capable of predictions that apply in different contexts. The most basic requirement for General Hypotheses is to be "reliable:" for the hypotheses to make predictions that match evidence when the same experiment is repeated. For example, consider a new teaching strategy hypothesized to result in better academic performance than a standard strategy. If the teaching strategy truly is effective, then the strategy should result in better performance than a standard strategy when repeated with many different groups of students. 

2) DiversityDoes evidence from many different approaches all support the hypothesis?

General Hypotheses (i.e. scientific models) can be tested with many different types of evidence. If a General Hypothesis can lead to predictions that are consistent with evidence from many different types of measurements, then it is more likely that the General Hypotheses are valid representations of underlying phenomena. For example, anthropogenic (human-caused) climate change is supported by evidence from many fields of science: direct measurements of temperature, mathematical models, complex computer simulations, biological measurements (e.g. changes to animal and plant distributions, flowering times, etc.), ocean chemistry measurements, and more (Intergovernmental Panel on Climate Change, 2016). A diversity of evidence supports the hypothesis of anthropogenic climate change. Similarly, the Theory of Evolution is consistent with every aspect of biology: from paleontology to anatomy to physiology to ecology to molecular and cell biology, etc.. There is an overwhelming diversity of evidence that past and present biological variety result from evolution (Dawkins, 2009).

3) PlausibilityAre there reasonable mechanisms that underlie observed outcomes? Are the mechanisms consistent with, and do not conflict with, other knowledge?

"Plausability" means that hypothesized mechanisms or relationships are consistent with other known processes. Examples of "known" processes include laws of physics, chemistry, mechanics, and other fundamental laws. Known processes also include more specific information. For example, the hypothesis that smoking causes cancer is plausible because smoke contains mutagens that damage DNA, and damaged DNA is one mechanism for the development of cancer. 

4) Experimental InterventionsCan direct interventions produce predicted outcomes?

Hypotheses can be supported using direct experiments to test predictions of the hypotheses. Using Strong Inference and deductive reasoning to experimentally test the predictions of a hypothesis can therefore be one contributor to an inductive argument for the validity of the hypothesis.

5) TemporalityAre there time-based dependencies (e.g. causes precede effects)?

For causal relationships, causes most often precede effects. For example, if depression causes disruptions to sleep, then other symptoms of depression should precede sleep problems. If depression and sleep problems are concurrent (as they often are), then causality is more difficult to establish.

6) Strength Is there a strong association between variables

A strong observed relationship among variables that make up a hypothesis (e.g. a correlation) can support the validity of the relationship (e.g. that the relationship reflects causality). For example, if a small exposure to a chemical consistently leads to a large outcome, then there is a strong association that suggests a causal relationship.

7) SpecificityAre there specific factors (i.e. not all factors) that result in observed outcomes?

Just as strong relationships among variables can support the validity of a hypothesis, specific relationships among variables can also support hypotheses. For example, if exposure to a chemical consistently results in specific consequences that are not otherwise observed, then there is a specific association that suggests a causal relationship.

8) Biological gradientAre there biological gradients or dose-response relationships?

Biological gradients can be naturally-occurring, or be part of experimental design. A "gradient" is an increase or decrease of one factor associated with a change in another factor. Experiments sometimes involve "dose-response" tests, where experimental systems are systematically exposed to different levels of a factor, and the responses of the system measured. Consistent biological gradients can support causality. In the simplest case of a "linear" gradient, the response will change directly with the change of dose. However, dose-response relationships do not need to be linear, and often involve thresholds or non-linear associations.

How can we use Hill's Criteria to help construct arguments to support hypotheses?

Most importantly, Inductive arguments should faithfully represent the available evidence, including a discussion of research findings that may NOT support a General hypothesis in addition to findings that DO support a hypothesis. For example, inductive arguments that we construct must avoid inductive fallacies and confirmation bias

Hill's Criteria can help organize information relevant to a General Hypothesis. For example, to evaluate the General Hypothesis "Non-repetitive practice results in more learning than blocked practice," we can organize our research according to Hill's Criteria (facilitated by specific categories in our literature grids). For simplicity, let's consider only three of Hill's Criteria: Diversity, Strength, and Plausibility. Expressing our research as a graphical outline could look like:

Having more supporting evidence in any one of Hill's criteria can clearly contribute to stronger inductive arguments. Supporting the validity of a hypothesis using evidence from many of Hill's criteria contributes to even stronger arguments.  Strong evidence that supports many or all of Hill's criteria can result in strong support for a General Hypothesis or Scientific Model.

Inductive arguments must faithfully represent available evidence in support and opposition to a hypothesis. Frameworks such as Hill's Criteria can help organize information and structure inductive reasoning.