We generally divide inference into two types: inductive and deductive. Inductive inference refers to the ability to make generalizations from specific observations, while deductive inference refers to coming to specific conclusions from a set of general premises.
But there are other types of inference, too, that come from academic disciplines as diverse as philosophy, cognitive sciences, and economics. Below, we’ll explore each of them, with examples, pros and cons.
Types of Inference
1. Deductive Inference
Deductive reasoning, also known as deduction or deductive inference, is a type of reasoning that involves taking a generally true statement and narrowing it down to apply to a specific instance.
So, when someone thinks that in general, something is true, then they will infer that it also is true in their specific circumstance.
Usually, we can come to a logical conclusion through the process of deductive inference. Most things necessarily follow from a set of general premises or hypotheses. Essentailly, if the generalized premises are universally true, then the conclusion must be true.
However, be cautious. Sometimes something is generally true but not necessarily true in all instances. Such is the case, for example, when we engage in stereotyping. While it’s generally true that people from rural Utah are Mormans, plenty of rural Utahns aren’t Mormons, too. The general premise is not a universal truth, so we cannot use deductive inference alone to reach our conclusion when we meet someone from rural Utah.
Example 1
Premises: All birds have feathers. Penguins are birds.
Conclusion: Therefore, penguins have feathers.
Example 2
Premises: If it rains, then the streets get wet. It’s raining.
Conclusion: Therefore, the streets are wet.
Example 3
Premises: No mammals are cold-blooded. All reptiles are cold-blooded.
Conclusion: Therefore, no reptiles are mammals.
| Pros of Deductive Inference | Cons of Deductive Inference |
|---|---|
| Provides conclusions that are logically certain. | Limited to what is contained in the premises. It cannot provide new information, only clarify what is already known. |
| If the premises are true and the form of the argument is valid, the conclusion must be true. | The certainty of the conclusion is dependent on the truth of the premises, which may not always be easily determined. |
| Used in various fields, including mathematics and logic, where certainty is required. | The premises must be universal – in every single case – to avoid making mistakes. |
2. Inductive Inference
Inductive reasoning, also known as induction or inductive inference, is a type of reasoning that involves making broad generalizations from specific observations. It is the opposite of deduction.
Here, we’re going from one instance to a generalization, rather than applying a generalization to a specific instance.
Inductive reasoning has its place in many instances of logical thinking, and even sometimes the scientific method. For example, a set of data may be collected, and based on the data, tentative generalized models are developed to describe that data.
But the conclusions drawn from inductive reasoning need to be considered probable rather than certain because oftentimes observations of one case study cannot be generalized to everyone.
Let’s take the example of swans. You might see a flock of swans in a pond, and they’re all white. So, you develop an inductive inference that “all swans are white.” While true in your pond, it turns out that elsewhere, there are black swans, so you’ve made a mistake making this inductive inference.
Example 1
Observation: Every time you have seen a swan, it has been white.
Generalization: Therefore, all swans are white.
Example 2
Observation: You’ve just eaten at a restaurant five times, and each time the food has been delicious.
Generalization: Therefore, the food at this restaurant is always good.
Example 3
Observation: Every winter that you’ve experienced has been cold.
Generalization: Therefore, every winter is cold.
| Pros of Inductive Inference | Cons of Inductive Inference |
|---|---|
| Allows for generalizations and predictions, making it particularly useful in science and everyday life. | Conclusions are not guaranteed to be true, even if the premises are true. |
| Can deal with premises that are uncertain or probabilistic. | Susceptible to the problem of induction – just because something has always been observed to be a certain way, doesn’t guarantee it will always be that way. |
Go Deeper: Observation vs Inference (Similarities and Differences)
3. Abductive Inference
Abductive inference, also known as abduction or inference to the best explanation, is a form of logical inference which starts with an observation or set of observations and then seeks the simplest and most likely explanation.
In abductive reasoning, the premises do not guarantee the conclusion. The conclusion is what best explains the premises and is subject to revision as new evidence emerges.
Remember, the conclusion in abductive inference is what seems most likely based on the information available at that moment, and you’re willing to change your mind. As new evidence becomes available, the conclusion might change.
Example 1
Observation: The grass is wet.
Best Explanation: It rained last night.
Example 2
Observation: You come home to find your house in disarray with items scattered around.
Best Explanation: A burglary took place while you were out.
Example 3
Observation: A patient is presenting symptoms like fever, cough, and loss of taste and smell.
Best Explanation: The patient might have contracted COVID-19.
| Pros of Abductive Inference | Cons of Abductive Inference |
|---|---|
| Useful in generating possible explanations, making it valuable in diagnostic and investigative settings. | Offers no logical guarantee that the best explanation is the correct one. |
| Allows for creative and innovative thinking by generating new hypotheses and theories. | Often relies on subjective judgement to determine what is the “best” explanation. |
4. Statistical Inference
Statistical inference is used in economics, mathematics, and quantitative research to produce generalizations and models. It involves the process of using data analysis to infer properties of an underlying probability distribution.
Statistical inference allows you to make predictions or draw conclusions about a larger set of data (population) based on a smaller set of data (sample).
The most important thing to remember about statistical inference is that your dataset needs to be representative of the general population that you are studying and be sizable enough to have statistical relevance.
Remember, statistical inference involves a degree of uncertainty because conclusions are drawn about a whole population based on a subset of it. Statistical tests can provide information about the degree of uncertainty, usually in the form of a p-value or confidence interval.
Example 1
Descriptive Statistics: A company might survey a sample of its customers about their satisfaction with the company’s products. The average satisfaction score among those surveyed is a descriptive statistic that summarizes the data.
Example 2
Inferential Statistics (Confidence Intervals): A pharmaceutical company tests a new drug on a small group of volunteers. The average improvement in symptoms serves as the basis for a confidence interval, from which the company predicts the range within which the average improvement for the entire population of patients (if all were treated) would fall.
Example 3
Inferential Statistics (Hypothesis Testing): An educational researcher wants to know if a new teaching method is more effective than the current one. They test the new method on a group of students and the old method on another group. They then compare average test scores between the two groups to determine if there is a statistically significant difference, which would suggest the new method is more (or less) effective.
| Pros of Statistical Inference | Cons of Statistical Inference |
|---|---|
| Allows predictions about a large population based on a smaller sample. | Subject to sampling error and bias, which can affect the accuracy of predictions. |
| Invaluable in research, economics, social sciences, and more for hypothesis testing, estimation, and prediction. | Requires assumptions about the population that may not hold true. |
5. Causal Inference
Causal inference is the process of drawing a conclusion about a causal connection, that is, cause and effect.
It is a complex task as it often involves establishing the direction and magnitude of cause and effect relationships.
One of the most valuable research methods for determining causal inference is experimental research where researchers can examine variables under controlled environments to test causal relationships between variables. Researchers may also use longitudinal studies, which takes cross-sectional data at various points in time to plot changes in variables, to make causal inferences.
Keep in mind, while causal inference suggests a possible cause-and-effect relationship, it does not confirm it. Correlation does not necessarily imply causation, and there could be other factors at play.
Example 1
Observation: Smoking rates increase. Lung cancer rates also increase.
Possible Causal Inference: Smoking might cause lung cancer.
Example 2
Observation: A city introduces a bike sharing program. The number of bike accidents in the city increases.
Possible Causal Inference: The introduction of the bike sharing program may have caused an increase in bike accidents.
Example 3
Observation: Students who participate in an after-school program have higher grades than those who don’t.
Possible Causal Inference: Participating in the after-school program may cause students to have higher grades.
| Pros of Causal Inference | Cons of Causal Inference |
|---|---|
| Helps establish cause-and-effect relationships, which are important for understanding and predicting phenomena. | Observational data can lead to confounding, where extraneous variables affect both the cause and effect, leading to spurious associations. |
| Invaluable in fields such as medicine, economics, and social sciences. | The complexity of real-world phenomena can make it difficult to establish clear causal relationships. |
6. Analogical Inference
Analogical inference (or analogical reasoning) is a type of reasoning that involves drawing conclusions based on the perceived similarity between separate cases.
In other words, if two things are similar in some ways, it’s likely that they will be similar in other ways, too.
While analogical inference can be a powerful tool, it’s also based on the assumption of similarity, which may not always hold true. As with most examples of inference explored here, there tends to be room for error and mistakes in reasoning, especially when confounding or hidden variables come into play.
For example, there can be differences between situations that are not immediately apparent, and these can affect the outcome.
The classic example of the flaw of analogical inference is that of Linnean taxonomic rankings in biology (i.e. species groupings). The taxonomic ranking system was entirely based on visible similarities between animals.
But as science developed, it was realized that visible similarities and traits did not necessarily imply evolutionary closeness, which gave rise to the more accurate phylogenetic classification which groups animals based on a more accurate evolutionary tree.
Therefore, conclusions reached through analogical inference should be treated as hypotheses that need further testing and validation.
Example 1
Observation: Animals that are mammals usually give birth to live young. Dogs are mammals.
Analogical Inference: Dogs likely give birth to live young.
Example 2
Observation: You studied diligently for your math test and scored an A.
Analogical Inference: If you study diligently for your physics test, you will likely score an A.
Example 3
Observation: In the past, cutting taxes has led to an increase in consumer spending.
Analogical Inference: If the government cuts taxes now, it will likely lead to an increase in consumer spending.
| Pros of Analogical Inference | Cons of Analogical Inference |
|---|---|
| Useful for problem-solving, decision-making, and generating hypotheses. | The validity of the inference is dependent on the degree of similarity between the cases, which can be subjective. |
| Allows for creativity and innovation by applying knowledge from one domain to another. | Risk of overlooking important differences between the cases. |
7. Invalid Inference
Invalid inference refers to a type of logical fallacy where the conclusion drawn does not logically follow from the premises. We might also call this a logical fallacy.
This can happen in several ways, including ignoring important information, assuming something that isn’t justified, or misapplying a valid form of reasoning.
These can all lead to conclusions that are not supported by the evidence or the argument.
Example 1: Affirming the Consequent
This is a logical fallacy where the consequent of a conditional statement is affirmed, leading to the affirmation of the antecedent. For instance:
Premise: If it is raining, then the ground is wet.
Observation: The ground is wet.
Invalid Inference: Therefore, it is raining.
The fallacy here is that there are other reasons why the ground could be wet (for instance, someone could’ve spilled water).
Example 2: Denying the Antecedent
This is a logical fallacy where the antecedent of a conditional statement is denied, leading to the denial of the consequent. For instance:
Premise: If John is a bachelor, then John is unmarried.
Observation: John is not a bachelor.
Invalid Inference: Therefore, John is not unmarried.
The fallacy here is assuming that being a bachelor is the only way John can be unmarried. He could be divorced or widowed and still be unmarried.
Example 3: Hasty Generalization
This is an informal fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence. For instance:
Observation: My Christian friend supports gay marriage.
Invalid Inference: Therefore, all Christians support gay marriage.
The fallacy here is generalizing about a large group (all Christians) based on a sample that is not large enough or representative enough (my friend).
These are just a few examples of invalid inferences. There are many other ways in which an inference can be invalid, including fallacies of relevance (where the premises are not relevant to the conclusion), fallacies of presumption (where the conclusion assumes something that isn’t justified), and fallacies of ambiguity (where unclear language leads to a misleading conclusion).
| Pros of Invalid Inference | Cons of Invalid Inference |
|---|---|
| There are generally no pros to invalid inferences as they don’t lead to logically sound conclusions. | Leads to conclusions that aren’t logically justified. |
| Can result in faulty reasoning and incorrect beliefs or actions. | |
| Can be used manipulatively to persuade or mislead. |
Another Type: Transitive Inference
Conclusion
If there is anything to take away from this article on the types of inference, it is that it’s important to critically evaluate the logic of any inference to ensure that it’s valid and reliable. Inferences by definition require us to draw conclusions based on observable data. The question, however, is always whether that data we are observing is accurate, valid, and reliable both internally (i.e. does it make sense for the case we’re looking at) and externally (i.e. is the observation generalizable to other situations). If we can obtain both internal and external validity of our observations, then we’re more likely to be able to use inference to achieve a valid conclusion.
Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]