Fact-checked by Grok 2 weeks ago

Post hoc

Post hoc, formally known as post hoc ergo propter hoc—a Latin phrase translating to "after this, therefore because of this"—is a logical fallacy that occurs when a person assumes a causal relationship between two events solely because one precedes the other in time. The term is also used in statistics to refer to analyses or tests conducted after initial data examination or hypothesis testing.^[1]^[2]^[3] This error confuses temporal sequence with causation, ignoring other potential factors or explanations that could link the events.^[4] As a subtype of false cause fallacies, it highlights the dangers of hasty generalizations in reasoning, where correlation is mistaken for direct influence without supporting evidence.^[5] Later thinkers, such as John Stuart Mill in his System of Logic, critiqued it as a form of overgeneralization that overlooks multiple contributing causes.^[4] In modern informal logic, it is classified among causal paralogisms, often appearing in arguments that fail to demonstrate a mechanistic process beyond mere chronology.^[4] For instance, claiming that a policy change caused an economic shift simply because the shift followed the change exemplifies this error, as alternative variables like market trends may be at play.^[3] Recognizing the post hoc fallacy is essential in critical thinking, scientific inquiry, and everyday discourse to avoid misleading conclusions.^[2] It frequently surfaces in pseudoscience, political rhetoric, and anecdotal evidence, where proponents attribute outcomes to prior actions without rigorous testing.^[5] To counter it, arguments must provide empirical data establishing causation, such as controlled experiments or statistical controls for confounding variables.^[4] By distinguishing sequence from cause, individuals can foster more accurate and reliable interpretations of events.^[3]

Etymology and General Meaning

Literal Translation

The Latin phrase post hoc directly translates to "after this," where post signifies "after" or "subsequent to," and hoc is the neuter accusative singular form of the demonstrative pronoun hic, haec, hoc, denoting "this" or "the thing."^[6] This construction in Latin typically indicates temporal or sequential relation, referring to an event or action following a specified one. In English adoption, post hoc retains this core meaning of "after this" or "subsequent," often implying retrospection or occurrence following a prior event. It entered English lexicon by the early 19th century, with the first attested use in 1843, used standalone to describe matters arising or addressed after the fact.^[7] The phrase is pronounced /poʊst ˈhɑːk/ in standard English contexts, approximating classical Latin phonetics with a stress on the second word.

Historical Usage

The phrase "post hoc," meaning "after this" in Latin, first appears in classical Latin literature as a standard expression denoting temporal sequence. It is attested in the works of Marcus Tullius Cicero, the Roman statesman and philosopher active in the 1st century BCE, where it is employed in rhetorical and philosophical contexts to describe events following one another without implying causal relationships. The adoption of "post hoc" into English occurred gradually through scholarly and legal channels, reflecting the influence of Latin on early modern intellectual traditions. This usage emphasized sequence in judicial reasoning without presuming causation, aiding in the clarification of timelines in litigation. In non-fallacious contexts, "post hoc" appeared in 18th-century philosophy texts to describe mere chronological succession in historical or empirical narratives. This neutral application persisted in philosophical writing to avoid erroneous inferences, focusing instead on descriptive chronology. By the 19th century, interpretations began shifting toward recognizing potential fallacious implications in certain contexts.^[8]

Logical Fallacy

Definition of Post Hoc Ergo Propter Hoc

Post hoc ergo propter hoc is a Latin phrase that literally translates to "after this, therefore because of this."^[4] This expression denotes an informal logical fallacy in which the temporal sequence of two events is mistakenly interpreted as evidence of a causal relationship between them.^[5] At its core, the fallacy occurs when one assumes that because event A precedes event B in time, event A must have caused event B, without additional evidence demonstrating a causal mechanism or accounting for potential confounding factors.^[4] This error represents a failure in causal reasoning, where chronological order is conflated with causation.^[5] Classified as a subtype of non sequitur fallacies, post hoc ergo propter hoc belongs to the broader category of informal fallacies, which involve defects in reasoning content or context rather than violations of formal deductive validity.^[4] Unlike formal fallacies, such as affirming the consequent, it arises in natural language arguments and inductive inferences, highlighting a disconnect between premises and conclusion without structural invalidity in syllogistic form.^[5] The essential logical structure of the fallacy can be outlined as follows: event A occurs, followed by event B; therefore, A caused B. This inference lacks justification unless supported by empirical data on mechanisms, correlations, or experimental controls.^[4]

Mechanisms and Common Errors

The post hoc ergo propter hoc fallacy stems from cognitive biases that predispose individuals to infer causation from temporal sequence alone. Confirmation bias plays a key role, as people selectively attend to and recall evidence that aligns with an assumed causal relationship while disregarding disconfirming instances, thereby reinforcing erroneous beliefs about event sequences.^[9] Illusory correlation further contributes by leading individuals to overestimate associations between unrelated events, particularly when those events co-occur frequently or saliently, fostering a perception of patterned causality in random or coincidental sequences.^[10] These biases are rooted in the brain's tendency to seek explanatory patterns for uncertainty, a heuristic that aids survival but falters in complex causal reasoning.^[9] Common errors in committing the fallacy include overlooking alternative causes, where intervening or confounding factors are ignored in favor of the temporally prior event; reverse causation, in which the assumed effect is mistakenly treated as the cause; and coincidental timing, attributing significance to chance alignments without verifying independence.^[11] Such mistakes often arise from failing to rigorously evaluate causal claims against established frameworks, such as the Bradford Hill criteria, which stress that mere temporal precedence is insufficient for inferring causation without supporting evidence like biological plausibility and dose-response relationships.^[12] In rhetorical contexts, the fallacy is frequently deployed in arguments, speeches, and media narratives to imply causality through sequential event descriptions, exploiting audience tendencies toward pattern recognition to persuade without empirical validation.^[13] This tactic simplifies complex issues by chaining events narratively, as seen in persuasive discourse where prior occurrences are framed as direct precursors to outcomes, bypassing the need for mechanistic explanation.^[14] Detecting the post hoc fallacy involves applying a structured checklist for causal validity: confirm temporal order as a baseline requirement, but supplement it with evidence of consistent correlation, a plausible underlying mechanism, and replicability across independent observations to rule out spurious links.^[15] The Bradford Hill criteria offer a comprehensive guide, evaluating aspects like association strength, specificity, and coherence to differentiate genuine causation from temporal artifacts, thereby mitigating errors in inference.^[12]

Historical Examples

In ancient Rome, superstitions often led to the post hoc fallacy, where preceding omens were blamed for subsequent calamities like plagues, as people attributed natural disasters to divine wrath without evidence of causation.^[16] The poet Lucretius critiqued this in his epic De Rerum Natura (c. 55 BCE), arguing that fear of gods and omens oppressed humanity, using atomic theory to explain phenomena naturally rather than through supernatural sequences.^[17] For instance, in Book VI, he described the Athenian plague of 430 BCE, detailing failed religious rituals and attributing the outbreak to environmental factors like contaminated winds, rejecting the idea that prior portents caused it as mere superstition. During the medieval period, celestial events were frequently interpreted as causal precursors to political upheavals, exemplifying the fallacy in historical chronicles. The appearance of Halley's Comet in 1066 was seen as an ill omen preceding the Norman Conquest, with contemporary accounts like the Bayeux Tapestry depicting it as a harbinger of King Harold II's defeat at the Battle of Hastings on October 14, 1066, implying the comet directly influenced the outcome despite no causal link.^[18] English and Norman sources, including the Anglo-Saxon Chronicle, reinforced this by linking the comet's visibility in April-May 1066 to the ensuing royal deaths and invasion, a view perpetuated in medieval astrology where temporal sequence was mistaken for causation.^[19] In the 19th century, philosophers began systematically identifying the post hoc fallacy within inductive reasoning, highlighting its pitfalls in scientific and everyday inference. John Stuart Mill addressed it explicitly in A System of Logic (1843), classifying "post hoc, ergo propter hoc" as a common error where mere temporal succession is assumed to prove causation, using examples from historical events and experiments to warn against uncritical generalizations.^[20] Mill emphasized that while sequence may suggest inquiry, it requires additional evidence like joint variation or elimination of alternatives to establish true cause, critiquing its role in flawed historical narratives and policy decisions. Early 20th-century political propaganda frequently exploited the fallacy to attribute economic downturns to prior policies or events, fostering scapegoating without substantiation. In Weimar Germany, Nazi rhetoric post-1919 blamed the Treaty of Versailles for the hyperinflation of 1923 and the Great Depression's onset in 1929, portraying the treaty's reparations as the direct cause of unemployment and poverty despite intervening factors like global trade collapse. This narrative, disseminated through speeches and publications like Joseph Goebbels' writings, assumed sequence implied causation to rally support, ignoring evidence that domestic fiscal policies and international lending played larger roles.^[21]

Statistical Applications

Post Hoc Analysis in Hypothesis Testing

In statistical hypothesis testing, post hoc analysis refers to exploratory procedures conducted after an initial omnibus test, such as analysis of variance (ANOVA), reveals a significant overall effect, allowing researchers to investigate specific patterns or differences in the observed data.^[22] These analyses are typically unplanned and retrospective, focusing on data that has already been collected and examined, rather than being specified in advance based on prior theory.^[23] The primary purpose of post hoc analysis is to pinpoint which particular groups or variables contribute to the detected significance, thereby facilitating the generation of new hypotheses for future research without assuming definitive causation from the exploratory findings alone.^[24] For instance, after an ANOVA indicates differences among treatment groups, post hoc methods can reveal pairwise comparisons that were not hypothesized a priori, aiding in the refinement of scientific understanding.^[22] This approach is valuable for uncovering unexpected relationships but requires cautious interpretation to avoid overgeneralization.^[23] Post hoc analysis is commonly applied in experimental designs, including randomized controlled trials (RCTs) where initial results prompt deeper subgroup explorations, and in observational studies to identify emergent patterns in large datasets.^[23] In RCTs, for example, it might examine differential effects across unexpected subgroups, such as varying doses or demographics, following primary outcome assessments.^[23] Unlike the logical fallacy of post hoc ergo propter hoc, which erroneously infers causation solely from temporal sequence, statistical post hoc analysis employs controlled, validated techniques to explore data retrospectively while emphasizing the need for subsequent confirmatory studies to establish reliability.^[24] This distinction underscores its role as a hypothesis-generating tool rather than a source of unsubstantiated causal claims.^[22]

Specific Post Hoc Tests

After an ANOVA indicates significant differences among group means, specific post hoc tests are employed to identify which pairs or contrasts differ. Tukey's Honestly Significant Difference (HSD) test is a widely used procedure for conducting all pairwise comparisons between group means when sample sizes are equal, controlling the family-wise error rate at the desired level. The test computes the difference between each pair of means and compares it to a critical value given by q_{\alpha, k, \nu} \sqrt{\frac{MSE}{n}}, where q_{\alpha, k, \nu} is the studentized range statistic for significance level \alpha, k is the number of groups, \nu is the degrees of freedom for the error term, MSE is the mean square error from the ANOVA, and n is the common sample size per group; if the absolute difference exceeds this value, the means are declared significantly different. Scheffé's method provides a more conservative approach suitable for examining all possible linear contrasts among group means, rather than just pairwise comparisons, and is particularly useful when the researcher has no predefined contrasts in mind.^[25] It adjusts the F-statistic for contrasts, where the critical value for a contrast estimate is based on \sqrt{(k-1) F_{\alpha, k-1, \nu}} times the standard error of the contrast, with F_{\alpha, k-1, \nu} being the critical F-value from the F-distribution with k-1 and \nu degrees of freedom; this ensures control over the family-wise error rate for any set of contrasts.^[25] The method's conservatism arises from protecting against all possible contrasts, making it less powerful for specific pairwise tests but more versatile for exploratory analyses.^[25] The Bonferroni correction offers a straightforward adjustment for multiple comparisons by dividing the overall significance level \alpha by the number of tests m, yielding an adjusted level \alpha' = \alpha / m, which is then applied to each individual test (such as t-tests) to maintain the family-wise error rate.^[26] This simple inequality-based procedure, while conservative especially for large m, is easy to implement and applicable to any set of hypothesis tests, including post hoc comparisons after ANOVA.^[26] These post hoc tests share common assumptions derived from ANOVA, including normality of the residuals within each group and homogeneity of variances across groups, which can be checked using diagnostic plots or Levene's test. Tukey's HSD is preferred when sample sizes are equal and the focus is on all pairwise comparisons due to its balance of power and error control, while Scheffé's method is chosen for complex contrasts or unequal sample sizes despite its lower power, and the Bonferroni correction is ideal for a small, planned set of comparisons or when computational simplicity is prioritized.

Addressing Multiple Comparisons

The multiple comparisons problem in post hoc testing occurs when multiple hypothesis tests are performed on the same dataset, substantially increasing the family-wise error rate (FWER)—the probability of incurring at least one Type I error (false positive) across the entire set of tests.^[27] For example, conducting 10 independent tests each at a significance level of α = 0.05 yields a probability of approximately 0.40 for at least one false positive, as calculated by 1 - (1 - α)^m, where m is the number of tests./06%3A_Multiple_Tests/6.01%3A_Multiple_Comparisons) This inflation arises because the nominal α level applies per test, but the cumulative risk escalates with more comparisons, undermining the reliability of exploratory findings./06%3A_Multiple_Tests/6.01%3A_Multiple_Comparisons) To address this, methods beyond basic corrections like Bonferroni or Tukey are employed, with the false discovery rate (FDR) providing a more powerful framework by targeting the expected proportion of false positives among significant results rather than strictly bounding all errors.^[28] The seminal Benjamini-Hochberg procedure controls FDR by sorting the m p-values in ascending order p_{(1)} \leq p_{(2)} \leq \cdots \leq p_{(m)} and rejecting all null hypotheses up to the largest i where

p_{(i)} \leq \frac{i}{m} q

with q denoting the target FDR level; this monotonic approach ensures FDR ≤ q under independence or positive dependence of test statistics.^[28] Effective management of post hoc analyses also involves best practices such as defining pre-planned contrasts a priori, grounded in theoretical predictions, to limit the scope of comparisons and preserve statistical power without necessitating broad corrections.^[29] Complementing this, reporting standardized effect sizes—like Cohen's d, which quantifies the mean difference in standard deviation units—offers insight into practical significance and helps interpret the magnitude of detected effects.^[30] Furthermore, replicating post hoc findings in independent datasets is crucial for establishing their robustness, as initial exploratory results are prone to capitalization on chance.^[31] Criticisms of multiple comparison corrections highlight their potential over-conservatism, particularly with stringent FWER methods, which can reduce power and increase Type II errors by failing to detect true effects in sparse-signal scenarios.^[32] Balancing this requires integrating power analysis to evaluate trade-offs, ensuring study designs maintain sufficient sensitivity to meaningful differences while controlling error rates.^[33]

References

[1]
Logical Fallacies - Purdue OWL
Post hoc ergo propter hoc: This is a conclusion that assumes that if 'A' occurred after 'B' then 'B' must have caused 'A.' Example: I drank bottled water ...
[2]
Fallacies - UNC Writing Center
This fallacy gets its name from the Latin phrase “post hoc, ergo propter hoc,” which translates as “after this, therefore because of this.” Definition: Assuming ...
[3]
Fallacies - Stanford Encyclopedia of Philosophy
May 29, 2015 · There are a number of fallacies associated with causation, the most frequently discussed is post hoc ergo propter hoc, (after this, therefore ...<|control11|><|separator|>
[4]
Fallacies | Internet Encyclopedia of Philosophy
Its four principal kinds are the Post Hoc Fallacy, the Fallacy of Cum Hoc, Ergo Propter Hoc, the Regression Fallacy, and the Fallacy of Reversing Causation.
[5]
https://iep.utm.edu/fallacy/
[6]
[PDF] §§1–14 Exordium. §§15–36 Narratio. §§37–82 Argumentatio. §§83 ...
of argument called post hoc ergo propter hoc, i.e., to argue that if X happened after Y, then. Y caused X), as each crime leads to that which follows: Pater ...
[7]
[PDF] Postema and the Common Law Tradition
One of them eschewed the notion that law was to be seen as a command, but saw it as the working out, post hoc, of rights and wrongs through adjudication. The ...
[8]
post hoc ergo propter hoc, phr. meanings, etymology and more
post hoc ergo propter hoc, phr. meanings, etymology, pronunciation and more in the Oxford English Dictionary.
[9]
Illusions of causality: how they bias our everyday thinking and ... - NIH
Illusions of causality occur when people develop the belief that there is a causal connection between two events that are actually unrelated.Missing: fallacy | Show results with:fallacy
[10]
[PDF] Using Informal Fallacies and Cognitive Biases to Win the War of Words
May 1, 2013 · The psy- chologist's label for such thought processes is illusory correlation, which is an inaccurate perception that a relationship exists ...
[11]
Non Causa Pro Causa - Logical Fallacy
Reverse Causation: When two events or event-types occur at the same time, we may be tempted to think that one caused the other when the direction of causation ...Missing: coincidental | Show results with:coincidental
[12]
Assessing causality in epidemiology: revisiting Bradford Hill to ... - NIH
The nine Bradford Hill (BH) viewpoints (sometimes referred to as criteria) are commonly used to assess causality within epidemiology.
[13]
Fallacies – Public Speaking - Maricopa Open Digital Press
A post hoc ero propter hoc fallacy is the assumption that one thing caused another without proof of the link. A faulty analogy is comparing things that are ...
[14]
Using Rhetorical Strategies for Persuasion - Purdue OWL
There are three types of rhetorical appeals, or persuasive strategies, used in arguments to support claims and respond to opposing arguments.
[15]
The role of causal criteria in causal inferences: Bradford Hill's
Jun 17, 2009 · The criteria used in the Report were the consistency, strength, specificity, temporal relationship, and coherence of the association. Following ...Missing: post | Show results with:post
[16]
https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0131%3Abook%3D1%3Acard%3D62
[17]
https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0131%3Abook%3D6%3Acard%3D757
[18]
8 Things You Didn't Know About 1066 - English Heritage
So what do we know (or not know) about the Battle of Hastings? The Appearance of Halley's Comet in 1066 was taken as an important omen. The Bayeux Tapestry ...Missing: hoc fallacy
[19]
955 Years Ago: Halley's Comet and the Battle of Hastings - NASA
Oct 14, 2021 · During its 1066 appearance, Halley's Comet approached within nine million miles of Earth. As it first appeared in April of that year ...Missing: hoc fallacy
[20]
The Project Gutenberg EBook of A System Of Logic, Ratiocinative ...
A system of logic, ratiocinative and inductive, being a connected view of the principles of evidence, and the methods of scientific investigation.
[21]
The role of economic instability in the Nazi rise to power
Jews and Communists also featured heavily in the Nazi propaganda as enemies of the German people. Joseph Goebbels was key to the Nazis use of propaganda to ...Missing: hoc fallacy
[22]
Sage Research Methods - Post Hoc Analysis
Post hoc analysis is conducted to explore which means are different. In this sense, post hoc analysis can be considered an exploratory ...
[23]
Types of Analysis: Planned (prespecified) vs Post Hoc, Primary ... - NIH
Post hoc analyses examine hypotheses that are conceptualized after the data are seen. All these terms are explained with the help of examples, and strengths ...
[24]
Post hoc analysis: use and dangers in perspective - PubMed
Post hoc analysis is of major importance in the generation of hypotheses. However, the hypothesis is created by the analysis and has not been proved by any ...
[25]
A Method for Judging all Contrasts in the Analysis of Variance - jstor
The paper is organized so that the reader who wishes to learn the method and ... SCHEFFE, H. (1952). An analysis of variance for paired comparisons. J ...
[26]
Multiple Comparisons Among Means - jstor
This paper considers picking m linear contrasts among k means, estimating them with confidence intervals using a Student t statistic, and evaluating its use.
[27]
What is the Family-wise Error Rate? - Statology
Feb 16, 2021 · When we perform one hypothesis test, the type I error rate is equal to the significance level (α), which is commonly chosen to be 0.01, 0.05, or ...
[28]
Controlling the False Discovery Rate: A Practical and Powerful ...
A simple sequential Bonferronitype procedure is proved to control the false discovery rate for independent test statistics.
[29]
https://files.eric.ed.gov/fulltext/ED426092.pdf
[30]
[PDF] A review of effect sizes and their confidence intervals, Part I
The Cohen's d family. This measure of effect size was inaugurated by Cohen. (1969). It is used to evaluate and to standardize the differ-.
[31]
What is replication? - PMC - PubMed Central - NIH
Mar 27, 2020 · Successful replication provides evidence of generalizability across the conditions that inevitably differ from the original study; unsuccessful ...
[32]
IS THE BONFERRONI CORRECTION REALLY SO BAD? - NIH
The Bonferroni correction (1) for multiple testing is sometimes criticized as being overly conservative. The correction is indeed conservative, and there ...<|control11|><|separator|>
[33]
Finding the right power balance: Better study design and ... - NIH
Jan 8, 2024 · Of relevance, researchers are often criticized for a lack of sufficient statistical power (or power analysis), not only in grant applications ...