Dear Editor,

P-values are a product of hypothesis testing, indicating the ‘probability that no effect of an intervention (null hypothesis) has occurred within a population’1. A high p-value implies a ‘higher probability for no effect’, while a low p-value suggests a potential intervention effect1. The smaller the p-value in a particular research, the greater the statistical significance of its assertions. Moreover, the p-value signifies the likelihood, within a given statistical model, that the statistical summary would be equal to or more extreme than the observed results if the null hypothesis is true2. According to Gibson3, the presence of a significantly noteworthy effect, unlikely under the assumption of no actual effect, invalidates the null hypothesis. A low p-value indicates the observation of something highly uncommon, casting doubt on the accuracy of the null hypothesis.

As public health practitioners, there exists an expectation that quality care must be evidence-based, i.e. supported by p-values in empirical studies. According to Cohen4, there have been instances where p-values in medical literature have justified the million-dollar development of various pharmacological drugs and secured the tenure of some academic researchers who have made statistically significant claims in various fields. In public health research, the balance between avoiding false positives and false negatives depends on the consequences of errors and the research stage. For example, during the exploratory phase, an excess of false positives may waste resources, while an abundance of false negatives can lead to overlooking meaningful discoveries. However, it is crucial to adjust the p-value for both multiplicity and selection bias to ensure accurate results3.

In recent times, the stellar position of p-values has come to the critical scrutiny of scholars. Statistical significance may not always imply scientific, human, or economic importance. Lower p-values do not always mean more substantial effects and higher p-values do not necessarily indicate a lack of importance2. A minute effect can generate a small p-value if the sample size or measurement precision is sufficiently high, and conversely, substantial effects may yield unremarkable p-values with a small sample size or imprecise measurements2. According to Altman and Bland5, in randomized controlled trials, a p-value exceeding 5% is conventionally considered non-significant, but labeling a study as non-significant does not necessarily mean there are no clinically relevant findings. Controlled trials with small sample sizes often lack the statistical power needed to identify significant differences in treatment outcomes5.

In this article, existing limitations of the p-value will be reviewed. In addressing such limitations, possible solutions, such as considering confidence intervals and Bayesian reasoning, will be explored.

Limitations of the p-value

One reason why p-values must not be regarded as sole criteria lies in the fact that chance errors can happen at any point in empirical studies4. Benjamin et al.6 highlight that, despite studies reporting statistically significant results with p<0.005, the replicability of such studies remains notably low. This underscores that the strength of evidence conveyed by a p-value is contingent on the nature of the research and its position within the research continuum. Differences in the level of study participants may also be difficult to control owing to the multitude of characteristics such as genetic composition and variations in environmental exposures or experiences of study participants, particularly in studies with large sample sizes4. Even if the possibility of confounding variables may be addressed by statistical models, it is essential to note that statistical models and various study designs may also have limitations7. Cross-sectional studies, for example, may only be able to provide a snapshot of a particular event or phenomenon without necessarily being true in the future8. The voting preferences of a group of individuals at one point may not be the same after a few months or after several years. Similarly, the findings of a non-experimental study may not be as rigorous as those of a randomized controlled trial.

Ioannidis9 also highlighted that as more scientific teams and conflicts of interests and prejudices gravitate towards a scientific field, it can be less likely that its findings will be true, thus rendering the reliance on p-values alone as dubious. Conflicts of interest pertain to circumstances that may cloud the judgment of a researcher while conducting a study10. One example of conflict of interest can come in the form of accepting favors or financial remuneration from companies or organizations that are engaged in business11. Another example can be evident in the act of coming up with a manuscript that may render strong socio-political support to an individual, organization, or ideology10. Furthermore, several other significant factors can impact the p-value in research. Multiplicity, which involves making multiple comparisons, can inflate the likelihood of obtaining false-positive results12,13. Selection bias, where certain groups are disproportionately included or excluded from the study, can also influence the p-value14. Additionally, small and noisy studies with low statistical power may produce unreliable or inconclusive p-values. In public health research, for example, a study investigating the effectiveness of multiple interventions simultaneously may face multiplicity issues, and selection bias may arise if certain demographic groups are overrepresented or excluded. Similarly, a small-scale study on a rare disease may encounter challenges related to both small sample size and noise, affecting the reliability of its p-values.

Potential strategies

Instead of relying only on p-values, Cohen4 suggests that researchers may consider the importance of confidence intervals because of their capacity in ‘estimating the range within which the true value can be expected’. Large studies in individual studies can have narrower confidence intervals, thereby indicating a more precise estimate15. In meta-analysis studies, the precision of estimates decreases as the heterogeneity of the studies included increases15.

Taking into account prior pieces of evidence drawn from Bayes’ theorem may also prove to be helpful because, in a way, other equally credible sources of information are taken into account4, and the p-value is given more context7. Bayesianism, by virtue of its being inductive, considers data to be partial. An example can be depicted in the study of Bland and Altman16,17 that aimed to determine the prevalence of diabetes in a region in the UK. In the original inquiry, the researchers relied on available survey results from the UK as a whole and from nearby areas. Given the information that diabetes in the UK has a prevalence of 2% and that some areas have a prevalence between 1 and 3%, it can be questionable to come up with a claim that the prevalence of diabetes in the locale of the study is 0 or exceeding 10%17. Bayesianism can be a good alternative because while it draws from multiple sources of data, it is open to the idea of changing a belief in the light of new evidence17. One specific example of Bayesianism presented in the above example pertains to disease prevalence estimation. Bayesian methods allow researchers to incorporate prior knowledge or beliefs about the prevalence of disease into their analysis, updating these beliefs based on observed data. This is particularly valuable when dealing with limited or imperfect data, as Bayesian approaches provide a flexible framework to combine prior information with current evidence, resulting in more robust estimates of disease prevalence.

Future challenges

P-values can provide an indispensable tool in making sense of various statistical tests. However, caution must be observed in integrating these statistical findings in actual settings. Even if the p-value has reached an elevated status in scientific scholarship, Ou18 warns that we must examine our tendency to have ‘uncritical adherence’ to its real-world implications. As such, we must be receptive to new forms of knowledge that call for re-examining existing frameworks18. Public health practitioners, in this regard, must assert their capacity to be actively involved in producing empirical evidence while being critical of the tools and methods that aim to provide generalizations in the name of empirical knowing. Policymakers in the realm of public health should be cautious of making decisions guided by p-values alone. Instead, components of empirical reports should be considered, such as confidence intervals and the possibility of selection bias in some research. Given the widespread misuse and misunderstanding of p-values, some statisticians advocate for alternative methods in public health research. These approaches prioritize estimation over testing and involve tools like confidence intervals, credibility intervals, or prediction intervals2. In public health situations, researchers may opt for Bayesian methods, likelihood ratios, or Bayes Factors to evaluate evidence more effectively. Decision-theoretic modeling and false discovery rates are additional strategies that can directly assess the magnitude of an effect and its uncertainty or scrutinize the correctness of a hypothesis in public health studies2.

Benjamin et al.6 also advise that instead of focusing merely on statistically significant results, readers also need to pay attention to how transparency is reflected so that other scholars may be adequately informed. In some instances, publication bias becomes apparent when only studies with statistically significant positive findings are published, while those with statistically insignificant or negative results are not19. In a similar vein, this may run parallel to the notion of publishing research findings that may not necessarily contain the desired p-values reflective of statistical significance, as in the case of the Journal of Negative Results20 that gives a platform for empirical studies in the fields of evolutionary biology and ecology without giving sole reliance on significance thresholds. Moreover, registering research protocols will increase trust in the reported findings by ensuring that the methodology was established beforehand and verifying that it was not manipulated to align with the authors’ preferences21.