Some Rights Reserved. Date last modified: May 16, Wayne W. Module 7 - Comparing Continuous Outcomes. P-Values What to Report. P-Values A test statistic enables us to determine a p-value, which is the probability ranging from 0 to 1 of observing sample data as extreme different or more extreme if the null hypothesis were true. Nature, March 7,] Consider two studies evaluating the same hypothesis. Cautions Regarding Interpretation of P-Values There is an unfortunate tendency for p-values to devolve into a conclusion of "significant" or "not significant" based on the p-value.
Before you run the test, use the Frequencies function to make sure there are no coded missing values in s1q1e. If there are, recode them. What are the results of your t test? Are they what you might expect? Univariate analysis Bivariate analysis Multivariate analysis: Linear.
Bivariate analysis. T test. Statistics p -value What a p -value tells you about statistical significance What a p -value tells you about statistical significance By Dr. Saul McLeod , published When you perform a statistical test a p -value helps you determine the significance of your results in relation to the null hypothesis. How do you know if a p -value is statistically significant?
How to reference this article: How to reference this article: McLeod, S. Further Information. Back to top. If subsequent studies also yielded significant p values, one could conclude that the observed effects were unlikely to be solely the result of chance.
For decades, 0. This cutoff has peculiar reasons. Early in the s, statistics textbooks reported many tables with long series of p values. Fisher shortened the tables previously published by Karl Pearson — , not only for reasons of editorial space but probably also for copyright reasons it seems that Fisher and Pearson were not on good terms.
Some p values were selected and became more important than others, as Fisher wrote for researchers the users and not for expert in statistics the theoreticians. Fisher himself provided a selection of probabilities which simplified the choice to help in decision-making [ 12 ] and attributed a special status to 0.
Research methodology in medicine is such that a comparison between two or more datasets groups is typically performed in terms of a given endpoint. For a reason or another, a study commonly comes up with different values for the measured endpoints in two or more groups, and researchers need to ascertain if the observed difference is actually due to random sampling or, instead, reflects a real difference among the groups [ 14 ].
These comparisons are typically carried out through one or more statistical tests. Briefly, statistical tests are based on the following question: if there is not an existing difference between the two compared groups , what is the probability to obtain the observed difference or a larger one that is only due to random sampling?
As such, it does not provide the probability for the null hypothesis i. Thus, the decision to reject the null hypothesis must necessarily be based on a threshold defined a priori. In practice, the smaller the calculated p value, the more we consider the null hypothesis to be improbable; consequently, the smaller the p value, the more we consider the alternative hypothesis to be probable i. Ioannidis based his proposal to reduce the threshold to 0. We think that such a solution makes biomedical research harder and that, adopting this solution, an improvement in research quality is not granted.
Lowering this way the p value threshold for significance is, at best, a palliative solution. Especially in clinical research, future trials would need to be larger, less feasible, and more expensive. Researchers could abandon some good ideas with the net effect of depressing spontaneous, investigator-initiated research.
Only the few treatments with large effect sizes would gain the evidence, thanks to the statistical power granted by medical industries. Conversely, treatments with a small yet clinically appreciable effect would be hardly proven as effective. This would be amplified in studies where the outcome of interest is quite infrequent such as interval cancers in breast cancer screening mammography, cardiovascular events, or cancer recurrence in longitudinal studies.
Not to mention rare diseases or those studies where the tested treatment or diagnostic tool is invasive and poses ethical or organisational issues. These arguments are not new. An article signed by 54 authors [ 18 ] has provided a similar view, with a deeper technical explanation on why the statements by Ioannidis [ 15 ] and Benjamin et al.
Another article, signed by 88 authors [ 17 ], has questioned the idea that the significance threshold should be based on the amount of relative evidence indicated by Bayesian factors Footnote 1 , as done by Benjamin et al. Causes of this include multiple testing, p -hacking, publication bias, and underpowered studies. A famous example of non-replication came in , when a group of researchers presented an algorithm using genomic microarray data that predicted cancer patients being responders to chemotherapy [ 19 ].
This paper drew immediate attention. Two statisticians later obtained the publicly available data and attempted to apply the algorithm [ 20 ]. What they found was a very poorly conducted data analyses, with errors ranging from trivial to devastating. It was not until that the original study was retracted from Nature Medicine. To better understand the impact of lowering the significance threshold from 0. In particular, the incidence of hard coronary events was 7.
The fully adjusted HR for stroke was 2. For stroke, the HR was 1. This would have been not feasible at all had the significance threshold set at 0. The updated NICE guidelines on cardiac computed tomography as the first-line test for coronary artery disease were based, among other things, on the article by Williams et al.
Being this the result of a subgroup analysis, it could not be found had the significance threshold set at 0. These few examples clearly show the difficulties in reaching statistical significance in clinical research. But similar problems are faced also in preclinical research on animal models, with specific ethical concerns [ 27 ]. In particular, the use of animal models should be discouraged and kept to the minimum, a criterion that is in contradiction with the need for a larger sample size following significance threshold reduction.
Regardless of the misuse of p value and lack of reproducibility, too much importance is given to the p value threshold rather than to biases as well as selective reporting and non-transparency in published studies. There are many stages from the original idea to data analysis of a study, with the p value being the very last. Decisions that are made prior to discuss the p value have a greater impact on results, including design, lack of adjustment for confounding factors, and simple measurement errors.
Biases may force significant findings to come out, with spurious effect sizes that are later rebutted. To a certain degree, biases may lead to a p value lower than any threshold. As acknowledged by Ioannidis [ 11 ], malicious researchers would easily avoid the obstacle by defining, perhaps a posteriori, weak surrogate endpoints. Yet, simply reducing the significance threshold probably would not attenuate these problems. More importantly, healthcare policymakers typically base their decisions on secondary evidence, such as systematic reviews and meta-analyses or cost-effectiveness analyses, which summarise the available evidence taking into consideration the methodological quality of the analysed studies.
Policymakers do not usually take decisions based on a single study of few patients reaching p just below the 0. Especially, data sharing has the potential for verification by independent authors of the results presented in a given publication [ 28 ]. When data are shared, they may be used by other researchers to perform alternative or supplementary analyses. An independent analysis may show results in support of the initial findings or could instead reveal errors or inconsistencies in the original research.
Finally, data sharing could potentially lead to an optimisation of time and costs of clinical research by preventing the duplication of trials.
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