How do you explain the importance of p-values to non-statisticians? (2024)

Imagine your friend Alice claims she can predict coin flips. To test her, you ask her to predict 100 flips, expecting her to guess correctly about 50 times if she's just guessing. Surprisingly, she predicts 80 flips correctly. You calculate a p-value to assess the probability of Alice guessing this many or more correctly just by chance, which turns out to be 0.01. This low p-value suggests there's only a 1% chance of such an accurate prediction under normal guessing conditions, leading you to question the assumption that Alice is just guessing. A small p-value like this indicates the observed outcome is highly unusual if the null hypothesis were true, suggesting an alternative explanation might be needed.

P-values are important in fields such as data science, scientific research, and marketing analysis, where data-driven decisions are crucial. They provide a measurable way to assess if the observed data significantly deviates from expected outcomes under a given hypothesis. By calculating a p-value, we can quantify the likelihood that any observed differences occurred by chance. This can help us in making objective decisions and distinguishing genuine effects from mere random fluctuations. Moreover, a p-value does not confirm the truth of the hypothesis itself, but rather informs us about the data's alignment with the hypothesis.

Conduct a study to check if medicine is effective in treating a certain illness. Some patients take the medicine, while others take a placebo (a dummy pill with no active ingredient). After the study, compare the results between the two groups if there's a difference in how well the medicine works compared to the placebo. If the p-value is low (typically below 0.05), it suggests that the observed difference between the medicine and the placebo is unlikely to have occurred just by chance. In other words, it provides evidence that there's a real difference between the two groups.In simpler terms, a low p-value suggests that the effect you're seeing is probably real, rather than just a coincidence or random variation.

Imagine you want to know if a coin is a special trick coin or just a regular one. You decide to flip the coin 10 times to see how many times it lands on heads.Say you flip the coin and it lands on heads 9/10. That seems a bit unusual for a regular coin, doesn’t it? This is where thep-valuecomes in.Thep-valuetells you how likely it is that you would get such an unusual result (like 9 heads out of 10 flips) if the coin was really just a regular coin. Alow p-valuemeans that it’s very unlikely to get that result if the coin is normal, so maybe the coin is indeed a trick coin. Ahigh p-valuemeans it’s more likely that the result is just due to chance, and the coin is probably just a regular coin.

P-values help determine the strength of evidence against a null hypothesis in a study. A small p-value (typically less than 0.05) suggests the data is unlikely to occur under the null hypothesis, indicating a potential effect or relationship. However, p-values alone do not prove the hypothesis or its effect size; they should be used alongside other information for a complete understanding of the results.

A p value of 5% means that if the null hypothesis were indeed true, and 100 statistician collect the data independently and perform the same analysis, only 5 of them would get answer as worse as you have found. Hence, a low p value can either mean that the null hypothesis is false or that you have been very unlucky. However, low p value does not necessarily mean that the alternative hypothesis is true or even more probable. Imagine your alternative hypothesis says <50% products are bad, and null hypothesis says = 50% products are bad, but your sample found 90% bad products. So it is important to look at p values in conjunction with the direction of alternative hypothesis to make a decision.

P-values are a statistical tool used to evaluate the strength of evidence against a hypothesis. If you're testing whether a new treatment is effective, the p-value helps determine whether the results you see could happen just by chance if the treatment were ineffective. A low p-value indicates that such results are unlikely to occur due to randomness alone, suggesting the treatment might truly be effective. However, it’s important to note that a p-value does not confirm the treatment’s effectiveness outright; it merely quantifies the probability of obtaining these results if the treatment had no real effect.

ften, there's a mistaken belief that p-values can determine whether a hypothesis is true or false. However, p-values do not constitute conclusive proof; rather, they provide evidence against the null hypothesis. A low p-value indicates that the observed data are unlikely if the null hypothesis were true, but this does not confirm the alternative hypothesis. Furthermore, it's crucial to understand that p-values do not reflect the magnitude or importance of an effect, but merely the strength of evidence against the null hypothesis.

P-values are indicators used in statistics to help decide whether the results of an experiment are significant. They represent the probability that the observed outcomes could occur by chance if there was no actual effect. Commonly, a p-value threshold of 0.05 is used. This means that if the p-value is below 0.05, the results are considered statistically significant, suggesting that the findings are unlikely to be due to random chance alone. Setting this threshold helps researchers determine when to consider their results as evidence of a real effect, guiding decisions in scientific and clinical research.

P-values are statistical tools that measure the likelihood that the results of a study or experiment could have occurred by chance. They are context-dependent, meaning their interpretation can vary based on the study design and the question being asked. For instance, a low p-value in a clinical trial suggests strong evidence that a treatment has a real effect, not just a random occurrence. However, the importance of the p-value also depends on other factors, like the size and consistency of the effect. Therefore, while p-values are a key piece of the puzzle, they should always be considered alongside other evidence in making decisions or drawing conclusions.

If enrolling in a university or doctorate level statistics class you might for example learn that if you perform 10 identical experiments (n=10) it would be enough to allow you to make certain assumptions because the math within the statistics tells you that performing any more experiment won't make a big difference. In reality however, at least within preclinical molecular biology, performing (at least) 3 identical experiments and drawing conclusions from that is often considered "good enough". So context really does matter and each field and each technique used comes with different conceptions about what is considered an acceptable approach.

Here is how I explain the central limit theorem (CLT) to learners using a simulation. I say imagine you make up a population of 100 people with a body mass index (BMI) for each of them, and you put it on a spreadsheet. Now, you choose a sample size - like n = 5 - and demonstrate taking the mean and standard deviation of a sample. You can also show how you can take the mean of the whole population of 100, and get the population mean, which is what you are trying to estimate from the samples. Then you can help the learner take 100 samples of 5 from this population, and calculate the 95% confidence interval for each sample. Of the 100 samples, 95 of the confidence intervals will include the population mean.

In Analytical studies (vs Enumerative studies), the "non trivial replication" of an effect is a stronger suggestion of the existence of that effect than the p value itself.For example, the "degree of belief" about the existence of an effect would be higher if that effect showed up across 2 experiments ran in different conditions, with say twice a p value around 23%, than if based on a single experiment with a p value of 5%... (and not just because 23%x23%=5%)Not to mention the roles of predictions and of practical significance...“Unlike a confidence level, or significance level, degree of belief is not a calculated value. It is about a prediction and there is not a proven theory to make quantitative statements about the future.”Moen

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Though the p-value can express the probability of observing extreme sample data (given the null hypothesis is correct), yet, depending on the context, I disagree with establishing and presenting it as the only / most important measure in the process of decision-making / on a particular hypothesis. The sample size, effect size, and clinical significance all play an equal role with statistical significance and I would argue to promote a confidence interval rather than a p-value.

🎚️ Statistical significance, assessed by p-values, measures the likelihood that an observed relationship between variables happened by chance. Below a certain predefined threshold, the p-value is considered statistically significant, indicating the result is unlikely to be due to chance. However, in certain analyses involving multicollinearity or multiple comparisons, traditional methods may not work correctly, requiring corrective measures like test adjustments or the selection of a more relevant test.📊 Practical significance evaluates the real-world importance of a finding, focusing on the magnitude of estimates and their practical impacts.🧩 Considering both statistical and practical significance is key, as they may not always align.

As a seasoned contributor on this topic, I've previously addressed the significance of p-values extensively, making this discussion somewhat redundant. However, I'd like to introduce a crucial aspect often overlooked: under the null hypothesis, the distribution of p-values from a continuous statistical test is uniform within the range [0,1]. Consequently, even in the absence of any true effect, there's a 100*alpha% chance of obtaining statistically significant results. Therefore, p-values should never be considered a measure of evidence on their own, emphasizing the importance of cautious interpretation and consideration of additional factors in statistical analysis.

Ronald H. Coase said, "if you torture the data long enough, it will confess." P-hacking and data dredging involve manipulating data to achieve significant results (p < 0.05), often by changing hypotheses or selectively reporting results. This increases the risk of false positives, undermining research integrity. Publication bias and funding further pressures researchers to produce sensational findings over accurate science, distorting the literature.