How can you explain the significance of p-values to a non-expert?

P values are great, but may not necessarily measure effect sizes, depending on your type of data and what you answering. I’d be more carefully when interpreting P values.

Explanation: Use p-values as one part of your decision, not the only part. Basic example: When you decide if something is special, think about other clues too, like how many candies you have and how many times you try.

Imagine you are a doctor testing a new drug to lower blood pressure. You compare the blood pressure (BP) of patients taking the new drug and another taking a placebo. The p-value helps you understand whether the difference in BP between the two groups is likely due to the new drug or random chance. The p-value is a measure of surprise. A high p-value, close to 1, is like flipping a coin 100 times and getting around 50 heads & 50 tails—not surprising and likely due to chance. Conversely, a low p-value, close to 0, is like flipping a coin 100 times and getting 95 heads—very surprising & unlikely by chance. If the p-value is ≤0.05, it indicates a surprising result that likely isn't by chance, suggesting the new drug probably works to lower BP

Start with an overview of what a p-value is. A p-value is a statistic that assesses the strength of evidence against a null hypothesis. Simply put, it tells us how likely we are to observe the data we have if the null hypothesis is true. For example, a low p-value indicates that the observed data is unlikely to be true under the null hypothesis, implying the possibility of a significant effect or relationship. This fundamental understanding is critical for comprehending the broader concept of statistical significance.

In science and statistics, the "significance threshold" helps determine if experiment results are meaningful or just happened by chance. It's like a rule to say, "This result is important and not just a lucky outcome." Imagine a carnival ring toss game where the organizer says, "If you get 8 or more rings on the bottles out of 10 throws, you win a prize." This "8 or more rings" is the threshold. If you get 9 rings, you win the prize. Similarly, the significance threshold helps scientists decide when a result is likely real and not due to random chance. If the p-value is less than or equal to the threshold (usually 0.05), the result is significant & likely real. If the p-value is higher, it suggests the result might just be a coincidence

Explanation: We use a magic number, usually 0.05, to decide if something is really surprising. Basic example: If the p-value is less than 0.05, it's like saying, "Wow, this is really special!" If it’s more than 0.05, it’s like saying, "This isn’t that surprising."

Explain the typical significance level used in hypothesis testing. A p-value threshold of 0.05 is commonly used to determine whether the results are statistically significant. If the p-value is less than this threshold, we reject the null hypothesis, implying that the results are statistically significant. A p-value greater than 0.05 indicates that we do not have sufficient evidence to reject the null hypothesis. It should be noted that while this threshold is somewhat arbitrary, it is widely accepted as a standard for determining significance in many scientific disciplines.

While the p-value is important in statistics, there are common misconceptions about its use. - Many think the p-value shows the probability that a hypothesis is true, but it actually indicates how likely the observed results are if there were no real effect (null hypothesis). - A smaller p-value doesn't mean the effect is larger or more important (better effect size); it only shows that the effect is unlikely to be by chance. - Although a small p-value indicates statistical significance, it does not necessarily mean practical real-world significance. - Statistical interpretation shouldn't be based only on p-value. It's important to consider the effect size, the logical/clinical plausibility of the result, & overall context of the analysis.

Explanation: A p-value doesn’t tell us for sure that something is true or false; it just gives us a clue. Basic example: Just because you pick 5 blue candies doesn’t mean the whole bag is blue. It’s just a hint that maybe something is different with the candies.

Correct common misconceptions about p-values. Many people believe that a p-value indicates the likelihood that the null hypothesis is correct. Clarify that the p-value represents the likelihood of receiving the observed results, or more extreme results, if the null hypothesis is true. It is also worth noting that a low p-value does not imply that a hypothesis is true, nor does a high p-value imply that it is false. Highlighting these nuances helps to prevent statistical results from being misinterpreted.

P-values quantify how consistent your data is with a particular hypothesis. For instance, imagine testing a new drug. A low p-value, typically under 0.05, suggests the effects observed are likely not due to chance—implying the drug could be effective. This is crucial in fields like medicine where decisions must be backed by robust evidence. Understanding p-values helps non-experts appreciate the rigor behind scientific claims, ensuring they're not misled by random fluctuations presented as significant findings.

When the p-value is high, it indicates results are likely due to random chance but doesn't prove statistical significance. P-values, often misunderstood. This can lead to incorrect interpretations and bad research practices. Engineers could have used p-values to identify significant O-ring failures in cold conditions before the Challenger disaster. Before the 2008 financial crisis, a p-value of 0.02 for high returns on mortgage-backed securities - suggested risky lending practices. This could have led to tighter lending standards, increased reserves, & diversified portfolios Understanding p-values could have provided early warnings to prevent the Challenger disaster & mitigate the 2008 financial crisis.

Simple real-world example involving a coin toss. Imagine you have a coin and you suspect it might be biased towards heads. To test this, you decide to flip the coin 100 times. If the coin were fair, you'd expect about 50 heads. However, if you get 60 heads, you might wonder if the coin is biased. A p-value helps you determine whether the number of heads you observed (60) is unusual or could reasonably happen by chance with a fair coin. In this context, the p-value answers the question: "What is the probability of getting at least 60 heads in 100 flips if the coin is actually fair?" If this p-value is very small (< 0.05), it suggests that getting 60 heads is unlikely to happen by chance so you might conclude that the coin is likely biased.

A typical example of context in biomedical research when interpreting p-values is considering clinical plausibility, meaning the findings should align with existing medical knowledge and biological mechanisms. Imagine a study finds that a new drug cures malaria with a statistically significant result (p-value < 0.05), suggesting the drug likely has an effect. However, suppose the drug works by targeting a pathway not previously associated with malaria. This result might raise questions about the clinical plausibility of the findings in relation to broader medical knowledge and biological processes. Without clinical plausibility, the statistically significant result might be due to an unknown confounding factor or a flawed study design.

When interpreting p-values, make sure to consider the context. A p-value should not be used in isolation. It is critical to consider the study design, sample size, and the practical implications of the results. A statistically significant result (low p-value) may not always be practically significant, indicating that it has little real-world impact. In contrast, a non-significant result (high p-value) in a poorly designed study may not accurately reflect the absence of an effect. Contextual interpretation is necessary for drawing meaningful conclusions.

Comprehending p-values is vital for correctly interpreting research outcomes. A p-value reflects the likelihood of obtaining results similar to those observed, under the assumption of the null hypothesis. Nevertheless, context is crucial. For instance, a study involving 10,000 participants, with a p-value of 0.01 indicating a new drug's effectiveness, carries more weight than a study with 20 participants showing the same p-value for an herbal supplement. Variables such as sample size and study design shape the importance of p-values, guiding our understanding of research findings.

Non-experts should consider their p-value alongside other statistics like confidence intervals, effect sizes, and overall study quality. Consult a statistician when in doubt, especially for complex analyses. Emphasise that statistical significance is only one aspect of research findings; other factors such as reproducibility, theoretical support, and practical implications must also be considered. These tips assist non-experts in making informed decisions based on p-values and other statistical evidence.

It’s impossible to explain p values to non-experts. Don’t even try. Draw pictures to present your findings. Cherry-pick facts to support your narrative. If anyone asks whether your findings are significant, just say yes.