What is the P-Value?

Simply put, a p-value indicates the probability that a result is due to chance alone. It works in conjunction with the null hypothesis, which posits that ‘no significant effect exists.’ Scientists aim to demonstrate that this assumption is unlikely, suggesting that there is indeed a noteworthy effect. A low p-value indicates that the null hypothesis is less probable.

For instance, consider an experiment with two groups of 20 participants each. Group A receives dark chocolate, while Group B gets white chocolate. Upon evaluating their performance on a cognitive test, I discover that Group B performs 5% better on average than Group A. Does this difference truly signify a meaningful distinction?

It's not enough to observe a disparity in average results. One must also consider the sample size and variability. After conducting a t-test, I may find a p-value of less than 0.05, which might lead me to conclude that I have established a significant correlation.

However, we must scrutinize what p-value really signifies. It serves as an output from a statistical test, suggesting that the results are less likely than a specified percentage to stem from the null hypothesis. Where do scientists and analysts commonly falter in applying these tests and interpreting their results?

Testing Multiple Factors

One prevalent mistake is in studies that examine numerous factors simultaneously. For instance, a study on obesity might analyze 20 different variables, concluding that one factor significantly contributes to obesity using a p-value threshold of 0.05. This approach is akin to tossing mud against a wall to see what sticks.

With 20 variables, the likelihood of obtaining at least one p-value less than 0.05 purely by chance exceeds 60%! This calculation is straightforward. By multiplying the failure rate (95%) by itself for each additional factor, we determine the probability of all factors failing to show significance. The reverse of that calculation reveals the chance that at least one variable will appear significant, even if it isn't.

Be cautious of studies that test dozens of variables to declare something significant, particularly if the findings seem sensationalized.

Using Inappropriate Tests

Another issue arises when the statistical tests applied to yield p-values are inappropriate. In our previous example, I used a t-test to compare the two groups. This test assumes that the results follow a normal distribution to provide reliable outcomes. If the data is not normally distributed or if the sample size is small, the conclusions drawn may be flawed.

This challenge varies based on the specific test employed and the incorrect assumptions made. For someone without a strong background in statistics, it can be nearly impossible to discern whether a paper has used the correct tests, given the multitude of options available.

Ignoring Outliers

When analyzing data, it's crucial to identify outliers that might skew the results. For example, if one participant has an exceptionally high IQ or a disability that affects their test performance, these outliers could dramatically alter the p-value. Methods exist for detecting outliers, and it's advisable to analyze the data both with and without these anomalies to assess their impact.

Overreliance on a P-Value of 0.05

Perhaps the most significant issue is the unwritten norm in many scientific fields that a p-value of 0.05 (indicating 95% confidence) is the benchmark for significance. This is not universally applicable. For instance, when groundbreaking discoveries are made at the Large Hadron Collider, physicists often seek a confidence level of 99.999% or higher. This level of certainty is warranted because such findings could necessitate a fundamental reevaluation of existing theories.

In fields like biology or business, a mere 95% confidence may suffice, but context matters. If a discovery has far-reaching implications for global health, a higher confidence level is prudent.

The Clickbait Dilemma

Thus far, we've discussed statistical principles in abstract terms. Now let's ground this in reality. In many scientific disciplines, a p-value of less than 0.05 is often a prerequisite for publication. Gaining publication is critical for researchers, as it can lead to funding opportunities, prestigious positions, and career advancement.

This pressure has given rise to a practice known as p-hacking, where researchers may manipulate data or selectively report findings to achieve a p-value below 0.05. This compromises the integrity of scientific analysis.

The more sensational the result, the greater the need for stringent validation. Unfortunately, many studies fail to provide rigorous follow-up analysis, leading to the rapid dissemination of misleading information. Clickbait headlines like "Chocolate Will Make You Thinner!" proliferate as a result.

Here's how the process often unfolds: A researcher publishes a study in a peer-reviewed journal, or worse, on a non-peer-reviewed platform like arXiv.org. The findings are then summarized by a specialized review site, which might include some nuances. Next, general interest science outlets simplify the findings further, and by the time these results reach mainstream media, they are often distorted and speculative.

This cycle happens frequently, particularly in the health and wellness arena. It's no surprise when subsequent studies contradict earlier claims, leaving people confused about whether their chocolate consumption is helping or hindering their weight loss efforts. The widening gap between scientific research and public understanding has indeed fostered better communication but has also led to increased misinterpretations.

Conclusion: The Takeaway

While the p-value can serve as a valuable tool for data analysis, it does not inherently validate a hypothesis. It is built upon numerous assumptions and should not be the sole determinant of scientific credibility.

When evaluating study results, my two recommendations are to seek articles that provide sufficient detail and depth to accurately explain findings, and to apply critical thinking to assess the credibility of those results based on what you already know.

This video, "Creativity vs. Practicality: Have Data Scientists Lost the Plot?" explores the current state of statistical practices in scientific research, emphasizing the need for accurate interpretation of p-values.

The second video, "Everything Wrong with Statistics (and How to Fix It)," delves into common statistical errors and offers solutions to enhance the integrity of data analysis.