Statistical significance: p‑values, confidence & common myths

If you've ever dipped your toes into the world of statistics, you've probably heard of p-values. They're those mysterious numbers that seem to hold the key to whether your results mean something or not. But what exactly are they, and why do they matter?

In this blog, we'll break down the concept of p-values in plain English. We'll explore their role in determining statistical significance, debunk some common myths, and look at why they might not tell the whole story on their own. Whether you're a seasoned data analyst or just curious about stats, we'll help you make sense of p-values and how they fit into the bigger picture.

Demystifying p-values: understanding their role in statistical significance

P-values are all about probabilities. In simple terms, a p-value measures the chance of seeing data as extreme as what you've got, assuming the null hypothesis is true. They're a big deal in hypothesis testing because they help us figure out if our results are statistically significant. Traditionally, if your p-value is below 0.05, that's a hint that your results are significant, suggesting that what you observed isn't just due to random chance.

But here's the thing: p-values have their limitations. They don't tell you how big or important an effect is in the real world. So even if you have a significant p-value, it doesn't always mean you've found something with a big impact. Interpreting p-values properly means you need to think about other factors too, like your sample size, how you designed your study, and the real-world context.

Relying only on p-values can sometimes lead to misunderstandings and putting too much weight on statistical significance. That's where effect sizes and confidence intervals come in. They give you more insight into how big and precise your results are, helping you judge the practical significance of your findings.

It's also helpful to visualize p-value distributions using histograms. This can reveal any weird patterns that might point to issues with your statistical tests, like conservative or anti-conservative p-values. If you spot something off, it might be time to dig deeper. Combining p-values with other statistical methods ensures you reach robust conclusions.

Beyond p-values: the importance of confidence intervals and effect sizes

P-values are just one piece of the puzzle when it comes to understanding statistical significance. Confidence intervals give you a range of plausible values for the true effect, showing how precise your estimate is. They help you grasp the uncertainty around your results, which is pretty important.

Then there's effect sizes, which tell you about the magnitude of the difference between groups or how strong the relationship is between variables. They go beyond just saying whether something is statistically significant—they let you know if your findings actually matter in the real world. After all, a statistically significant result with a tiny effect size might not be that exciting.

When you put p-values together with confidence intervals and effect sizes, you get a fuller picture of what's going on. P-values assess the likelihood of your data under the null hypothesis, but confidence intervals and effect sizes tell you about the size and precision of the effect. This combo helps you make better decisions based on both statistical and practical significance.

At Statsig, we recognize that relying on p-values alone isn't enough. We focus on providing tools that help you understand the full story behind your data, including effect sizes and confidence intervals.

Debunking common myths about p-values and statistical significance

There are quite a few myths floating around about p-values. One big one is that a significant p-value proves the null hypothesis is false. But actually, a p-value just tells you the probability of seeing results as extreme as yours if the null hypothesis is true. It doesn't directly tell you that the null hypothesis is false.

Another misconception is that p-values show the probability that your results are due to chance. In reality, p-values quantify the probability of obtaining results as extreme as yours, assuming the null hypothesis is true. They don't directly measure the probability that your results are just due to chance.

Some folks think that a small p-value means there's a big or important effect. But p-values don't tell you about the size or practical significance of an effect. For example, if you have a huge sample size, you might get a small p-value even if the difference is tiny. On the flip side, with a small sample size, you might have a large p-value even if the effect is substantial.

To avoid getting tripped up, it's important to consider p-values along with other factors like sample size, effect size, and practical implications. Visualizing the distribution of p-values can also help spot any issues with your statistical testing. By understanding what p-values can and can't tell you, you can make more informed decisions based on statistical significance.

Best practices for interpreting and reporting statistical results

When you're interpreting and sharing your statistical results, it's key to give a complete picture. P-values on their own aren't enough. You should include confidence intervals and effect sizes to provide context and show the practical significance. If you rely only on p-values, you might misinterpret your results or overestimate the effects you've observed.

Also, steer clear of p-hacking and data dredging. That's when you manipulate your data or analysis methods to get statistically significant results. These practices compromise the integrity of your research and can lead to false positives. Instead, consider preregistering your study designs and analysis plans to keep things transparent and reduce bias.

Encourage transparent reporting by sharing all the relevant statistical information—p-values, confidence intervals, effect sizes, and any adjustments for multiple comparisons. This way, others can critically evaluate your findings and assess how reliable they are. Be cautious when interpreting results, and don't forget to acknowledge any limitations or potential confounding factors.

It's also a good idea to visualize p-value distributions using histograms. This can help you spot potential issues like anti-conservative, uniform, or bimodal patterns. These visuals can guide further analysis if you notice something unusual. Remember, p-values should be seen as a spectrum of evidence, not just a black-and-white indicator of significance.

By following these best practices, you'll enhance the reproducibility and validity of your research findings. Embrace a nuanced approach to statistical analysis that appreciates the complexity and uncertainty involved. Doing so contributes to more reliable and meaningful conclusions in your field.

At Statsig, we promote these best practices by providing tools and resources to make statistical analysis more transparent and reliable. We help you avoid the pitfalls of misinterpreting p-values and encourage a holistic view of your data.

Closing thoughts

Understanding p-values is a crucial part of statistical analysis, but they’re just one piece of the puzzle. By considering p-values alongside confidence intervals and effect sizes, and being mindful of common misconceptions, you can make more informed decisions based on your data. Remember, statistical significance doesn't always mean practical significance.

If you want to dive deeper into these topics, check out the resources we've linked throughout the blog. At Statsig, we're here to help you navigate the complexities of statistical analysis. Hope you found this useful!