90% vs. 95% confidence interval: which to use?

Ever wondered how statisticians estimate the unknown with such confidence? Confidence intervals are the secret sauce that provide a range of plausible values for an unknown parameter. They don't just spit out a single number but offer a window into the precision and reliability of our estimates.

In this blog, we'll chat about what confidence intervals are, the difference between 90% and 95% confidence levels, and how to choose the right one for your analysis. We'll also explore practical applications and factors influencing these choices. So, let's dive right in!

The significance of confidence intervals in statistical analysis

Confidence intervals are a big deal in statistics. They give us a range where we believe the true value of an unknown parameter lies. This range reflects the precision and reliability of our sample estimates. By considering the margin of error, confidence intervals help us understand how much our findings might vary if we took different samples.

So, how do you decide between confidence levels like 90% vs 95%? It really depends on your research context and objectives. A 95% confidence level provides a wider interval but more assurance that the true value is within that range. On the flip side, a 90% level gives a narrower interval but comes with a slightly higher risk that the true value is outside it.

The width of the confidence interval isn't random. It's influenced by factors like sample size and variability. Larger samples and less variable data usually lead to narrower intervals, signaling more precise estimates. Sometimes, Bayesian credible intervals are used instead, incorporating prior knowledge to fine-tune the range of plausible values.

Understanding confidence intervals is key for making informed decisions based on statistical results. They help us gauge how certain we can be about our findings and how well they might apply to other situations. By considering the role of confidence levels and the implications of choosing between 90% vs 95% confidence intervals, we can draw more nuanced conclusions from our data.

Understanding the difference between 90% and 95% confidence levels

Choosing between a 90% and 95% confidence level is all about balancing risk and precision. With a 90% confidence level, you're accepting a 10% chance of being wrong. A 95% level lowers that risk to 5%, but at the cost of a wider interval. Statsig's blog post on confidence levels explains that higher confidence levels provide more certainty but less precision.

In a Reddit discussion, someone grapples with using a 90% confidence level to account for potential outliers in traffic accident data. They notice that using a 95% level makes most of their data statistically insignificant by a slim margin. Another Reddit thread debates the choice between 90% and 95% confidence levels for a quantitative survey, considering things like risk appetite and resources.

David Robinson's blog posts on credible intervals and empirical Bayes estimation with baseball stats show how different confidence levels affect how we interpret data. He shows how adding prior knowledge through Bayesian methods can make intervals more informative, especially when data is limited.

At the end of the day, picking between a 90% and 95% confidence level depends on what you're trying to achieve. As Statsig's blog post on the 95% confidence interval suggests, you might need to adjust the standard 95% level based on your unique risk profiles or statistical power needs.

Factors influencing the choice of confidence level

Your risk tolerance plays a huge role in deciding between 90% and 95% confidence intervals. If you're okay with a higher chance of being wrong, a 90% confidence level might do the trick. But if you need to be more precise, you'd probably go with a 95% or even 99% confidence level.

Sample size is another big factor. Larger samples usually give you narrower intervals, so you can afford to choose higher confidence levels without losing precision. On the other hand, if your sample is small, you might opt for a lower confidence level to keep the interval reasonably narrow.

Think about how precise you need your estimates to be. If high precision is a must, go for higher confidence levels. If you're okay with some uncertainty, lower levels might be acceptable.

Ultimately, the choice between 90% and 95% confidence intervals boils down to the specifics of your analysis. Consider what happens if you're wrong, how big your sample is, and how precise you need to be. By weighing these factors, you can pick a confidence level that strikes the right balance between risk, precision, and what's feasible for your study.

Practical applications of selecting confidence intervals in analysis

Picking the right confidence level comes down to context and goals. For high-stakes decisions, a 95% confidence interval is common because it minimizes the risk of false positives. This level gives you more certainty but at the cost of precision.

If you're doing exploratory research or early-stage experiments, a 90% confidence interval might be more suitable. It allows for more efficient detection of potential trends or effects, even though there's a slightly higher risk of false positives. A Reddit discussion highlights how important it is to think about risk appetite and resources when choosing your confidence level.

When working with low-count data or imbalanced samples, methods like empirical Bayes estimation can help sharpen your estimates. By bringing in prior information, these techniques make comparisons more reliable and adjust individual estimates toward the mean. This is especially handy in fields like genetics and advertising.

Don't forget about credible intervals, the Bayesian take on confidence intervals. They can offer narrower, more informative ranges when data is limited by leveraging the overall dataset. Knowing the differences between credible and confidence intervals is key for interpreting results accurately.

At the end of the day, choosing between 90% and 95% confidence intervals—or any other level—should be decided before you collect data. Keeping things consistent across similar experiments helps avoid bias. By carefully considering your unique risk profiles and statistical power needs, you can pick the confidence level that best fits your analysis.

Statsig understands the importance of selecting the right confidence levels in your experiments and provides tools to help you make these decisions. Their platform assists in setting up and analyzing experiments, ensuring you have the statistical power you need.

Closing thoughts

Confidence intervals are more than just numbers—they're essential tools that help us understand the uncertainty in our estimates. Whether you choose a 90% or 95% confidence level depends on your risk tolerance, sample size, and the precision you need. By carefully considering these factors, you can make informed decisions that best suit your analysis.

If you're interested in learning more, check out Statsig's resources on confidence levels and confidence intervals. Understanding these concepts can significantly improve the quality of your statistical analyses.

Hope you found this useful!