Understanding p-values and Confidence Intervals: A Guide to 90% Confidence
In the realm of statistics, we often use confidence intervals and hypothesis testing to draw conclusions about populations based on sample data. One of the most common questions that arises is: What p-value threshold corresponds to a 90% confidence interval?
The Problem:
The direct relationship between p-values and confidence intervals is often misunderstood. It's crucial to understand that they are two distinct concepts used for different purposes.
Rephrasing:
Imagine you're trying to find out the average height of all students in a large university. You take a random sample of 100 students and calculate their average height. Now, you want to estimate the true average height of all students with a certain level of confidence. Here's where confidence intervals come in.
Understanding the Concepts:
- Confidence interval: A range of values that is likely to contain the true population parameter (in our example, the true average height). A 90% confidence interval means we are 90% confident that the true average height falls within that range.
- p-value: The probability of observing the data we have, or something more extreme, assuming the null hypothesis is true. The null hypothesis typically states there is no difference or effect.
How They Relate:
While they are distinct concepts, p-values and confidence intervals are connected. A p-value helps us decide whether to reject or fail to reject the null hypothesis, while a confidence interval gives us an estimate of the true population parameter.
P-value Thresholds and Two-Sided 90% Confidence Interval:
To understand the relationship between p-values and confidence intervals, consider a two-sided 90% confidence interval. This means there is a 5% chance that the true population parameter lies outside the interval on each side. This translates to a p-value threshold of 0.10 (or 10%).
Example:
If we perform a hypothesis test with a p-value of 0.07, we would reject the null hypothesis at a 10% significance level (or a 90% confidence level). This is because the p-value is less than the threshold of 0.10.
Why It Matters:
Understanding the relationship between p-values and confidence intervals is crucial for correctly interpreting statistical results. Using the wrong p-value threshold can lead to erroneous conclusions about the population.
Key Points to Remember:
- A 90% confidence interval corresponds to a 10% significance level.
- The p-value threshold for a two-sided 90% confidence interval is 0.10.
- Always consider the context and research question when interpreting statistical results.
Additional Resources:
By understanding the relationship between p-values and confidence intervals, researchers and data analysts can draw more accurate and informed conclusions from their data.
