Title: How Hypothesis Tests Work: Confidence Intervals and Confidence Levels - Statistics By Jim
Headings: How Hypothesis Tests Work: Confidence Intervals and Confidence Levels
How Hypothesis Tests Work: Confidence Intervals and Confidence Levels
How to Interpret Confidence Intervals
Confidence Intervals Indicate the Precision of the Estimate
Creating Confidence Intervals Graphically
Confidence Intervals and the Inherent Uncertainty of Using Sample Data
Confidence Intervals and P Values Always Agree on Statistical Significance
Why They Always Agree
I Really Like Confidence Intervals!
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Content: Confidence intervals help you navigate the uncertainty of how well a sample estimates a value for an entire population. With this in mind, confidence intervals can help you compare the precision of different estimates. Suppose two different samples estimate the same population parameter with 95% confidence intervals. One interval is [5 15] while the other is [9 11]. The later confidence interval is narrower, which suggests that it is a more precise estimate. Related post: Sample Statistics Are Always Wrong (to Some Extent)! Creating Confidence Intervals Graphically
Let’s delve into how confidence intervals incorporate the margin of error. Like the previous posts, I’ll use the same type of sampling distribution that showed us how hypothesis tests work. This sampling distribution is based on the t-distribution, our sample size, and the variability in our sample.