What is the relationship between confidence level and confidence interval size?
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09/12/2022
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Because we almost always sample a fraction of the users from a larger population, there is uncertainty in our estimates. Show Confidence intervals are an excellent way of understanding the role of sampling error in the averages and percentages that are ubiquitous in user research.
We have a chapter dedicated to confidence intervals in our book Quantifying the User Experience (Chapter 3) and in the Companion Book (Chapter 3) which contains step-by-step instructions for computing the interval in R or the Excel statistics package. I’ll be offering a tutorial which will include confidence intervals this fall at the Denver UX Boot Camp. What is the relationship between significance level and confidence interval?The confidence level is equivalent to 1 – the alpha level. So, if your significance level is 0.05, the corresponding confidence level is 95%. If the P value is less than your significance (alpha) level, the hypothesis test is statistically significant.
Does confidence interval depend on confidence level?Different confidence levels translate in slightly different ways of calculating the confidence interval with different chances of including the true score. For example, if your confidence level is 95%, it means that 95% of the time, the corresponding confidence interval will include the true score.
What happens to the confidence interval if you increase the confidence level?Changing the Confidence Level
If you increase the confidence level (e.g., 95% to 99%) while holding the sample size and variability constant, the confidence interval widens. Conversely, decreasing the confidence level (e.g., 95% to 90%) narrows the range.
How does a 90% confidence interval compare to a 95% confidence interval?With a 95 percent confidence interval, you have a 5 percent chance of being wrong. With a 90 percent confidence interval, you have a 10 percent chance of being wrong. A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).
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