Does confidence interval affect power?
The statistical power of a hypothesis test is closely related to the precision of the accompanying confidence interval. In the case of a t-test, statistical power affects the probability of achieving a certain width of confidence interval, which is equivalent to the probability of obtaining a certain value of φ.
What affects the width of a confidence interval for a mean?
The width of the confidence interval decreases as the sample size increases. The width increases as the standard deviation increases. The width increases as the confidence level increases (0.5 towards 0.99999 – stronger).
How is the width of the confidence interval determined?
The width of the confidence interval is a function of two elements: The greater the confidence level, the wider the confidence interval. If we assume the confidence level is fixed, the only way to obtain more precise population estimates is to minimize sampling error. Sampling error is measured by the standard error statistic.
What is the 95% confidence interval for 94.66%?
We see that although we calculate 94.66% power, a 95% confidence interval for power is (31.79%, 99.99%). This indicates that we need to be quite cautious about how we use the 94.66% power figure since the actual power can be as low as 31.79% with 95% confidence.
Why is there a 95% confidence interval in cell AA8?
Note that the alpha in cell AA8 is based on the fact that we want a 95% confidence interval, while the alpha in cell AA12 is based on the significance level desired for the t-test (and power calculation). We see that although we calculate 94.66% power, a 95% confidence interval for power is (31.79%, 99.99%).
What are some misconceptions about confidence intervals?
The confidence level misconception. Some believe that a 95 percent CI for an initial experiment has a 95 percent chance of capturing the sample mean for a repeat of the experiment. This would only be true if the initial sample mean landed directly on the population mean.