For the power analysis below, we are going to focus on Example 1 testing the average lifespan of a light bulb. Our first goal is to figure out the number of light bulbs that need to be tested. That is, we will determine the sample size for a given a significance level and power. Next, we will reverse the process and determine the power, given the sample size and the significance level.
numeric vector whose sample quantiles are wanted, or anobject of a class for which a method has been defined (see also‘details’). and values are notallowed in numeric vectors unless is .
We are almost ready for our power analysis. But let's talk about the standard deviation a little bit. Intuitively, the number of light bulbs we need to test depends on the variability of the lifespan of these light bulbs. Take an extreme case where all the light bulbs have exactly the same lifespan. Then we just need to check a single light bulb to prove our point. Of course, this will never happen. On the other hand, suppose that some light bulbs last for 1000 hours and some only last 500 hours. We will have to select quite a few of light bulbs to cover all the ground. Therefore, the standard deviation for the distribution of the lifespan of the light bulbs will play an important role in determining the sample size.
Next, suppose we have a sample of size 10, how much power do we have keeping all of the othernumbers the same? We can use the same program, sampsi, to calculate it.