Today we discuss Six Sigma power and sample size so that you can intelligently trade risk, sample size, and smallest detectable difference. Watch the video below to learn more. Have any questions? Please leave a comment below!
Here in the tool box you’ll find power and sample size tool and you’ll use that when you’re planning a t-test or proportion test in order to determine in advance approximately how many samples you need to take. Now, basically you have some decisions to make. We need to fill in some blanks down here. Do we want to do a two-sided test? That is, are we going to test not equal? Or we going to do a one-sided test? Which is either greater than or less than. Now, we also have to fill in the significance level that we plan to use in our test and normally that’s 0.05 that your alpha risk.
Up here, we just set the pointer to what we want to find and usually that’s going to be the sample size. Now, I’m going to put in a the power, that is the probability of seeing the effect, if it is actually there, and what that tells me is that I need two samples of 23 items each in order to do t-test to have that this power and to use this alpha risk and basically detecting a one sigma shift. See the difference is equal to the standard deviation and you can get an idea how that works conceptually by looking at these. Here’s our alternative, excuse me, our null hypothesis distribution. Here’s our alternative hypothesis distribution, and the idea is that whatever we have done has shifted the distribution up this way. Well, the question is are they different? Well, 5 percent of the area, that’s this number here, is out here. So we might make a mistake and say that we’re part of this distribution, the null hypothesis distribution where really we’re just out here a long way in the tail, well not really a terribly long way. Or the other mistake that we can make, we look at the alternative hypothesis distribution. We say yeah, we’re different, and actually we could make a mistake because we’re out in this tail. So you can graphically see what’s going on. But the numbers you need are down here. Now similarly, I could say okay, how much difference can I detect of a 15 sample in each 15 each sample and the answer is I can detect a difference as small as 18.3. I can detect that ninety-five percent of the time. If I’m using a 0.05 alpha which I normally do.
Now, similarly I can use a proportion test and let’s say that what I want to know is my sample size and I’m going to need two samples this size. So I set my pointer there and let’s say that we think that we want to detect a shift to 70 percent. So it’s a 70/30 split. We’re going to leave our power at .95 and let’s say that the process has been running at .6 or 60% and that I want it one-sided. Okay, so that tells me that I need two samples of 490 items each. I think you can begin to see why the t-test is preferable to the proportion test. Something that you’re taking an actual measurement is a lot more powerful than something that you’re counting.