anybody understand basic stats???

[iwantanewcomputer]

i must be a moron...I took 3 college stats/DOX classes. i know how to find the confidence interval that 2 populations are different. how do you find the confidence that one attribute rate is less than another????

im just looking for the confidence that 1/3339 (.000229) is less than 0.0005 (actual defect rate)

anyone know?

 

[sactoking]

I'm not 100% sure of what it is exactly that you want, but it sounds like you have a multi-attribute sample across two separate populations, in which case ANOVA is the way to go.

 

[iwantanewcomputer]

dont think so...its one attribute. one population i know the true rate, one i measured 1 out of 3339.

 

[mugs]

I can tell you with 100% confidence that .000229 is less than 0.0005

 

[iwantanewcomputer]

lol that is exactly what i wanted to say...but i'd get fired. i know one is .0005. the other one i only measured 3k samples, not infinity.

 

[sactoking]

So you have one population that you sampled where n != N (i.e. your sample size was not the entire population). From that n you get xbar equals 0.000229 and are given that Xbar equals 0.0005. You are asked to determine the confidence level (not interval) that xbar <Xbar, is that correct?

 

[sactoking]

If that's what you're looking for, you want a one-sided t-test.

H-naught: xbar >= Xbar
H-subone: xbar < Xbar

t=(xbar-Xbar)/(sample standard deviation/square root of the sample size)
with n-1 degrees of freedom.

Calculate your t and convert to a p score, then compare your p-statistic to the relevant confidence levels (.1, .05, .01).

 

[DingDingDao]

What sactoking said-- 1-tail non-paired T-test.

 

[iwantanewcomputer]

Originally posted by: sactoking
So you have one population that you sampled where n != N (i.e. your sample size was not the entire population). From that n you get xbar equals 0.000229 and are given that Xbar equals 0.0005. You are asked to determine the confidence level (not interval) that xbar <Xbar, is that correct?

yah thats how you do it for variables. im measuring attribute defect rates. so those #s are % of samples that are defective. cant find this anywhere googling or in my texts but i know its possible.

you are right i meant to say confidence level...not interval. so my conclusion should be something like there is 92% confidence that the process i measured (1 defect out of 3339 samples) is less defective than the old process (500ppm defective = .0005)

 

[Paperdoc]

Stop talking t-tests etc. Those tools are specifically for statistics properly modeled by a Normal distribution. But you are talking about the defect rate found in a sample of known finite size. This is Attribute statistics, modeled by a Binomial Distribution. In Statistical Process Control jargon, this is a p-Chart, where p is the Proportion of defects in the sample of size n. In your case, you have been told that the expected value of p is 0.0005 (based on prior studies of a large sample) and the sample in question had one defect in a sample of 3339, so n = 3339 and p = 0.00029949. Let's use the term "pbar" for the expected value of p.

For a p-Distribution, the formulae are that (for a Confidence level of 0.997, or 99.7%) the Lower Control Limit (LCL) is

LCL = (pbar) - 3 x SQRT{[(pbar) x (1 - (pbar)] / n},

and the Upper Control Limit (UCL) is

UCL = (pbar) + 3 x SQRT{[(pbar) x (1 - (pbar)] / n}

NOTE that there is NO "Standard Deviation" in this - the Standard Error for a binomial distribution is derived solely from pbar, the expected value of p, and the Confidence Interval uses this plus the sample size. In your case, plugging values in yields

LCL = -0.0006606, which is impossible so the real LCL is zero.

It also yields UCL = 0.0016606

If the value of p found for the current sample falls within this range, it is still considered part of the regular population being examined, but if it is outside those limits, it is considered statistically different. Well, your measured value of 1 defect in 3339 items was p = 0.00029949 and that is NOT outside the Limits, so your sample is NOT different from the whole population in question.

As a simpler view on this, consider that the expected value you were given is ½ defect per thousand, or 1 defect in 2,000 units, or 5 defects in 10,000 units. What you observed was 2.99 defects per 10,000 in your sample. Do you consider 3 significantly different from 5? Don't forget, in defect counting, there are no fractions in the actual counted number of defects. In a sample of n units, you could have 1 defect, or 2, or 3, or 4, etc. But you cannot have exactly 2.356 defects in a sample. The RATE of defects is 2.99 per 10,000, but we calculated that from an integer number, 1 defect, found in 3,339 units.

 

[krylon]

Originally posted by: Paperdoc
Stop talking t-tests etc. Those tools are specifically for statistics properly modeled by a Normal distribution. But you are talking about the defect rate found in a sample of known finite size. This is Attribute statistics, modeled by a Binomial Distribution. In Statistical Process Control jargon, this is a p-Chart, where p is the Proportion of defects in the sample of size n. In your case, you have been told that the expected value of p is 0.0005 (based on prior studies of a large sample) and the sample in question had one defect in a sample of 3339, so n = 3339 and p = 0.00029949. Let's use the term "pbar" for the expected value of p.

For a p-Distribution, the formulae are that (for a Confidence level of 0.997, or 99.7%) the Lower Control Limit (LCL) is

LCL = (pbar) - 3 x SQRT{[(pbar) x (1 - (pbar)] / n},

and the Upper Control Limit (UCL) is

UCL = (pbar) + 3 x SQRT{[(pbar) x (1 - (pbar)] / n}

NOTE that there is NO "Standard Deviation" in this - the Standard Error for a binomial distribution is derived solely from pbar, the expected value of p, and the Confidence Interval uses this plus the sample size. In your case, plugging values in yields

LCL = -0.0006606, which is impossible so the real LCL is zero.

It also yields UCL = 0.0016606

If the value of p found for the current sample falls within this range, it is still considered part of the regular population being examined, but if it is outside those limits, it is considered statistically different. Well, you measured value of 1 defect in 3339 items was p = 0.00029949 and that is NOT outside the Limits, so your sample is NOT different from the whole population in question.

As a simpler view on this, consider that the expected value you were given is ½ defect per thousand, or 1 defect in 2,000 units, or 5 defects in 10,000 units. What you observed was 2.99 defects per 10,000 in your sample. Do you consider 3 significantly different from 5? Don't forget, in defect counting, there are no fractions in the actual counted number of defects. In a sample of n units, you could have 1 defect, or 2, or 3, or 4, etc. But you cannot have exactly 2.356 defects in a sample. The RATE of defects is 2.99 per 10,000, but we calculated that from an integer number, 1 defect, found in 3,339 units.

tl;dr

The answer is 6