1. ## Defect Rates

I have two sample sizes with different defect rates because of the size differences. I need a way, preferably in Excel, to determine if the defect rates would be the same if the sizes were the same. Can someone please assist?

2. ## Re: Defect Rates

Why does sample size impact the *rate* of defects in your opinion? I mean surely it would change the raw count of defects but not really the rate in a significant way.

3. ## Re: Defect Rates

Originally Posted by Dason
Why does sample size impact the *rate* of defects in your opinion? I mean surely it would change the raw count of defects but not really the rate in a significant way.
What we are trying to figure out is why Group A is getting a different defect rate than Group B if they SHOULD both find the same errors from the same sampling; the variable is that Group A looks at a sample size twenty times larger. So in my business if Group A looks at 200 items and finds 10 errors and Group B looks 10 items from that same 200 Group A looked at, we expect that Group B will find the any of the same errors that Group A found. Though when we calculate a defect rate using the formula "errors/sample size=defect rate" the number is always different because of the obvious different size in samples. I am trying to find out a way to show that they, if they are, the same.

4. ## Re: Defect Rates

Group B is looking at a small sample from exactly the same large sample as group A. Group B find some (or possibly none) of the defects found by Group A.
This might help. You can calculate the probability of Group B finding their number assuming that things are perfectly random using the hypergeometric distribution.
In Excel type =HYPGEOMDIST(number group B found,number Group A found,Total in Group B sample,Total in group A sample)
So, Group A found 15 defects in 200. Group B found 3 defects in 10 from the same set. How likely is that?
=HYPGEOMDIST(3,15,10,200) = 0.027 about 1 chance in 40 - fairly unlikely. You can now make a decision about the two groups.

5. ## The Following User Says Thank You to katxt For This Useful Post:

Compliance Carl (09-22-2017)

6. ## Re: Defect Rates

Originally Posted by katxt
Group B is looking at a small sample from exactly the same large sample as group A. Group B find some (or possibly none) of the defects found by Group A.
This might help. You can calculate the probability of Group B finding their number assuming that things are perfectly random using the hypergeometric distribution.
In Excel type =HYPGEOMDIST(number group B found,number Group A found,Total in Group B sample,Total in group A sample)
So, Group A found 15 defects in 200. Group B found 3 defects in 10 from the same set. How likely is that?
=HYPGEOMDIST(3,15,10,200) = 0.027 about 1 chance in 40 - fairly unlikely. You can now make a decision about the two groups.
I tried the formula a few different ways and I keep getting a Number Error "#NUM!" but I appreciate your assistance

7. ## Re: Defect Rates

Oops. I think I put the numbers round the wrong way. Try
=HYPGEOMDIST(number defects group B found,Total in Group B sample,number Group A found,Total in group A sample). kat

8. ## The Following User Says Thank You to katxt For This Useful Post:

Compliance Carl (09-25-2017)

9. ## Re: Defect Rates

Originally Posted by katxt
Oops. I think I put the numbers round the wrong way. Try
=HYPGEOMDIST(number defects group B found,Total in Group B sample,number Group A found,Total in group A sample). kat
That worked, thanks again

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