# Meaning of percent bound by stratum

#### garcianc

##### New Member
This might be a very simple question. I searched through the forum and did not see a similar post.

I am a logistician and I am having a tough time interpreting a DoD policy document that prescribes statistical parameters for inventory sampling.

These are the parts that we understand fairly well (we think): The document calls for 95% confidence level, +/- 2.5% margin of error. The test is binomial. Each trial (item inventoried) would either pass or fail based on reconciliation with inventory records. The policy calls for stratification, but does not mandate any specific allocation strategy, so we are using proportionate allocation. So far, so good.

Here is the part I don't seem to understand from the policy: There is a footnote below the table where the categories (strata) are enumerated that simply says "+4 percent bound applicable to each category". I have attached a screenshot of the table.

Is this calling for a calculation of a binomial proportion confidence interval? If so, how does the +4% play into this?

Thanks in advance for any responses.

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#### garcianc

##### New Member
I might have been on the right track when I suspected binomial proportion confidence intervals. Anyway, unless someone tells me otherwise, that is how I will interpret it.

My theory is that the statement "+4 percent bound per category" is referring to using the binary confidence interval upper confidence bound as a way to address small sample sizes within each strata.

For example, if a strata only has 20 items and we found 1 error. That would theoretically give a passing score of 95% +/- 2.5%. However, the upper confidence bound would be 99.9% (or +4.9% above our result) - meaning that strata actually would fail to meet the +4% bound criteria.

Anyway, that is what I am telling myself so I can move on...