# Is my company being cheated? (Sadistics) **URL:** \ **Category:** Factual Questions\ **Created:** [July 11, 2006, 7:19pm UTC](https://boards.straightdope.com/t/is-my-company-being-cheated-sadistics/364072 "2006-07-11T19:19:37Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![JohnT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnt/32/15048_2.png) [@JohnT](https://boards.straightdope.com/u/JohnT)\ **Post date:** [July 11, 2006, 7:19pm UTC](https://boards.straightdope.com/t/is-my-company-being-cheated-sadistics/364072/1 "2006-07-11T19:19:37Z")
In distributing a product a poll is taken to see if the product was delivered. The population is 550,000, the poll sample was 300. There is no “mean” as this is a one-time poll taken about a one-time distribution - however, our “score” was 94.7% delivered and our bonus depends upon our achieving a 95%. My problem is that the verification company is saying that their sample size viz their population corresponds to a 95% confidence level and a 2.6% margin of error… and I just don’t see that. But perhaps it’s my source… after all, I’m not a statistician. [http://www.raosoft.com/samplesize.html](http://www.raosoft.com/samplesize.html) This tells me that I need to call 1,400+ people if I want a 95%/2.6% CL/ME, as claimed by the verification company. Of course, we do our own audits, one far more detailed than the verification company: to call the same job, we contacted 21,000 people, not 300. Of course, our survey is for distribution quality, not just a sample from a population, so it must be far more detailed. Plugging in the numbers in the above calculator shows me that our CL is 99% and our ME is .87%. Anyway, my question is: Is it possible, on a population of 550,000 and a sample size of 300, assuming a standard response distribution, to achieve a confidence level of 95% with a margin of error of just 2.6%? Is there some higher-order statistics that’s being done here… or are we being cheated? ---
**Author:** ![Freddy\_the\_Pig](https://avatars.discourse-cdn.com/v4/letter/f/a587f6/32.png) [@Freddy\_the\_Pig](https://boards.straightdope.com/u/Freddy_the_Pig)\ **Post date:** [July 11, 2006, 9:55pm UTC](https://boards.straightdope.com/t/is-my-company-being-cheated-sadistics/364072/2 "2006-07-11T21:55:39Z")
> [@JohnT](#): > > In distributing a product a poll is taken to see if the product was delivered. The population is 550,000, the poll sample was 300. There is no “mean” as this is a one-time poll taken about a one-time distribution - however, our “score” was 94.7% delivered and our bonus depends upon our achieving a 95%. There _is_ a mean; you just don’t know what it is. The mean is the percentage of people that actually got on-time delivery. You don’t know that value–if you did, you wouldn’t be taking the survey–but you can make a reasonable guess. Let’s guess that it is in fact 95%. Plugging that number and your other figures into the sample estimator, I get a sample size of 270–pretty much as the survey company says. You left the prior estimate of affirmative responses at 50%, which makes a huge difference. ---
**Author:** ![drachillix](https://avatars.discourse-cdn.com/v4/letter/d/48db29/32.png) [@drachillix](https://boards.straightdope.com/u/drachillix)\ **Post date:** [July 11, 2006, 10:30pm UTC](https://boards.straightdope.com/t/is-my-company-being-cheated-sadistics/364072/3 "2006-07-11T22:30:13Z")
> [@JohnT](#): > > In distributing a product a poll is taken to see if the product was delivered. The population is 550,000, the poll sample was 300. There is no “mean” as this is a one-time poll taken about a one-time distribution - however, our “score” was 94.7% delivered and our bonus depends upon our achieving a 95%. If you have significant bonuses riding on a .3% shortfall with a 2.8% margin of error you need a more accurate survey. IMHO the range of the margin of error falls well within the shortfall you have earned the bonus unless they want to tighten up that margin with a larger survey. My next Q is with a breakpoint so close to a bonus line, is there anyone who handles this data with an incentive to see your department/co-workers not recieve their bonus like ops managers who may be charged against their labor dollars for the awarded bonuses, shifting their labor numbers below a breakpoint for their bonuses. ---
**Author:** ![JohnT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnt/32/15048_2.png) [@JohnT](https://boards.straightdope.com/u/JohnT)\ **Post date:** [July 12, 2006, 1:22am UTC](https://boards.straightdope.com/t/is-my-company-being-cheated-sadistics/364072/4 "2006-07-12T01:22:30Z")
Actually, they’re not calling us on this one… but they have with 1 other (in a 6 year contract totalling ~250 chances at the bonus, meaning we have acheived 99.6% of all possible bonuses). Perhaps “cheating” was a bit strong, but I wasn’t thinking about the monetary aspect as I was the mathematical… were they cheating on their sample size figures to provide the cheapest audit possible? I kept on getting ratios closing on 90% CL and a 10%MoE and figured that I was wrong (most likely), they were doing higher-order statistics than I’m aware of (almost as likely), or that they were fudging the numbers (least likely, but then, _we’re_ not the ones paying for it. 😉 ) > [@FreddyThePig](#): > > There is a mean; you just don’t know what it is. The mean is the percentage of people that actually got on-time delivery. You don’t know that value–if you did, you wouldn’t be taking the survey–but you can make a reasonable guess. > > Let’s guess that it is in fact 95%. Plugging that number and your other figures into the sample estimator, I get a sample size of 270–pretty much as the survey company says. This is obviously my gap in knowledge… thanks! (You’ve just reproved Occams razor: The most likely explanation (that I don’t know what I’m talking about) is, in fact, the correct one! 😉 ) > [@](#): > > You left the prior estimate of affirmative responses at 50%, which makes a huge difference. The “prior estimate” is the part that I didn’t understand… the only thing I noticed was that the further it deviated from 50, the smaller the sample. Since my argument was going to be “your survey company should call more people”, a _declining_ figure just obviously wasn’t going to do! 😉 Thank y’all for your help!