Sample Size: Why are Sample Sizes not Linear according to the Lot Size?

Hi.. have a question as I'm a newbie at this and I will be asked WHY

I have a program with 3541 samples.. with error rate of 10% and accuracy of 5% and Zscore of 1.96 I get a sample size of 136.

Now I've been asked to do one with 9700 samples, same parameters and I get a sample size of 133?

I'm not soo good with Stats, I can understand why it would be the same as the calc is not linear.. but my colleages will definately want to understand how a lot of twice the size means we need to do the same # of samples.

Thanks!

Re: Sample Size Questions: Why are Sample Sizes not Linear?

For sample sizes are based on statistical informations (like error rate and accuracy), they are independent of the lot size. The difference between 133 and 136 occurs presumably due to rounding in the equation. (If not, please provide the formula which was taken to determine this sample sizes.)

But if you're going with standards like ANSI, the results will slightly differ because those who set up the tables went with "if we get more pieces we have to test a bigger sample". On the first glance this seems to be rational, but from a statistical point of view it's not the matter of lot size but the matter of numbers (difference to detect in shift of the mean or proportion assumed, type I risk / confidence level, type II risk / power, standard deviation).

Let me clarify this with an example: For a couple of years you bought 1.0l of your favorite chocolate ice cream per month. To assure if the quality over the years met your expectations, you tried 1 table spoon from each package before feeding yourself and others with the ice cream.
So 1 table spoon is a sufficient amount of ice cream to get the taste.

But on Monday you went to the store and found a new label on the container of your favorite brand of chocalate ice cream stating "completely new and optimized recipe". (Damn, they changed it!) Additionally they made a special offering and the 1.0l container was replaced by a 5.0l container, so you had to buy five times as much ice cream.

At home you want to try the new chocalate ice cream out of the 5.0l container. (Remember: For the old one you always took 1 table spoon to evaluate the taste.)

The 1 Million Dollar question is: How many table spoons are sufficient for the 5.0l container?

• 5*1 table spoon = 5 table spoons as you bought 5 times as much ice cream
• 1 table spoon as this is sufficient to get the taste

Best regards,

Barbara

[SOLVED] Re: Sample Size: Why are Sample Sizes not Linear according to the Lot Size?

Barbara! That is exactly what I need! That was basically what the feeling was I had about why the sample sizes were the same, but I just couldn't express it, and then being as I am not a statiscial expert (but am starting down the path and now that I have something to concrete to use it is starting to become much more understandable and clearer to me than when I was at Uni and almost flunked it!)

I also wasn't confident that I would give the "right" answer.

The formula I used was:

Sample size = ( Z2 x N x p x (1 - p) ) / ( A2 x N + Z2 x p x (1 - p) )

THANK YOU SO MUCH!