# Best fitting model for one gold standard value ?

#### marca

##### New Member
Hello,

trying to solve the following statistical problem in jmp:

1. I got a gold standard y (for example: y = 100)

2. I got three data sets x1,x2,x3: (for example x1=92;94;99 / x2=92;94;99;101;103 / x3=92;94;99;101;103;107;100;99;100)
please note: the data sets have similar data, but the number of data points are different. all variables are continuous.

3. now I can calculate mean and sd for x1, x2, x3

I am looking for with a statistical test or function, to evaluate which dataset x1, x2 or x3 has the closest mean AND the lowest SD to match the gold standard y ? - please note: the gold standard y has no sd, just a fixed value.

Any advice much appreciated. Many thanks, Marc

#### rogojel

##### TS Contributor
hi,
do you have any measure of how much deviation from the gold standard is still acceptable? A deviation of 0.5 is probably better then a deviation of 1.5.

If you can have something like this then you could calculate for each dataset the probability of landing outside the acceptable range, and the set with the lowest probability is best.
regards

#### marca

##### New Member
Yes. I can certainly an equivalence test to test if my resulting x is within limites, but for example
if I get resulting mean1 = 101 and SD +- 3 is this better or worse than a model where I would have mean2 = 102 and SD +-1 ?
How could I rank those ?

#### rogojel

##### TS Contributor
Assuming that your acceptable values are 100 +/_ 0.5, and the standard deviation to be in the first case 3/2 and the second case 1/2 in the first case you would have a roughly 20% chance if landing in the acceptable region while in rhe second only 0.16 %, so obviously the first case would be much better.

You need to calculate the probability of a value to be between 99.5 and 100.5 for the normal distribution with mean 101 and stddev 3/2 and the same for the other distribution.

regards