Patent Document ID: 8335660
Application ID: 12550981
Patent Flag: 1

Claim One:
1. A method for sampling a population of units of multivariate data where the distribution of X and Y variables are unknown by evaluating ratio mean measurements on a computer to determine a confidence interval comprising: obtaining a sample from a population having two variables X and Y; using a bootstrapping method, generating from the sample a number B of boot strap samples (BSS), where B is a number greater than 100; generating a standardized {circumflex over (Z)} distribution for the ratio mean MR from the B bootstrap samples using the equation Z ^ ( i ) = MR ^ ( i ) - MR ^ SE ^ ( i ) ⁢ ⁢ where ⁢ ⁢ MR ^ ( i ) = ∑ j = 1 n ⁢ ⁢ X j ⁡ ( i ) ⁢ is an estimate of the ratio mean for the i th boot strap sample, ∑ j = 1 n ⁢ ⁢ Y j ⁡ ( i ) X j(i) ,Y i(t) are the n paired units for the i th boot strap sample where j(i) corresponds to the j th unit for the i th bootstrap sample, where i can range from 1 to B; ŜE (i) is the standard error for the i th boot strapped sample and wherein standard error ŜE (i) is determined by the equation SE ^ ( i ) = ∑ j = 1 n ⁢ [ AdjMR j ⁡ ( i ) - MR ^ ( i ) ] 2 n 2 where adjMR j ⁡ ( i ) = n * X j ⁡ ( i ) / ∑ k = 1 n ⁢ ⁢ Y k ⁡ ( i ) for the j th unit for the i th bootstrap sample where k is indexed from 1 to n, and j is in the range of 1 to n where n is the size of the sample; computing on a computer the α th and the (1−α) th percentile of the {circumflex over (Z)} distribution; computing on a computer the lower and upper bounds of the confidence interval CI using the equations 
 Lower CI bound={circumflex over (M)}R−ŜE* {circumflex over (t)} 1−α 
 Upper CI bound={circumflex over (M)}R−ŜE* {circumflex over (t)} α where MR ^ = ∑ j = 1 n ⁢ ⁢ X j ∑ j = 1 n ⁢ ⁢ Y j is the estimated ratio mean for the original sample; where ŜE is the standard error for the original sample computed by SE ^ = ∑ j = 1 n ⁢ ⁢ [ AdjMR j - MR ^ ] 2 n 2 , where adjMR j = n * X j / ∑ k = 1 n ⁢ ⁢ Y k and {circumflex over (t)} α and {circumflex over (t)} 1−α correspond to 1/α and 1/(1−α) respectively, whereby the bounds of the confidence interval CI are used to make a determination as to whether or not the number of samples taken from the population is statistically adequate to evaluate the entire population.