Background:
I have two data sets, each with 16 elements that are estimates (with unknown bounds on the errors) of various values of variables A and B at various times. I want to test whether the estimates have some degree of reliabity. I have good reason to believe that there is a negative correlation between the variables being estimated. Unfortunately, I have excellent reason to believe that any functional relationship between the variables is not stable over time, and I have no reason to prefer any particular form of functional relationship between the variables. Consequently, regression analysis seems inappropriate, or at least fruitless, to me.
In 16 rows of column 1, I calculate the signum functions of the difference between the estimates of A and the mean of the estimates. In 16 rows of column 2, I calculate the signum functions of the difference between the estimates of B and the mean of the estimates. In column 3, I calculate the product of the two preceding columns. If there is a positive correlation between the estimates, the products would be expected to be mostly positive. If there is no correlation, the number of positives would be expected to equal the number of negatives.
In column 3, I get 15 minus ones and one positive one. Under the null hypothesis that there is no negative correlation between A and B, the probability of getting at most one positive one does not exceed
\(\displaystyle 0.5^{16} + 16 * 0.5^{15} \approx 0.0000153 + 16 * 0.0000305 = .0000153 + .000488 = .000533 < 0.6\%.\)
Consequently, I reject the null hypothesis and conclude that the estimates are reliable.
Questions:
Is this a proper inference?
Is it correct to call this a sign test?
If not, does it have a name?
I have two data sets, each with 16 elements that are estimates (with unknown bounds on the errors) of various values of variables A and B at various times. I want to test whether the estimates have some degree of reliabity. I have good reason to believe that there is a negative correlation between the variables being estimated. Unfortunately, I have excellent reason to believe that any functional relationship between the variables is not stable over time, and I have no reason to prefer any particular form of functional relationship between the variables. Consequently, regression analysis seems inappropriate, or at least fruitless, to me.
In 16 rows of column 1, I calculate the signum functions of the difference between the estimates of A and the mean of the estimates. In 16 rows of column 2, I calculate the signum functions of the difference between the estimates of B and the mean of the estimates. In column 3, I calculate the product of the two preceding columns. If there is a positive correlation between the estimates, the products would be expected to be mostly positive. If there is no correlation, the number of positives would be expected to equal the number of negatives.
In column 3, I get 15 minus ones and one positive one. Under the null hypothesis that there is no negative correlation between A and B, the probability of getting at most one positive one does not exceed
\(\displaystyle 0.5^{16} + 16 * 0.5^{15} \approx 0.0000153 + 16 * 0.0000305 = .0000153 + .000488 = .000533 < 0.6\%.\)
Consequently, I reject the null hypothesis and conclude that the estimates are reliable.
Questions:
Is this a proper inference?
Is it correct to call this a sign test?
If not, does it have a name?