Sameness is a mathematical concept created as a way of comparing both changes in mean and standard deviation from one population of data to another.
yieldHUb’s own research into the mathematics behind sameness found that the formula provided would only detect increases in std deviation and mean. By adjusting the formula to create a symmetric sameness function, sameness in yieldHUB provides a single number that can be compared across tests using different values, ranges and units of data and will show shifts in mean and standard deviation.
This basically means the value of standard deviation is calculated and the comparison is always done with the wider distribution as the reference and the smaller as the comparison. The resulting sameness function is shown in figure 1.
The sameness value will be 1 if both mean and standard deviation are exactly the same in the groups of data being compared. If the mean shifts then sameness will reduce. If the standard deviation changes then the sameness value will reduce.
So a list of tests can be compared to each other using the sameness value. The test with the lowest value shows the greatest difference between the groups of data.
This value is used in the yieldHUB sensitivity analysis report. Sameness can also be used to automatically compare new production data and alert if the new lot of data is varying more than expected.