A Statistical Theory of Bidirectionality

Original concepts related to the quantification and assessment of bidirectionality in strain-gage balances were introduced by Ulbrich in 2012. These concepts are extended here in three ways: 1) the metric originally proposed by Ulbrich is normalized, 2) a categorical variable is introduced in the regression analysis to account for load polarity, and 3) the uncertainty in both normalized and non-normalized bidirectionality metrics is quantified. These extensions are applied to four representative balances to assess the bidirectionality characteristics of each. The paper is tutorial in nature, featuring reviews of certain elements of regression and formal inference. Principal findings are that bidirectionality appears to be a common characteristic of most balance outputs and that unless it is taken into account, it is likely to consume the entire error budget of a typical balance calibration experiment. Data volume and correlation among calibration loads are shown to have a significant impact on the precision with which bidirectionality metrics can be assessed.