﻿ Zscore minimum for reported bias (bias size/t-statistic) = 0, 0

# Zscore minimum for reported bias terms (bias size/t-statistic value) = 0, 0

Bias analysis calculates a bias measure, reported in Table 13 and Table 14, based on the data for which the elements include one from each of the facets specified. Most bias measures are small in logit size and statistically insignificant. This specification is a selection filter for which terms to report. The first control parameter places a lower limit on the absolute logit (in logits or user-units if user-scaled) of the bias measures to report. Thus, to report only bias measures that are outside of or equal to ±1 logit,

Zscore = 1 ; 1 logit

The second control parameter places a lower limit on the absolute value of the bias t-statistics to report. The t-statistic is obtained by dividing the bias measure by its standard error. With more than 30 observations, a t-statistic is approximately normally distributed, i.e., a z-statistic. To report only bias measures which have t-statistic outside of or equal to ±2:

Zscore = , 2 ; Leading comma, then 2 t-statistic units for bias control

To report bias measures which are either large in logits or significant statistically or both, specify both control parameters:

Zscore = 1,2 ; 1 logit or 2 t-statistic units

To report all bias measures:

Zscore= 0,0 ; include everything

Historical note: Facets used to assume that bias terms have approximately infinite degrees of freedom. Consequently they were reported as t-statistics with infinite degrees of freedom. These have the form of a unit-normal distribution, which is the same distribution as z-scores. Facets now reports bias significance using t-statistics with more exact finite degrees of freedom.

For reporting purposes, the absolute value of the t-statistic is compared with the specified second value in Zscore = bias-size, t-statistic value.

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