Table 2.

Conditions sufficient for measures to be unbiased.

Number	Description^a	Scale	Notation^b	Sufficient for these summary measures to be unbiased.
1	There is no bias in any group in any time period.	Absolute	α_0,0 = α_0,1 = α_1,0 = α_1,1 = 0.	${\hat{D}}_{j}$ , $\hat{D ı D}$
1	There is no bias in any group in any time period.	Relative	β_0,0 = β_0,1 = β_1,0 = β_1,1 = 1.	${\hat{R}}_{j}$ , ${\hat{P D}}_{j}$ , $\hat{R O R}$ , $\hat{R P D}$
2	Bias is the same in all groups and time periods.	Absolute	α_0,0 = α_0,1 = α_1,0 = α_1,1 = α.	${\hat{D}}_{j}$ , $\hat{D ı D}$
2	Bias is the same in all groups and time periods.	Relative	0 ≠ β_0,0 = β_0,1 = β_1,0 = β_1,1 = β.	${\hat{R}}_{j}$ , ${\hat{P D}}_{j}$ , $\hat{R O R}$ , $\hat{R P D}$
3.1.	Bias is the same between time periods within group.	Absolute	α_0,0 = α_0,1 = α_0,t, and α_1,0 = α_1,1 = α_1,t.	${\hat{D}}_{j}$ , $\hat{D ı D}$
3.1.	Bias is the same between time periods within group.	Relative	0 ≠ β_0,0 = β_0,1 = β_0,t, and 0 ≠ β_1,0 = β_1,1 = β_1,t.	${\hat{R}}_{j}$ , ${\hat{P D}}_{j}$ , $\hat{R O R}$ , $\hat{R P D}$
3.2.	Bias is the same between groups within time period.	Absolute	α_0,0 = α_1,0 = α_j,0, and α_0,1 = α_1,1 = α_j,1.	$\hat{D ı D}$
3.2.	Bias is the same between groups within time period.	Relative	0 ≠ β_0,0 = β_1,0 = β_j,0, and 0 ≠ β_0,1 = β_1,1 = β_j,1.	$\hat{R O R}$
4.1.	The between-time-period trend in bias is the same between groups.	Absolute	α_1,1 − α_1,0 − α_0,1 − α_0,0 = α_j,1 − α_j,0.	$\hat{D ı D}$
4.1.		Relative	$\frac{β_{1, 1}}{β_{1, 0}} = \frac{β_{0, 1}}{β_{0, 0}} = \frac{β_{j, 1}}{β_{j, 0}}$ .	$\hat{R O R}$
4.2.	The between-group trend in bias is the same between time periods.	Absolute	α_1,1 − α_0,1 − α_1,0 − α_0,0 = α_1,t − α_0,t.	$\hat{D ı D}$
4.2.		Relative	$\frac{β_{1, 1}}{β_{0, 1}} = \frac{β_{1, 0}}{β_{0, 0}} = \frac{β_{1, t}}{β_{0, t}}$ .	$\hat{R O R}$
5	Neither the between-time-period trend in bias is the same between groups, nor is the between-group trend in bias the same between time periods.	Absolute	α_1,1 − α_1,0 ≠ α_0,1 − α_0,0 and α_1,1 − α_0,1 ≠ α_1,0 − α_0,0.	None
5		Relative	$\frac{β_{1, 1}}{β_{1, 0}} \neq \frac{β_{0, 1}}{β_{0, 0}}, and \frac{β_{1, 1}}{β_{0, 1}} \neq \frac{β_{1, 0}}{β_{0, 0}}$ .	None

The meaning of the word trend in conditions 4.1. and 4.2 depends on the scale. Please refer to the notation for further precision.

For expressions involving the multiplicative bias factor, we stipulate that β_j,t ≠ 0 so that the adjacent Y_j,t does not drop out of the expression, creating unusual results.