We develop analytical models to identify three (four) key parameters of Type I error (power) to evaluate the effects of important design choices used in four prior papers that propose alternative methods for dealing with the non-linearity of accruals in tests of earnings management. The key parameters for Type I errors are: (1) μ, the average value of the measured Mod-Jones discretionary accrual (DA) where event dates are randomly chosen. We refer to μ as the mean displacement (average DA scaled by lagged total assets); (2) σ, the standard deviation of the DA in a given partition; and (3) n, the sample size. Power is a function of these three parameters plus δ, the amount of earnings management seeded into raw accruals. Prior papers have used year-over-year changes in selected balance sheet (BS) accounts minus depreciation to calculate accruals, sample sizes of 100 to evaluate Type I error and earnings management seeds of 1% to 4% of lagged assets to evaluate power. Chen et al. (2025) identify two sources of error in these BS measures of accruals: (1) Non-articulation error (NON_ART); and (2) EXCLUSION error. We show that these two sources of error in BS accruals introduce significant non-linearity into accruals that contribute to moderate (substantial) Type I error in sample sizes of 100 (1,000 observations). Two models—Mod-Jones + quintile dummies and Mod-Jones + restricted cubic spline along ROA, SG, MB and TA dimensions—exhibit the lowest Type I errors and greatest power among the models considered.