Application of least squares spectral analysis and multiple linear regression techniques to the 1981 southern California field test for leveling refraction has revealed that in addition to differential refraction, rod/instrument settlement and an effect attributed to differential rod miscalibration are also detectable. The object of our analysis was the discrepancy between the forward and backward runnings of a section as this quantity properly reflects the direction of running thereby allowing for the detection of direction dependent effects. A multiple regression model using three arguments representing differential refraction, rod/instrument settlement, and differential rod miscalibration reduced the observed variation of the discrepancies by 61% as opposed to 53% when only the National Geodetic Survey (NGS) computed refraction correction is applied. It was found that of the original 23-mm accumulated discrepancy, 14 mm was attributed to differential refraction, 20 mm to settlement, and -14 mm to differential rod miscalibration. Analyses with the NGS computed refraction corrections applied (based on Kukkam¿ki's single sight equation with observed temperatures) gave similar results. It is also shown that the settlement effect is always present in any discrepancy and accumulates in the discrepancies between the forward and backward runnings while it cancels and is thus hidden in the accumulation of the NGS-derived discrepancies between the short and long sight length runnings.