Choose the level of adjustment
A direct method adjusts the total series. An indirect method adjusts its components separately and then combines them. Distinct seasonal patterns can favour the second approach: heating equipment and garden supplies may peak in different months. Adjusting the total can still be preferable when narrow components are short, erratic or poorly measured. The relevant comparison is between the stability and residual seasonality of the results, not between the apparent smoothness of two lines.
Make the aggregation explicit
Suppose two divisions record illustrative monthly sales of 120 and 80 units. If their estimated seasonal factors are 1.20 and 0.80, the indirectly adjusted total is 100 plus 100, or 200. If the separately estimated factor for the raw total is 1.02, direct adjustment gives about 196.1. These factors are hypothetical; neither calculation disproves the other. A percentage change must be computed from the adjusted levels in both months. Simply averaging division growth rates assumes an inappropriate weighting unless their starting levels are equal.
Keep shocks visible
Movable holidays, the number of trading days and exceptional closures can change the interpretation of a month. Check which effects the publisher models and whether an exceptional event is retained in the published adjusted series. New observations may revise previous seasonal estimates near the end of the sample. Where a monthly shift rests mainly on one component, compare several successive vintages before treating it as evidence of a change in the industrial cycle.
Practical check
Use one adjustment route across both comparison months and document whether the published total must add up from its components.