Statistical Methods
Separate recurring seasonal levels from drift within seasons
Set the calendar convention
Choose the period from the collection design, such as four quarters per year. Preserve the ordering within each quarter across years. Confirm that changes in reporting deadlines, business days or the start of the fiscal year have not shifted the meaning of a quarter. A seasonal display requires a meaningful phase assignment.
Read across and within phases
Place all first-quarter values together, then all second-quarter values, continuing through the cycle. Mark a mean or median for each phase. Compare phase levels, and inspect the direction of change within each phase. Report the number of observations contributing to each summary, especially when a season is missing.
Hypothetical example
Two complete years of quarterly counts are (10, 20, 12, 18) and (12, 22, 14, 20). Quarter means are 11, 21, 13 and 19. Every quarter also rose by 2 between years. A high second-quarter mean describes a recurring level, while the paired within-quarter differences describe movement between years. Two years give little evidence about long-run stability.
If observation opportunities differ, consider a well-defined rate with an exposure denominator before comparing counts. Leave missing quarters explicit. Replacing a missing quarter with zero changes both its phase average and the appearance of drift.
Method checked 9 November 2026. NIST/SEMATECH Engineering Statistics Handbook, 6.4.4.3.1. Seasonal Subseries Plot.