A generalization of Hewitt's test for seasonality

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Hewitt's statistic identifies seasonality in monthly data using maximal rank sums over 6-month periods.
• This research generalizes Hewitt's test to detect hypothesized 3-, 4-, or 5-month periods of elevated incidence.

Purpose of the Study:

• To extend Hewitt's seasonality test for detecting shorter, specific periods of raised incidence.
• To evaluate the test's performance and power compared to existing methods.

Main Methods:

• Utilized Monte Carlo simulations to approximate the distribution of the extended test statistic for k=3, 4, or 5 months.
• Employed combinatorial methods for exact test levels.
• Applied the test to monthly adolescent suicide data.
• Conducted Monte Carlo simulations to compare the power of the extended test against the chi-squared statistic.

Main Results:

• The distribution of the test statistic was determined, enabling hypothesis testing for seasonality.
• The generalized test rejected the null hypothesis of no seasonal variation in monthly adolescent suicides for a 3-month period.
• Monte Carlo simulations indicated the extended test statistic possesses greater power than the chi-squared statistic for small sample sizes.

Conclusions:

• The generalized Hewitt's test provides a quick and simple method for detecting seasonality against specific alternative hypotheses of 3-, 4-, or 5-month periods of raised incidence.
• This approach is particularly valuable when researchers have a priori hypotheses about the duration of seasonal patterns.