Spectral and cross-spectral analysis-A tutorial for psychologists and social scientists

Area of Science:

• Social Sciences
• Quantitative Psychology
• Behavioral Data Analysis

Background:

• Intensive longitudinal methods are increasingly used to study dynamic social phenomena.
• Many social processes exhibit cyclical fluctuations (e.g., mood, sleep).
• Existing analytical methods often fail to capture these temporal patterns.

Purpose of the Study:

• Introduce spectral and cross-spectral analysis for social science research.
• Demonstrate their application to time-series data, including dyadic and group-level data.
• Provide guidance on estimating significance and effect size for these analyses.

Main Methods:

• Spectral analysis to decompose time series into periodic components.
• Cross-spectral analysis to identify synchrony and phase offsets in dyadic data.
• Nonparametric bootstrapping for significance testing and effect size estimation.

Main Results:

• Spectral analysis effectively identifies periodicities in univariate and bivariate time-series data.
• Cross-spectral analysis reveals synchrony and time offsets in dyadic time series.
• Circular statistics and polar plots aid in visualizing phase relationships.

Conclusions:

• Spectral and cross-spectral analyses offer powerful tools for studying cyclical social phenomena.
• These frequency-domain methods complement traditional time-domain approaches.
• Accessible application via provided Jupyter Notebook facilitates adoption in social science research.