Testing tests on AGN microvariability

TL;DR

This paper evaluates various statistical tests for detecting microvariability in AGN lightcurves, emphasizing the importance of using well-tested, unbiased methods to improve research reliability.

Contribution

It provides a comprehensive comparison of statistical methodologies for AGN microvariability detection, highlighting the robustness of ANOVA and chi-square tests.

Findings

ANOVA and chi-square tests are effective for microvariability detection.

C-statistics is unreliable and should be avoided.

Properly tested methods reduce biased results in AGN studies.

Abstract

Literature on optical and infrared microvariability in Active Galactic Nuclei (AGNs) reflects a diversity of statistical tests and strategies to detect tiny variations in the lightcurves of these sources. Comparison between the results obtained using different methodologies is difficult, and the pros and cons of each statistical method are often badly understood or even ignored. Even worse, not properly tested methodologies are becoming more and more common, and biased results may be misleading to realize the origin of the AGN microvariability. This paper intends to point future research on AGN microvariability to the use of powerful and well tested statistical methodologies, providing a reference for choosing the best strategy to obtain unbiased results. Lightcurves monitoring have been simulated for quasars, reference and comparison stars. Changes for the quasar lightcurves include both Gaussian fluctuations and linear variations. Simulated lightcurves have been analyzed using chi-squaretests, F tests for variances, One-Way Analysis of Variances and C-statistics methodologies. Statistical Type I and Type II errors, which indicate the robustness and the power of the tests, have been obtained in each case. One-Way Analysis of Variances and chi-square show to be powerful and robust estimators for microvariations, while the C-statistics is not a reliable methodology and its use should be avoided.