20. Significance analysis of a period
Peranso includes a unique mechanism to help you determine whether a detected period in your data is genuinely significant or simply the result of noise or other artifacts. This is achieved by calculating two complementary measures known as False Alarm Probabilities (FAPs).
What is a False Alarm Probability (FAP)?
A False Alarm Probability quantifies the likelihood that a detected period (or signal) in your data could arise by chance, rather than representing a true periodic signal. By assessing the statistical significance of a detected period, FAPs help you differentiate between genuine periodic signals and noise.
How Does Peranso Calculate FAPs?
Peranso employs the Fisher Randomization Test to compute two complementary FAPs. This test uses a Monte Carlo Permutation Procedure (MCPP), where the observed data is repeatedly randomized, and the period analysis is recalculated for each random permutation. This process generates a distribution of periods and corresponding peak strengths that represent what would be expected under random conditions. By comparing the observed data's periodogram to this distribution, Peranso calculates the following two FAPs:
- FAP1: Represents the probability that a random permutation contains a period with a peak strength greater than or equal to the observed peak strength at any frequency. This tests the overall likelihood that the detected peak is significant, considering the entire range of frequencies analyzed. A low FAP1 value indicates that the detected period is unlikely to arise purely by chance.
- FAP2: Represents the probability that a random permutation contains a period with a peak strength greater than or equal to the observed peak strength at the specific frequency of the detected period. This tests the significance of the detected period at the exact frequency of interest, providing additional confirmation of its reliability. A low FAP2 value suggests that the observed period is likely to be real and not just a random result at that particular frequency.
Illustrating FAPs with an Example
To demonstrate this process, this tutorial will use a synthetic dataset consisting of random observations that lack any clear periodic signal. When Peranso analyzes this dataset:
- FAP1 will reveal the probability that a strong peak could occur anywhere in the frequency range by chance. In a random dataset, FAP1 is typically high (close to 1.0), indicating that the data lacks a significant periodic component.
- FAP2 will indicate the probability that the specific frequency of the detected period is due to chance. Since the dataset contains no true periodic signal, FAP2 will also be high (close to 1.0).
Why Use Both FAP1 and FAP2?
By combining these complementary FAPs, Peranso provides a comprehensive evaluation of period significance. FAP1 helps identify whether the dataset contains any notable periodicity, while FAP2 focuses on the reliability of the specific detected period. Together, they allow for robust decision-making when interpreting results.