Launch Peranso. This brings up the Peranso Desktop Window.
Select Open in the File menu (or click on in the Desktop Toolbar) to display the File Open box.
Navigate to the Peranso Tutorials20 folder. To do so, first locate your My Documents folder (typically C:\Users\<your_user_name>\Documents). In there is a subfolder Peranso, then select the subfolder Tutorials. Finally, select the folder 20. Significance analysis of a period. Select the file Synthetic random data.nper and click the Open button.
This loads the contents of the file and creates an Observations Window (ObsWin) which contains 100 observations that are clearly random.
Click on the Period Determination button in the ObsWin toolbar to display the Period determination box. In the Methods section, select ANOVA. Select Days as Base and select Time as Unit. Enter 1 in the Start field, and 100 in the End field of the Range section. Enter 1500 in the Steps field and 3 in the Nbr harmonics field. Click Apply to start the ANOVA calculations.
This creates a Period Window (PerWin) with a weird periodogram and a "dominant" period at 1.97 d. Optionally, click the Phase Window button to confirm that there's is no real periodic signal at 1.97 d.
Select Period significance analysis in the Period analysis menu of the PerWin you created or click on in the PerWin toolbar to display the Significance analysis box.
The Significance analysis box has an Input section and a Results section. The dominant period is already pre-entered in the Input section. Change the Number of permutations to 100 and click the OK button. Peranso starts calculating period diagrams for each permutation. The progress of the calculations is is shown in the above box through 2 green bars. The upper bar shows the progress of calculations for one permutation, while the lower bar shows the overall progress across all 100 permutations. Intermediate FAP values and their 1-sigma error values are displayed while calculations are ongoing.
Wait for the calculations to finish, after which the following window will appear. Note that because the Fisher Randomization Test involves a random component, the values you see may not match the ones in our screenshot exactly. However, they should be of the same order of magnitude. The Cancel button is used to interrupt calculations. The Info icon to display a pop-up help window with some background information on the Significance calculations.
A FAP1 of 0.931 indicates that there is a very high probability (93.1%) that the detected peak could have occurred by chance at any frequency, clearly indicating that the dataset does not contain a significant periodic signal.
Similarly, a FAP2 of 0.842 means there is an 84.2% chance that the specific period detected at the observed frequency is also due to random noise.
Together, these values convincingly indicate that the detected period is not statistically significant and is a false positive.