#### Polish AstroStatistics

I am visiting Copernicus Astronomical Center in Warsaw this week and this is the reason for Polish connection! I learned about two papers that might interest our group. They are authored by** Alex Schwarzenberg-Czerny **

*1. Accuracy of period determination, (1991 MNRAS.253, 198)*

Periods of oscillation are frequently found using one of two methods: least-squares (LSQ) fit or power spectrum. Their errors are estimated using the LSQ correlation matrix or the Rayleigh resolution criterion, respectively. In this paper, it is demonstrated that both estimates are statistically incorrect. On the one hand, the LSQ covariance matrix does not account for correlation of residuals from the fit. Neglect of the correlations may cause large underestimation of the variance. On the other hand, the Rayleigh resolution criterion is insensitive to signal-to-noise ratio and thus does not reflect quality of observations. The correct variance estimates are derived for the two methods.

*2. On the advantage of using analysis of variance for period search (1989 MNRAS. 241,153)*

One-way analysis of variance (AoV) is recommended as a method for detection of sharp periodic signals. Application of the method requires folding and binning data with a trial period. Among several methods of this type employed in astronomy, AoV has the advantage that its probability distribution is known for any number of observations, so that its usefulness for small samples is unquestionable. Comparison of the AoV test with other tests in use demonstrate that for large samples it is at least as powerful as any of them. Examples of application of the AoV method for photometric observations are discussed. An error in the phase dispersion minimization method, namely an incorrect probability distribution and significance criterion, is also discussed. It is argued that the power of the Lafler and Kinman test is comparable to that of the AoV2 test, the AoV test with narrow bins, containing two observations each. However, the AoV2 test is less powerful than any AoV test with a reduced number of bins and so is the Lafler and Kinman test.

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