Report 02 — Number and position uniformity

Wheel 'fingerprints': 90 frequencies and five extraction positions

Each number on one wheel has probability 5/90 = 1/18 of appearing in a five-number draw. The global test accounts for the fact that the five numbers within one draw are sampled without replacement. P-values are then Holm-adjusted so that the smallest value among many tests is not mistaken for an anomaly merely because many tests were run.

P(number in one draw) = 5/90 = 1/18 ≈ 0.05556
None of the 11 wheels is anomalous after multiple-testing correction. The same is true for all 55 wheel × position tests. A few raw p-values fall below 0.05, exactly as expected when many comparisons are made; none survives the Holm correction.

Uniformity of the 90 numbers by wheel

WheelNminmaxmax |z|p rawp HolmResult
Bari107525456652.8490.043570.43574not significant after Holm
Cagliari72773604542.5450.121081.00000not significant after Holm
Firenze109185576672.5250.425621.00000not significant after Holm
Genova73493644482.2550.915321.00000not significant after Holm
Milano109245526803.0540.121871.00000not significant after Holm
Napoli109205576903.4810.721821.00000not significant after Holm
Nazionale34861592312.7600.392501.00000not significant after Holm
Palermo109005606481.9050.799181.00000not significant after Holm
Roma109245616521.9170.806431.00000not significant after Holm
Torino109245526642.3850.251121.00000not significant after Holm
Venezia109235346843.2230.029420.32361not significant after Holm

Extraction-position uniformity

Each extraction position (1st…5th) is tested separately against a uniform 1–90 distribution. The table is ordered by the smallest raw p-value.

WheelPositionp rawp Holm
Cagliari10.021691.00000
Napoli40.045281.00000
Bari30.050031.00000
Venezia40.065521.00000
Firenze10.076141.00000
Nazionale10.125131.00000
Napoli10.134691.00000
Firenze40.135461.00000
Cagliari50.150581.00000
Venezia50.167821.00000
Torino20.168791.00000
Torino40.189551.00000
Milano20.211651.00000
Palermo20.227981.00000
Venezia20.228181.00000
Torino50.261071.00000
Nazionale40.289091.00000
Bari50.294371.00000
Bari40.309821.00000
Nazionale20.316161.00000
Milano50.319691.00000
Palermo40.325871.00000
Cagliari20.360381.00000
Genova20.360831.00000
Firenze50.429851.00000
Genova10.441311.00000
Nazionale50.455281.00000
Palermo10.457011.00000
Milano10.458391.00000
Roma10.486831.00000
Venezia10.488621.00000
Bari10.509211.00000
Bari20.509711.00000
Torino10.533921.00000
Napoli30.549161.00000
Roma20.560271.00000
Napoli20.610981.00000
Cagliari30.617111.00000
Cagliari40.632431.00000
Napoli50.659241.00000
Firenze30.672191.00000
Genova50.730081.00000
Torino30.751191.00000
Palermo30.784511.00000
Venezia30.787641.00000
Roma40.804211.00000
Genova40.804451.00000
Palermo50.810471.00000
Roma30.829821.00000
Nazionale30.846941.00000
Milano40.927441.00000
Milano30.948831.00000
Roma50.955321.00000
Firenze20.982321.00000
Genova30.984901.00000
Method note: the frequency test uses the finite-population factor 85/89, because 5 distinct numbers are drawn from 90 without replacement.
LottoStatistics 1.0.1 — reproducible descriptive/inferential analysis; not a prediction system.