Statistical significance: wen a result mean sumting
“Significant” mean it nuh likely pon a fair wheel, nuh seh it “real” an nuh seh it “profitable”.
A p-value a 0.05 mean seh a fair wheel woulda gi a pattern weh lopsided suh one time outta twenty. If yuh look pon twenty wheel, one wi pass by accident.
Wah a di p-value
Di probabilitymathsProbabilityDi chance fi a result, fram 0 to 1 or 0% to 100%. One numba: 1/37 = 2.70%.Read di whole ting → fi see a deviation at least as big as di one yuh see, if di wheel did fair. It a statement bout di data unda a assumption, nuh bout di wheel. A p-valuelabp-valueDi probability fi see a deviation at leas as big as di one yuh see, if di wheel did fair.Read di whole ting → a 0.03 seh: a fair wheel do dis 3% a di time. It nuh seh: a 97% chance seh di wheel bias. Fi seh dat second ting, yuh woulda need fi know ow common bias wheellabBias wheelA wheel weh have physical defect weh mek some pocket more likely dan 1/37. It rare, an yuh can only find it out wid thousands a spin weh yuh write dung.Read di whole ting → deh fi start wid, an inna a modern casino dem very rare, suh one significant result more likely a fluke dan a real find.
Nuff comparison
Evry test yuh run pon a fair wheel have a 5% chance fi pass at di 5% level. Test twenty wheel an one pass. Test one wheel inna twenty time window an one pass. Test one sample wid 37 pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting → groupin, six sectorpon di wheelSectorA piece a di wheel weh di pocket dem follow one anodda roun di arc, nuh a group pon di betting layout.Read di whole ting → groupin an tree colour groupin, an sumting wi pass. Di cure a fi decide di test bifo yuh look pon di data, run it one time, an confirm it pon new data. Di searchin weh find a “bias” wheel most time a di same ting weh mek di result.
Significance an size
A huge sample can mek a tiny bias significant. A pocket weh hit at 1/36.5 instead a 1/37 a one real defect weh woulda reach significance inna a few million spin, an it woulda still lose money pon a 35 to 1 payoutmoney mattaPayoutWah a bet weh win gi yuh back, weh dem quote as “X to 1” on top a di stake weh come back.Read di whole ting →. Wah matter fi a playa a di effect size: any pocket hit at 1/36 or betta, an by ow much? Di chi-square tell yuh bout di wheel; only di hit rate tell yuh bout di bet.
Di power
Di odda mistake a fi miss a bias weh deh deh. Wid 1,000 spin, a pocket at 1/30 (a very big bias) get find only bout half a di time at di 5% level. Sample size, nuh smartness, fix dis. Di sample size page gi di numba dem.
A standard fi real life
Fi a bias claim fi interestin: a test yuh pick bifo time, p < 0.01 instead a 0.05, do it again pon a separate sample a similar size, an a estimated hit rate pon di favour pocket dem a 1/34 or betta afta yuh do it again. Dat standard get meet only a handful a time inna di game history, an neva, as far as public record show, pon a modern wheel weh dem maintain.
Question dem
A suh dem do it since di 1920s. Nutten special bout it; 0.01 a more sensible bar wen yuh a check nuff wheel.
It probably nuh a gi even result. It coulda be a dealer effect, a recordin mistake or a problem wid di data entry. Do it again.
No. It tell yuh di distribution off. Sector analysis an effect size tell yuh weh.
Fun wid maths
Try dem yuhself fus. Evry ansa fold up; open it wen yuh ready.
Dem report seh pon a double-zeropon di wheelZeroDi one green pocket weh no even-money, dozen or column bet nuh cover; a weh di house edge come fram. Nex name: single zero, 0.Read di whole ting → wheel di fus dozenbet demDozen1–12, 13–24 or 25–36, pay 2:1.Read di whole ting → come up 742 time inna 3,000 spin. Ow much standard deviationmathsStandard deviationDi square root a variance; ow far a result usually deh fram di expected value.Read di whole ting → unda di average dat deh, an ow often a fair wheel woulda do it?
Show di ansa
Ansa Bout 8.1 standard deviation low. A fair wheel woulda do it bout one time outta 3 × 10¹⁵ try, an dat a neva. Di ansa weh dem publish wid di question seh 11.75; wi get 8.07.
Di fus dozen hold 12 a di 38 pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting →. Inna 3,000 spin it average 3,000 × 12/38 = 947.4 hit, wid a spread a √(3,000 × 12/38 × 26/38) = 25.5.
742 deh 205.4 unda di average: 205.4/25.5 = 8.07 spread.
A fair wheel come up tree spread short bout one time outta 740 try; eight spread short, bout one time outta 3 × 10¹⁵ (bell curve, one side). Even if yuh allow fi di reada notice di worse a tree dozen, nutten weh matta nuh change. A result like dis seh di wheel, or di count, wrong. Pon a single-zero wheel di same count woulda be 9.0 spread low (average 973.0, spread 25.6).
Sumting fi laugh
One outta twenty fair wheel “significant”. A dat di numba mean.
Source dem
- Pearson, K. “On the criterion that a given system of deviations from the probable…”
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Ask the Wizard”, roulette questions.