Re: Thoroughly shuffled [long]

"\"Luis A. Afonso\"" <licas_@xxxxxxxxxxx> writes:

> ADDENDA
>
> The program I referred in the precedent post is

[BASIC source code snipped]

> Note: It is not strange but inevitable that there is not a value cv such that exactly p(Q>cv)= 0.05 exactly. This is due to the fact (seldom pointed out in textbooks) that the sample statistics Q is discontinuous, i.e., the values jumped to one to the next. Therefore the vc I evaluated is in excess, the cumulative probability is a little greater, 0.956, instead of 0.950. We can find by trial and error which is the value immediately lesser than our reference value = 16.92 (but is quite uninteresting).
> Any feedback, critique or corroborative, welcomed.

You are correct that Q is discrete. It is approximately chi square. The
exact distribution is not too big a problem to solve with a computer. I
wrote a little Mathematica code that produced the following table. (The
cumulative relative frequencies were calculated as exact fractions, but
I reduced them to decimals for this table.) Your reference value of 16.92
is actually the fraction 220/13.

"chisq" cumulative relative frequency

12
--
13 0.00093141967840245057317

20
--
13 0.0051228082312134781524

28
--
13 0.011409891060430019521

36
--
13 0.035219306589592662298

44
--
13 0.054972534953637383211



4 0.095649960858668405868

60
--
13 0.13009374413853122776

68
--
13 0.20057822973687787304

76
--
13 0.24376962429970649497

84
--
13 0.31369120641541061926

92
--
13 0.36161596226710718970

100
---
13 0.45131440169982250706

108
---
13 0.49827276858410164652

116
---
13 0.56488141132298667614

124
---
13 0.60658695490153258093

132
---
13 0.67758724974033229360

140
---
13 0.71322480290178664337

148
---
13 0.76146798752338716646



12 0.79010267226134659084

164
---
13 0.83484606720075308344

172
---
13 0.85633477101884912354

180
---
13 0.88397092816544639872

188
---
13 0.89912452371212576911

196
---
13 0.92364387024273360776

204
---
13 0.93454672437159612854

212
---
13 0.94798209042747903193

220
---
13 0.95583033460154087471

228
---
13 0.96720424194685466263

236
---
13 0.97225001460625299789

244
---
13 0.97855535103098635447

252
---
13 0.98183736713653461703



20 0.98668200825875122550

268
---
13 0.98888296761601508909

276
---
13 0.99148441202706479245

284
---
13 0.99282975796466487274

292
---
13 0.99487236827034482644

300
---
13 0.99573742878437669445

308
---
13 0.99674042391607849773

316
---
13 0.99729839723888481187

324
---
13 0.99807940464593580281

332
---
13 0.99840395719268606854

340
---
13 0.99880607819545247958

348
---
13 0.99901297653134179593

356
---
13 0.99929665446270018789



28 0.99942188636251925950

372
---
13 0.99956589992958795440

380
---
13 0.99963870116107214351

388
---
13 0.99974864565512367410

396
---
13 0.99979443359878787745

404
---
13 0.99984592656317232284

412
---
13 0.99987269663321655754

420
---
13 0.99991098907806243206

428
---
13 0.99992709632599685886

436
---
13 0.99994600295740861441

444
---
13 0.99995571009019486660

452
---
13 0.99996892303495588128

460
---
13 0.99997469599267924620



36 0.99998117122949273631

476
---
13 0.99998441339303561892

484
---
13 0.99998919789642921304

492
---
13 0.99999115897647176046

500
---
13 0.99999341532793701651

508
---
13 0.99999466470845705370

516
---
13 0.99999633703066396444

524
---
13 0.99999695885181235369

532
---
13 0.99999777838294130348

540
---
13 0.99999817697712293697

548
---
13 0.99999871062059930800

556
---
13 0.99999896236543215338

564
---
13 0.99999923162481029995



44 0.99999936502603964339

580
---
13 0.99999956177049674883

588
---
13 0.99999965068246203737

596
---
13 0.99999974136230890989

604
---
13 0.99999978462951763343

612
---
13 0.99999985339671396378

620
---
13 0.99999987922414174460

628
---
13 0.99999991097780844105

636
---
13 0.99999992764524290714

644
---
13 0.99999994912206765734

652
---
13 0.99999995900569570279

660
---
13 0.99999996953692601099

668
---
13 0.99999997509189719716



52 0.99999998295892415208

684
---
13 0.99999998594137040515

692
---
13 0.99999998974023410209

700
---
13 0.99999999175177730314

708
---
13 0.99999999446748763625

716
---
13 0.99999999536369314033

724
---
13 0.99999999650573084733

732
---
13 0.99999999712095960216

740
---
13 0.99999999797272113419

748
---
13 0.99999999838025253235

756
---
13 0.99999999883084211815

764
---
13 0.99999999903533974748

772
---
13 0.99999999932380124359



60 0.9999999994753603074

788
---
13 0.9999999995995121424

796
---
13 0.9999999996724434036

804
---
13 0.9999999997725504324

812
---
13 0.9999999998164224892

820
---
13 0.9999999998701366397

828
---
13 0.9999999998895430167

836
---
13 0.9999999999244548909

844
---
13 0.9999999999358746353

852
---
13 0.9999999999538130427

860
---
13 0.9999999999605762586

868
---
13 0.9999999999725954488

876
---
13 0.9999999999787046567



68 0.9999999999838485672

892
---
13 0.9999999999879347822

900
---
13 0.9999999999917969401

908
---
13 0.9999999999929715481

916
---
13 0.9999999999944922173

924
---
13 0.9999999999954948217

932
---
13 0.9999999999968164166

940
---
13 0.9999999999973362486

948
---
13 0.9999999999982131851

956
---
13 0.9999999999985834397

964
---
13 0.9999999999990324104

972
---
13 0.9999999999991655701

980
---
13 0.9999999999993632766



76 0.9999999999994451626

996
---
13 0.9999999999996136259

1004
----
13 0.9999999999997096415

1012
----
13 0.9999999999997781224

1020
----
13 0.9999999999998257275

1028
----
13 0.9999999999998834741

1036
----
13 0.9999999999999174477

1044
----
13 0.9999999999999335055

1052
----
13 0.9999999999999419465

1060
----
13 0.9999999999999519493

1068
----
13 0.9999999999999586854

1076
----
13 0.9999999999999732343

1084
----
13 0.9999999999999772819



84 0.9999999999999880411

1100
----
13 0.9999999999999894104

1108
----
13 0.9999999999999924956

1116
----
13 0.9999999999999936743

1124
----
13 0.9999999999999949840

1132
----
13 0.9999999999999954920

1140
----
13 0.9999999999999965203

1148
----
13 0.9999999999999973343

1156
----
13 0.9999999999999982618

1164
----
13 0.9999999999999987267

1172
----
13 0.9999999999999990179

1180
----
13 0.9999999999999993390

1188
----
13 0.9999999999999995364



92 0.9999999999999996078

1212
----
13 0.9999999999999996488

1220
----
13 0.9999999999999997479

1228
----
13 0.9999999999999997974

1236
----
13 0.9999999999999998934

1244
----
13 0.9999999999999999216

1252
----
13 0.9999999999999999522

1260
----
13 0.9999999999999999585

1268
----
13 0.9999999999999999674

1284
----
13 0.9999999999999999730

1292
----
13 0.9999999999999999760



100 0.9999999999999999805

1308
----
13 0.9999999999999999873

1316
----
13 0.9999999999999999931

1324
----
13 0.9999999999999999953

1332
----
13 0.9999999999999999973

1340
----
13 0.9999999999999999977

1356
----
13 0.9999999999999999981

1380
----
13 0.9999999999999999987

1388
----
13 0.9999999999999999990

1396
----
13 0.9999999999999999996



108 0.9999999999999999997

1412
----
13 0.9999999999999999999

1436
----
13 0.9999999999999999999

1452
----
13 0.9999999999999999999

1468
----
13 0.9999999999999999999

1476
----
13 1.0000000000000000000

1484
----
13 1.0000000000000000000

1500
----
13 1.0000000000000000000

1548
----
13 1.0000000000000000000

1556
----
13 1.0000000000000000000

1572
----
13 1.0000000000000000000

1644
----
13 1.0000000000000000000

1652
----
13 1.0000000000000000000

1676
----
13 1.0000000000000000000

1740
----
13 1.0000000000000000000

1836
----
13 1.0000000000000000000



156 1.0000000000000000000



Scott
--
Scott Hemphill hemphill@xxxxxxxxxxxxxxxxxx
"This isn't flying. This is falling, with style." -- Buzz Lightyear
.