%!PS-Adobe-2.0 %%Creator: dvips 5.493 Copyright 1986, 1992 Radical Eye Software %%Title: ctrandom.dvi %%Pages: 21 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: C:\EMTEX\DVIPS.EXE ctrandom %DVIPSSource: TeX output 1993.08.31:1114 %%BeginProcSet: texc.pro %! /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N} B /TR{translate}N /isls false N /vsize 11 72 mul N /@rigin{isls{[0 -1 1 0 0 0] concat}if 72 Resolution div 72 VResolution div neg scale isls{Resolution hsize -72 div mul 0 TR}if Resolution VResolution vsize -72 div 1 add mul TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{/nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array /BitMaps X /BuildChar{ CharBuilder}N /Encoding 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FF(i)196 1222 y Fx(This)12 b(co)q(de)e(is)i(used)e(in)i(section)d (7.)113 1334 y FI(9.)42 b FG(What)13 b(has)i(to)e(b)q(e)i(done.)113 1395 y(The)h(announcemen)o(ts)g(of)e(the)i(top)g(lev)o(el)f(descriptions)h (has)f(to)h(b)q(e)g(replaced)g(b)o(y)f(elab)q(orated)h(ideas)f(that)h(are)113 1445 y(more)d(detailed)h(and)g(at)g(the)g(end)g(can)h(directly)f(b)q(e)g (translated)h(in)o(to)e(pure)h FD(APL)p FG(2-co)q(de.)113 1557 y FI(10.)42 b FG(The)14 b(function)g FH(con)o(tab)p FG(.)113 1618 y(Before)i(discussing)e(further)h(re\014nemen)o(ts)g(w)o(e)g(w)o(an)o(t) e(to)i(concen)o(trate)h(on)d(a)h(sp)q(ecial)h(problem)e(that)h(has)g(to)g(b)q (e)113 1668 y(solv)o(ed)g(in)g(an)o(y)f(case:)19 b(Ho)o(w)14 b(can)g(w)o(e)g(get)g(the)g(con)o(tingency)h(table)f(from)e(the)i(data)g (matrix?)113 1730 y(Asking)h(Berni)h(he)g(replied:)21 b("This)15 b(problem)f(has)h(b)q(een)i(solv)o(ed)e(b)o(y)g(the)g(function)g FH(con)o(tab)p FG(.)24 b(Just)16 b(a)f(momen)o(t)113 1779 y(please!)k(Here)c (w)o(e)f(are!")217 1883 y FH(Oo\012a)g(con)o(tab)h(o;Oy)q(;Ox;x;y)q(;o)o(x;o) o(y;o0)o(x;o0y;O0x;O0y;oO;)o(o)q(o;OO;Oo\334)o(o)217 1932 y(Oy)q(\012\217y)q (\012o[;2])e(\233)g(y)q(\012y)q([Oy)q(])g(\233)h(Ox\012\217x\012o[Oy)q(;1])f (\233)g(x\012x[Ox])217 1982 y(o)o (x\012\(o0x\0121,\(1\010x\)\242\3351\010x\)\346x)g(\233)g(o)o(y)q(\012\(o0y)q (\0121,\(1\010y)q(\)\242\3351\010y)q(\)\346y)217 2032 y(O0x\012+\350o0x)h (\233)g(O0y)q(\012\(+\350o0y)q(\)[Ox])f(\233)h(Oo\012\(\(\006o)o(x\),\006o)o (y)q(\)\0110)217 2082 y(oO\012O0y)q(+\(O0x\0141\)\0151\010\006Oo)h(\233)e(o)q (o\012oO\004oO)h(\233)f(OO\012\(\(1\010o)q(o\),1+\006o)q(o\)\014o)q(o)217 2132 y(Oo\334o\012,Oo)g(\233)h(Oo\334o[oO]\012OO)f(\233)h (Oo\012\(\006Oo\)\006Oo\334o)f(\233)h(\013\(0=\222NC)f(\336a\336\)\3460)217 2181 y(Oo\012Oo)h(o)o(x)g(o)o(y)g(\(+\346Oo\))g(\(+\347Oo\))h(\(+\346,Oo\)) 113 2285 y FG("No,)h(no,)g(that's)g(not)g(an)f(answ)o(er|it)h(seems)h(to)e(b) q(e)i(a)f(complicated)e FD(APL)p FG(2-o-o)q(o-oO-Oo-OO-O-puzzle!)25 b(I)113 2334 y(am)13 b(sure)i(y)o(ou)e(didn't)g(dev)o(elop)h(it)g(in)f(this)h (w)o(a)o(y)m(.)j(Please)d(send)h(us)g(an)e(understandable)i(solution!")113 2396 y("Ok)n(a)o(y)m(,)d(y)o(ou)i(are)g(righ)o(t.)k(I)c(will)e(mail)f(y)o(ou) j(the)g(original)e Fy(WEB)p FG(-pap)q(er.")113 2458 y(The)j Fy(WEB)p FG(-pap)q(er)f(of)f FH(con)o(tab)i FG(is)e(reprin)o(ted)i(as)f(the)h (second)g(ma)r(jor)d(section)j(of)e(this)h(pap)q(er.)p eop %%Page: 5 6 5 5 bop 113 183 a FD(P)o(art)14 b(2:)g(The)g FH(con)o(tab)p FD(-function)1242 b FG(5)113 366 y FI(11.)48 b(The)16 b FH(con)o(tab)p FI(-function.)113 478 y(12.)p 216 436 648 2 v 216 498 2 62 v 56 w FG(Computational)11 b(Statistics)j(Problem)p 862 498 V 216 500 648 2 v 113 604 a(A)g(function)f(is)g(to)g(b)q(e)h(written)g(whic)o (h)f(computes)g(the)h(con)o(tingency)g(table)f(from)e(a)i(t)o(w)o(o)g(column) f(data)h(matrix)113 653 y(of)h(discrete)h(random)e(v)n(ariables)g(organized)h (as)g(column)e(v)o(ectors.)113 770 y FI(13.)p 216 729 790 2 v 216 791 2 62 v 56 w 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FE(x)p FG(-v)n(alues,)g(the)g FE(y)q FG(-v)n(alues,)g(the)g(sum)f(o)o(v)o (er)h(the)g(columns,)f(the)h(sum)f(o)o(v)o(er)h(the)g(ro)o(ws,)g(and)113 1195 y(the)f(n)o(um)o(b)q(er)e(of)g(en)o(tries.)113 1307 y FI(14.)p 216 1265 337 2 v 216 1327 2 62 v 56 w FG(Syn)o(tax)h(of)f FH(con)o(tab)p 550 1327 V 216 1329 337 2 v 113 1433 a FG(The)i(function)e (header)i(lo)q(oks)e(lik)o(e)h(this:)196 1494 y FH(\214)h(res\012mar)f(con)o (tab)h(m)40 b FG(14)196 1631 y Fx(See)11 b(also)g(section)f(16.)196 1695 y Fw(con)o(tab)h Fx(app)q(ears)f(in)h(sections)f(2,)h(10,)g(13,)g(16,)f (24,)h(28,)g(32,)g(and)g(38.)113 1807 y FI(15.)p 216 1765 179 2 v 216 1819 2 54 v 56 w FG(Solution)p 392 1819 V 216 1821 179 2 v 113 1927 a(Of)j(course,)g(there)h(are)f(sev)o(eral)g(metho)q(ds)f(to) h(solv)o(e)f(this)h(task)g(but)f(this)h(time)e(let's)i(imagine)d(that)j(our)f FD(APL)p FG(2-)113 1977 y(function)e(m)o(ust)g(b)q(e)h(as)f(fast)h(as)f(p)q (ossible.)17 b(So)12 b(it's)e(wise)i(to)f(a)o(v)o(oid)f(the)i(ob)o(vious)f (double)g(lo)q(op.)17 b(But)12 b(ho)o(w?)k(What)113 2027 y(has)e(to)g(b)q(e)h (done?)113 2088 y(W)m(ell,)9 b(certainly)g(w)o(e)h(ha)o(v)o(e)f(to)h(compute) f(the)h(di\013eren)o(t)g FE(x)p FG(-)f(und)h FE(y)q FG(-v)n(alues.)17 b(Then)10 b(w)o(e)g(can)f(construct)i(a)f(protot)o(yp)q(e)113 2138 y(of)15 b(the)g(result.)22 b(F)m(urthermore,)14 b(w)o(e)h(m)o(ust)f (coun)o(t)h(the)g(n)o(um)o(b)q(er)g(of)f(app)q(earances)i(of)e(eac)o(h)i FE(xy)q FG(-com)o(bination)c(in)113 2188 y(our)j(data)f(matrix)e(and)j(w)o(e) f(m)o(ust)g(assign)g(this)g(n)o(um)o(b)q(er)g(at)g(the)h(righ)o(t)f(p)q (osition)1390 2173 y FB(1)1408 2188 y FG(.)20 b(W)m(e)14 b(m)o(ust)f(not)i (forget)f(that)113 2238 y(the)h FE(x)p FG(-)e(and)h FE(y)q FG(-v)n(alues)g(should)g(b)q(e)g(sorted)h(in)f(ascending)g(order,)g(so)g(w)o (e)g(will)f(ha)o(v)o(e)g(to)h(do)g(some)f FC(gr)n(adeups.)113 2355 y FI(16.)p 216 2313 390 2 v 216 2367 2 54 v 56 w FG(De\014nition)g(of)g FH(con)o(tab)p 604 2367 V 216 2369 390 2 v 113 2475 a FG(W)m(e)h(are)g(ready) g(to)g(do)g(the)g(\014rst)h(re\014nemen)o(ts)g(of)e FH(con)o(tab)p FG(.)196 2537 y FH(\214+)i(res\012mar)f(con)o(tab)h(m)40 b FG(14)196 2599 y FF(h)7 b FG(Sort)15 b FH(m)d FG(in)i(ascending)g(order!)83 b(17)7 b FF(i)196 2660 y(h)g FG(Remo)o(v)o(e)13 b(duplicated)h(elemen)o(ts)f (and)h(compute)f(the)i(\\ranks")f(of)f FH(x)h FG(and)g FH(y)q FG(!)82 b(19)7 b FF(i)196 2722 y(h)g FG(Build)14 b(a)f(protot)o(yp)q(e)i(of)e (the)i(result!)83 b(21)7 b FF(i)196 2783 y(h)g FG(Coun)o(t)14 b(the)h(n)o(um)o(b)q(er)e(of)g(app)q(earances)j(of)d(eac)o(h)h FE(xy)q FG(-pair!)83 b(22)7 b FF(i)196 2845 y(h)g FG(Do)14 b(the)g(\014nal)g(assignmen)o(t!)81 b(24)7 b FF(i)p 113 2882 709 2 v 160 2909 a Fv(1)177 2921 y Fx(This)k(is)h(a)f(kno)o(wn)g(problem)e (called)h(\\scattered)f(assignmen)o(t".)p eop %%Page: 6 7 6 6 bop 113 183 a FD(P)o(art)14 b(2:)g(The)g FH(con)o(tab)p FD(-function)1242 b FG(6)196 366 y FF(h)7 b FG(Add)15 b(the)f(margins)e(if)h (a)h(left)g(argumen)o(t)e(is)i(giv)o(en!)82 b(26)7 b FF(i)113 472 y FI(17.)42 b FG(W)m(e)16 b(will)g(certainly)h(need)h(the)f FE(x)p FG(-)g(and)g FE(y)q FG(-v)n(alues)g(as)g(v)o(ectors,)i(so)e(instead)g (of)f(sorting)h(the)h(matrix)d(w)o(e)113 521 y(will)d(carefully)h(sort)h(the) g(column)d(v)o(ectors)k(of)d FH(m)g FG(without)h(losing)f(the)i(information)d (ab)q(out)i(the)h(sample)e(pairs.)113 571 y(That)i(means,)f(me)g(m)o(ust)f (remem)o(b)q(er)h(the)i(p)q(ositions)f(of)f(the)h(elemen)o(ts)g(of)f(the)i FE(x)p FG(-)e(and)h(the)g FE(y)q FG(-v)o(ectors.)113 633 y(These)k(p)q (ositions)d(will)g(b)q(e)i(sa)o(v)o(ed)f(in)g(the)g(lo)q(cal)f(v)n(ariables)h FH(orig\334x)f FG(and)h FH(orig\334y)g FG(while)f(the)i FE(x)p FG(-)f(and)g FE(y)q FG(-v)n(alues)113 683 y(will)d(b)q(e)h(sa)o(v)o(ed)g(in)g (the)g(lo)q(cal)f(v)n(ariables)g FH(x)h FG(and)g FH(y)q FG(,)f(resp)q(ectiv)o (ely)m(.)196 744 y FF(h)7 b FG(Sort)15 b FH(m)d FG(in)i(ascending)g(order!)83 b(17)7 b FF(i)23 b(\021)196 810 y FH(orig\334y)q(\012\217y)q(\012m[;2])196 872 y(y)q(\012y)q([orig\334y)q(])196 933 y (orig\334x\012\217x\012m[orig\334y;1])11 b(\240)j(Do)g(not)g(forget)g(the)h (pairs!)196 995 y(x\012x[orig\334x])196 1070 y Fx(This)d(co)q(de)e(is)i(used) e(in)i(section)d(16.)113 1176 y FI(18.)60 b FF(h)7 b FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(con)o(tab)p FG(\(14\))84 b(18)7 b FF(i)23 b(\021)196 1242 y FH(orig\334x,orig\334y)m(,x,y)196 1317 y Fx(See)11 b(also)g(sections)f(20,)g(23,)h(and)g(25.)113 1423 y FI(19.)42 b FG(No)o(w)12 b(w)o(e)h(are)f(ready)h(to)f(coun)o(t)h(the)g (n)o(um)o(b)q(er)f(of)g(di\013eren)o(t)h FE(x)p FG(-)f(and)g FE(y)q FG(-v)n(alues)h(and)f(their)h(\\ranks".)k(Ranks)113 1472 y(in)12 b(this)g(sense)i(are)f(somewhat)e(di\013eren)o(t)j(from)c(the)j (usual)f(de\014nition)g(in)f(statistics.)19 b(F)m(or)12 b(example,)e(the)j(v) o(ector)113 1522 y FH(4)h(5.2)f(5.2)g(7)h(7)f(8)h FG(has)g(in)f(our)h(sense)i (the)e(ranks)g FH(1)g(2)g(2)f(3)h(3)g(4)f FG(while)h(the)g(statistics)h (de\014nition)e(of)h(ranks)g(w)o(ould)113 1572 y(giv)o(e)g FH(1)f(2.5)g(2.5)g(4.5)g(4.5)g(6)p FG(.)113 1634 y(W)m(e)h(will)f(start)i (with)f(the)h(remo)o(ving)d(of)i(duplicated)g(elemen)o(ts)h(in)e FH(x)i FG(and)f FH(y)q FG(.)19 b(Since)c(the)g(v)o(ectors)g FH(x)f FG(and)h FH(y)g FG(are)113 1683 y(already)e(sorted,)g(w)o(e)g(could)g (use)g(the)h(idiom)c FH(\(v)q(\2421\203v)q(\)\346v)i FG(if)g(they)i(are)f (not)g(all)e(equal)h(but)h(for)g(e\016ciency)g(reason)113 1733 y(w)o(e)h(prefer)h(to)f(do)g(the)g(compression)g(\\man)o(ually")c(through)k FH(\(1,\(1\010v)q(\)\242\3351\010v)q(\)\346v)q FG(.)113 1795 y(The)i(computation)d(of)h(the)i(ranks)f(is)g(a)g(simple)e(task:)20 b FH(+\350v)q(\2421\203v)c FG(will)d(do)i(the)g(job.)21 b(Therefore,)16 b(w)o(e)f(will)f(sa)o(v)o(e)113 1845 y(the)i FC(note)n(qual)g(one)g(r)n (otate)h FG(part)e(of)g(our)f FC(r)n(emove)i(duplic)n(ate)n(d)g(statement)i FG(in)d(the)g(lo)q(cal)f(v)n(ariables)g FH(neq\334x)h FG(and)113 1895 y FH(neq\334y)q FG(.)113 1956 y(W)m(e)e(sa)o(v)o(e)h(the)g(elemen)o(ts)f (of)g FH(x)g FG(and)g FH(y)h FG(in)f FH(elem\334x)f FG(and)i FH(elem\334y)q FG(,)d(the)j(ranks)g(of)f FH(x)g FG(and)g FH(y)h FG(are)g(sa)o(v)o(ed)f(in)g FH(rank\334x)113 2006 y FG(and)h FH(rank\334y)q FG(.)196 2068 y FF(h)7 b FG(Remo)o(v)o(e)13 b(duplicated)h(elemen)o(ts)f(and)h(compute)f(the)i(\\ranks")f(of)f FH(x)h FG(and)g FH(y)q FG(!)82 b(19)7 b FF(i)23 b(\021)196 2133 y FH(elem\334x\012\(neq\334x\0121,\(1\010x\)\242\3351\010x\)\346x)196 2195 y(elem\334y)q(\012\(neq\334y)q(\0121,\(1\010y)q(\)\242\3351\010y)q (\)\346y)196 2257 y(rank\334x\012+\350neq\334x)196 2318 y(rank\334y)q (\012\(+\350neq\334y)q(\)[orig\334x])15 b(\240)f(Do)g(not)g(forget)g(the)g (pairs!)196 2394 y Fx(This)e(co)q(de)e(is)i(used)e(in)i(section)d(16.)113 2499 y FI(20.)60 b FF(h)7 b FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(con)o(tab)p FG(\(14\))84 b(18)7 b FF(i)k FG(+)h FF(\021)196 2565 y FH(elem\334x,elem\334y)m(,rank\334x,rank\334y)m(,neq\334x,neq\334y)113 2670 y FI(21.)42 b FG(W)m(e)14 b(kno)o(w)f(ho)o(w)h(man)o(y)e(columns)h(and)h (ro)o(ws)h(our)f(result)h(m)o(ust)e(ha)o(v)o(e:)18 b FH (\(\006elem\334x\),\006elem\334y)q FG(.)f(W)m(e)d(build)113 2720 y(a)g(matrix)e(with)i(that)f(shap)q(e)i(and)f(\014ll)f(it)g(up)h(with)g (zeros.)196 2782 y FF(h)7 b FG(Build)14 b(a)f(protot)o(yp)q(e)i(of)e(the)i (result!)83 b(21)7 b FF(i)23 b(\021)196 2848 y FH (res\012\(\(\006elem\334x\),\006elem\334y)q(\)\0110)196 2923 y Fx(This)12 b(co)q(de)e(is)i(used)e(in)i(section)d(16.)p eop %%Page: 7 8 7 7 bop 113 183 a FD(P)o(art)14 b(2:)g(The)g FH(con)o(tab)p FD(-function)1242 b FG(7)113 366 y FI(22.)42 b FG(No)o(w)12 b(for)h(the)g(tric)o(ky)g(part.)18 b(This)13 b(is)f(the)i FC(sc)n(atter)n(e)n (d)f(assignment.)19 b FG(It)12 b(is)h(needed)h(so)f(frequen)o(tly)g(that)g (the)113 416 y(idea)h(b)q(ehind)g(it)g(is)f(w)o(orth)h FC(taking)h(a)h (closer)e(lo)n(ok.)113 478 y FG(W)m(e)i(will)f(use)h(a)g FC(de)n(c)n(o)n(de)p FG(-idea)g(to)g(transform)f(matrix)f(indices)j(in)o(to)e(a)h(v)o(ector.)25 b(Then)17 b(w)o(e)f(are)g(able)g(to)g(assign)113 527 y(v)n(alues)e(to)g(a)f (ra)o(v)o(elled)h(matrix)e(through)i FC(indexe)n(d)h(assignment)j FG(without)c(lo)q(op)f(constructions.)19 b(F)m(or)14 b(example,)113 577 y(if)g(w)o(e)g(w)o(an)o(t)g(to)g(assign)g(the)h(elemen)o(ts)f(of)g FH(5)33 b(6)h(7)14 b FG(to)g(the)h(matrix)d FH(M\0122)33 b(4\0110)14 b FG(at)g(the)h(index)f(p)q(ositions)g FH([1;1])p FG(,)113 627 y FH([1;3])p FG(,)e(and)i FH([2;2])f FG(w)o(e)h(w)o(ould)f(b)q(e)h (tempted)g(to)g(write)217 722 y FH(\(,M\)[1+2)f(4\260\3351+1)h(1)f(2,[.1]1)f (3)i(2]\0125)f(6)g(7)p FG(.)113 817 y(Unfortunately)m(,)i(this)h(giv)o(es)f (a)h FH(SYNT)m(AX)115 b(ERR)o(OR)p FG(.)16 b(Therefore,)h(w)o(e)f(m)o(ust)e (do)i(something)e(similar)f(to)113 867 y FH(Shap)q (e\012\006M\233M\012,M\233M[1+2)g(4\260\3351+1)g(1)h(2,[.1]1)e(3)h(2]\0125)g (6)h(7\233M\012Shap)q(e\006M)p FG(.)113 928 y(But)19 b(since)f(the)g(left)g (argumen)o(t)e(of)h FH(\260)h FG(is)f(the)i(shap)q(e)f(of)f FH(res)i FG(|)e(a)g(t)o(w)o(o)g(elemen)o(t)h(v)o(ector)g(|)f(w)o(e)h(can)g (do)f(the)113 978 y(\\deco)q(ding")c(whic)o(h)g(is)g(in)g(this)g(case)h(one)f (v)o(ector)h(m)o(ultiplication)c(and)j(one)g(v)o(ector)h(addition)e(more)g (e\016cien)o(tly)113 1028 y(\\b)o(y)i(hand":)113 1089 y(In)g(place)g(of)g FH(1+\(\006res\)\260\3351+rank\334x,[.1]rank\334y)i FG(w)o(e)e(shorter)h (write)f FH(rank\334y)q(+\(rank\334x\0141\)\0151\010\006res)p FG(.)113 1151 y(F)m(unn)o(y)m(,)f(\014rst)i(w)o(e)f(found)f(a)h(w)o (ounderful)f FC(de)n(c)n(o)n(de)18 b FG(tric)o(k,)13 b(then)i(w)o(e)f (refused)h(to)f(use)h FH(\260)p FG(.)113 1213 y(W)m(e)f(store)h(the)f(v)o (ector)h(of)e(index)h(p)q(ositions)g(in)f(the)h(lo)q(cal)f(v)n(ariable)g FH(idx)p FG(.)113 1274 y(W)m(e)i(notice)g(that)g FH(idx)g FG(is)g(sorted)h (in)e(ascending)i(order)f(b)q(ecause)i(w)o(e)e(used)h(the)f(shap)q(e)h(of)e FH(res)i FG(as)f(the)h(\(virtual\))113 1324 y(left)e(argumen)o(t)f(of)g(our)h (\(virtual\))f(deco)q(de)j(statemen)o(t.)113 1386 y(No)o(w)d(w)o(e)f(ha)o(v)o (e)h(to)f(coun)o(t)h(ho)o(w)f(often)g(eac)o(h)h(elemen)o(t)f(of)g FH(idx)h FG(app)q(ears)g(in)f FH(idx)p FG(.)18 b(Therefore,)13 b(w)o(e)g(\014rst)g(use)g FC(dyadic)113 1436 y(iota)18 b FG(to)d(\014nd)g FH(idx)g FG(in)g(itself.)20 b(These)c(p)q(ositions)f(are)g(stored)h(in)f FH(found)p FG(.)21 b(Then)15 b(w)o(e)h(easily)e(\014nd)h(the)g(n)o(um)o(b)q (er)g(of)113 1485 y(o)q(ccurrences)h(of)11 b(eac)o(h)i(elemen)o(t)e(in)h FH(found)g FG(b)o(y)g(subtracting)g FH(found)h FG(from)d FH (\(1\010found\),1+\006found)i FG(and)g(store)h(this)113 1535 y(result)i(in)e FH(o)q(cc\334n)o(um)p FG(.)196 1597 y FF(h)7 b FG(Coun)o(t)14 b(the)h(n)o(um)o(b)q(er)e(of)g(app)q(earances)j(of)d(eac)o (h)h FE(xy)q FG(-pair!)83 b(22)7 b FF(i)22 b(\021)196 1663 y FH(idx\012rank\334y)q(+\(rank\334x\0141\)\0151\010\006res)196 1724 y(found\012idx\004idx)196 1786 y(o)q(cc\334n)o (um\012\(\(1\010found\),1+\006found\)\014found)196 1861 y Fx(This)12 b(co)q(de)e(is)i(used)e(in)i(section)d(16.)113 1973 y FI(23.)60 b FF(h)7 b FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(con)o(tab)p FG(\(14\))84 b(18)7 b FF(i)k FG(+)h FF(\021)196 2039 y FH(idx,found,o)q (cc\334n)o(um)113 2150 y FI(24.)42 b FG(W)m(e)11 b(can)h(create)h(a)f(v)o (ector)g FH(res\334v)i FG(b)o(y)d FC(r)n(avel)r(ling)k FH(res)e FG(and)e(assign)h(the)g(n)o(um)o(b)q(er)f(of)g(o)q(ccurrences)k FH(o)q(cc\334n)o(um)113 2200 y FG(at)g(the)g(index)f(p)q(ositions)g(giv)o(en) g(b)o(y)g FH(idx)p FG(.)19 b(A)o(t)c(last)f(w)o(e)h(only)e(ha)o(v)o(e)h(to)h FC(r)n(eshap)n(e)i FH(res)p FG(,)e(divide)f(b)o(y)g(the)h(n)o(um)o(b)q(er)f (of)113 2250 y(pairs,)g(and)f FH(con)o(tab)i FG(is)f(complete.)196 2311 y FF(h)7 b FG(Do)14 b(the)g(\014nal)g(assignmen)o(t!)81 b(24)7 b FF(i)23 b(\021)196 2377 y FH(res\334v)q(\012,res)196 2439 y(res\334v)q([idx]\012o)q(cc\334n)o(um)196 2500 y (res\012\(\006res\)\006re)q(s\334v)196 2576 y Fx(This)12 b(co)q(de)e(is)i (used)e(in)i(section)d(16.)113 2687 y FI(25.)60 b FF(h)7 b FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(con)o(tab)p FG(\(14\))84 b(18)7 b FF(i)k FG(+)h FF(\021)196 2753 y FH(res\334v)113 2864 y FI(26.)42 b FG(In)13 b(some)g(applications)g(one)g(needs)i(the)f(margins)e (of)h(the)h(table.)k(If)13 b(there)i(is)f(a)f(left)g(argumen)o(t)g(w)o(e)g(w) o(an)o(t)113 2914 y(to)h(b)q(e)h(giv)o(en)e(the)i(margins.)p eop %%Page: 8 9 8 8 bop 113 183 a FD(P)o(art)14 b(2:)g(The)g FH(con)o(tab)p FD(-function)1242 b FG(8)196 366 y FF(h)7 b FG(Add)15 b(the)f(margins)e(if)h (a)h(left)g(argumen)o(t)e(is)i(giv)o(en!)82 b(26)7 b FF(i)23 b(\021)196 432 y FH(\013\(0=\222NC)14 b Fu(\336mar\336)p FH(\)\3460)196 494 y(res\012res)i(elem\334x)d(elem\334y)q(\(+\346res\)\(+\347res\)\(+)q (\346,res\))196 569 y Fx(This)f(co)q(de)e(is)i(used)e(in)i(section)d(16.)p eop %%Page: 9 10 9 9 bop 113 183 a FD(P)o(art)14 b(3:)g(F)m(rom)e(announcemen)o(ts)i(to)f(co)q (de)1078 b FG(9)113 366 y FI(27.)48 b(F)l(rom)15 b(announcemen)o(ts)e(to)i (co)q(de.)113 428 y FG(No)o(w)f(it)f(is)h(necessary)i(to)e(elab)q(orate)g (the)g(announcemen)o(ts)g(stated)h(ab)q(o)o(v)o(e.)113 539 y FI(28.)42 b FG(Construction)14 b(of)g(the)g(con)o(tingency)g(table.)113 601 y(This)k(isn't)f(an)o(y)g(problem)f(no)o(w.)28 b(The)18 b(names)e(of)h(the)h(v)n(ariables)f(are)h(c)o(hosen)g(as)f(usual.)29 b FE(n)1613 607 y FA(ij)1642 601 y FG(,)18 b FE(n)1697 607 y FA(:j)1724 601 y FG(,)g FE(n)1779 607 y FA(k)1799 601 y FG(,)g FE(T)1853 607 y FA(k)1874 601 y FG(,)113 651 y(etc.)d(are)f(translated)g(to)g (v)n(ariables)f FH(n\334ij)p FG(,)g FH(n\334\334j)p FG(,)g FH(n\334k)p FG(,)h FH(T\334k)p FG(,)f(etc.)196 712 y FF(h)7 b FG(construct)16 b(the)e(con)o(tingency)h(table)f(from)e(the)i(input)g(data) f(matrix)82 b(28)7 b FF(i)22 b(\021)196 778 y FH(\(n\334ij)14 b(mar\334left)f(mar\334top)g(n\334i\334)g(n\334\334j)h(n\)\012)p Fu(\336with)21 b(margins\336)p FH(con)o(tab)13 b(dm)196 840 y(p\334ij\012n\334ij\016n)196 915 y Fx(This)f(co)q(de)e(is)i(used)e(in)i (section)d(8.)113 1027 y FI(29.)42 b FG(Global)12 b(v)n(ariables)h(could)h (in)o(terfer)h(with)e(other)i(things)f(in)f(the)i(w)o(orkspace,)f(so)g(w)o(e) g(de\014ne)h(all)e(v)n(ariables)113 1076 y(used)i(as)f(lo)q(cal.)196 1138 y FF(h)7 b FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(dm\334random\334test) p FG(\(5\))83 b(29)7 b FF(i)22 b(\021)196 1204 y FH (n\334ij;mar\334left;mar\334top;n\334i\334)o(;n\334\334j)o(;n;p\334ij)196 1279 y Fx(See)11 b(also)g(sections)f(31,)g(33,)h(36,)g(and)g(39.)113 1391 y FI(30.)42 b FG(The)15 b(left)f(argumen)o(ts)g(are)h(split)g(to)f(mak)o (e)f(them)h(more)g(handy)m(.)19 b(Default)14 b(v)n(alues)h(for)f(the)h (optional)e(left)113 1441 y(argumen)o(t)g(are)h(de\014ned)h(as)f(describ)q (ed)i(ab)q(o)o(v)o(e.)196 1502 y FF(h)7 b FG(set)15 b(default)f(v)n(alues,)f (initialize)f FH(dm\334random\334test)83 b FG(30)7 b FF(i)22 b(\021)196 1568 y FH(\0130\015\0042\242\006\006dm)13 b(\233)h (n\012\355\006\006dm)196 1630 y(\251\(2\242\222NC)g Fu (\336nbatches\334nruns\336)p FH(\)\346)p Fu(\336n)o(batch)o(es\334nr)o (uns\012\()o(\254n\210.5)o(\),10)o(0\336)196 1691 y FH(n)o(batc)o (hes\334nruns)q(\0122\011n)o(batches)q(\334nruns)q(,100)196 1753 y(nk\012\254n\016n\334batc)o(hes\012n)o(batc)o(hes)q(\334nrun)q(s[1])196 1815 y(n\334runs\012n)o(batc)o(hes)q(\334nrun)q(s[2])196 1890 y Fx(This)e(co)q(de)e(is)i(used)e(in)i(section)d(7.)113 2001 y FI(31.)196 2063 y FF(h)e FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(dm\334random\334test)p FG(\(5\))83 b(29)7 b FF(i)k FG(+)h FF(\021)196 2129 y FH(n\334batc)o(hes;n\334runs;nk)113 2240 y FI(32.)42 b FG(Ha)o(ving)9 b(initialized)g(the)i(lo)q(op)e(o)o(v)o(er)h (the)h(batc)o(hes)h(the)f(computation)d(of)i(the)h(statistic)f FH(T\334dm)f FG(is)h(straigh)o(t-)113 2290 y(forw)o(ard.)28 b(T)m(ec)o(hnical)16 b(Remark:)23 b(T)m(erms)16 b(of)h(the)h(sum)e(with)g (denominator)g(that)h(is)g(equal)g(to)g(0)g(ha)o(v)o(e)f(to)h(b)q(e)113 2340 y(deleted)e(b)q(ecause)h(of)d FH(1=0\0160)p FG(.)j FH(p)q(os)e FG(sa)o(v)o(es)h(the)f(p)q(osition)f(of)h(the)g(elemen)o(t)f(of)h FH(dm)f FG(treated)i(at)f(last.)196 2402 y FF(h)7 b FG(compute)14 b(the)g(statistic)h FH(T)83 b FG(32)7 b FF(i)22 b(\021)196 2467 y FH(T\334dm\012p)q(os\0120)176 2529 y(lo)q(op)q(dm:)196 2591 y(\(nk\334ij)14 b(mark\334left)f(mark\334top)g(nk\334i\334)h (nk\334\334j)f(nk\)\012)p Fu(\336with)22 b(margin\336)p FH(con)o(tab)13 b(dm[p)q(os+\004nk;])196 2652 y(exp)q(ected\012nk)q (\015p\334ij[mar\334left\004mark\334left;mar\334top\004mark\334top])196 2714 y(Tk\012+\346\(0\242,exp)q(ected\)\346Tk\012,\(Tk\015Tk\012n)q (k\334ij\014exp)q(e)q(cte)q(d\)\016exp)q(e)q(cte)q(d)196 2775 y(T\334dm\012T\334dm+Tk)196 2837 y(\013lo)q(op)q(dm\015\004n\246nk+p)q (os\012p)q(os+nk)196 2913 y Fx(This)f(co)q(de)e(is)i(used)e(in)i(section)d (8.)p eop %%Page: 10 11 10 10 bop 113 183 a FD(P)o(art)14 b(3:)g(F)m(rom)e(announcemen)o(ts)i(to)f (co)q(de)1058 b FG(10)113 366 y FI(33.)196 428 y FF(h)7 b FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(dm\334random\334test)p FG(\(5\))83 b(29)7 b FF(i)k FG(+)h FF(\021)196 494 y FH(p)q (os;T\334dm;nk\334ij;mark\334left;m)o(ark\334top;nk\334i\334)o(;nk\334\334j;) o(nk;exp)q(ected;Tk)113 605 y FI(34.)42 b FG(The)12 b(sim)o(ulation)d(runs)k (iterativ)o(ely)m(.)k(This)11 b(is)h(p)q(erformed)g(b)o(y)g(a)f(simple)g(lo)q (op)g(construction.)18 b(Within)11 b(the)113 655 y(lo)q(op)j(a)f(new)i(p)q (erm)o(utation)d(of)i(the)g(data)g(matrix)e(is)i(found)f(for)h(whic)o(h)f (the)i(statistic)f FH(T\334run)h FG(is)e(computed)h(as)113 705 y(sho)o(wn)f(ab)q(o)o(v)o(e.)18 b(It)13 b(is)g(p)q(ossible)g(to)f(sa)o(v) o(e)h(some)f(lines)h(of)g(co)q(de)g(but)g(for)g(clarities)g(sak)o(e)g(w)o(e)g (sp)q(end)h(an)f(additional)113 754 y(section)i(for)f(the)g(computation)e(of) h FH(T\334run)p FG(.)196 816 y FF(h)7 b FG(\014nd)14 b(an)g(appro)o(ximate)e (distribution)h(of)h FH(T)83 b FG(34)7 b FF(i)22 b(\021)196 882 y(h)7 b FG(initialize)13 b(lo)q(op)g(o)o(v)o(er)h(sim)o(ulation)d(runs)84 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FH(T;run\334coun)o(t)113 1930 y FI(37.)42 b FG(No)14 b(commen)o(t.)196 1992 y FF(h)7 b FG(\014nd)14 b(a)g(new)g(p)q (erm)o(utation)f(of)g FH(dm)82 b FG(37)7 b FF(i)23 b(\021)196 2058 y FH(dm\012dm[n?n;])196 2133 y Fx(This)12 b(co)q(de)e(is)i(used)e(in)i (section)d(34.)113 2244 y FI(38.)42 b FG(This)18 b(co)q(de)h(is)f(almost)e(a) i(cop)o(y)g(of)g(the)h(one)f(describ)q(ed)i(in)e(the)g(section)h(ab)q(out)f (the)h(computation)e(of)113 2294 y FH(T\334dm)p FG(.)196 2356 y FF(h)7 b FG(calculate,)14 b(sa)o(v)o(e)g(the)g FH(T)p FG(-statistic)h FH(T\334run)f FG(of)f(the)i(sim)o(ulation)c(run)83 b(38)7 b FF(i)23 b(\021)196 2422 y FH(T\334run\012p)q(os\0120)176 2483 y(lo)q(opinner:)196 2545 y(\(nk\334ij)14 b(mark\334left)f(mark\334top)g (nk\334i\334)h(nk\334\334j)f(nk\)\012)p Fu(\336with)22 b(margin\336)p FH(con)o(tab)13 b(dm[p)q(os+\004nk;])196 2607 y(exp)q(ected\012nk)q (\015p\334ij[mar\334left\004mark\334left;mar\334top\004mark\334top])196 2668 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y(e\013ect)h(of)e(di\013eren)o(t)h(prop)q(ortions)f(of)g (non-randomness)f(is)h(our)g(main)f(in)o(terest)i(the)g(prop)q(ortions)f (will)f(b)q(e)h(the)113 1001 y(righ)o(t)f(argumen)o(t)f(of)g(the)h(function.) k(F)m(or)c(eac)o(h)g(prop)q(ortion)g(a)f(plot)h(will)e(b)q(e)i(constructed.) 113 1117 y FI(44.)p 216 1076 692 2 v 216 1137 2 62 v 56 w FG(Syn)o(tax)g(of)f FH(dm\334random\334test\334DEMO)p 906 1137 V 216 1139 692 2 v 196 1243 a(\214)i(dm\334random\334test\334DEMO)e(prop\334of\334random)40 b FG(44)196 1380 y Fx(See)11 b(also)g(section)f(46.)196 1443 y Fw(dm\334random)o(\334te)o(st\334D)o(EMO)f Fx(app)q(ears)h(in)h(sections)f (2,)h(42,)g(46,)g(and)f(56.)113 1554 y FI(45.)p 216 1513 562 2 v 216 1575 2 62 v 56 w FG(Data)j(structures)k(of)c(argumen)o(ts)p 776 1575 V 216 1577 562 2 v 113 1680 a FH(prop\334of\334random)30 b FG(is)g(the)g(v)o(ector)h(of)f(prop)q(ortions)g(of)g(randomness)f(of)h(the) h(input)f(data)f(used)i(in)113 1730 y FH(dm\334random\334test)14 b FG(calls.)113 1792 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FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(dm\334random\334test\334DEMO)p FG(\(44\))83 b(48)7 b FF(i)22 b(\021)196 494 y FH(prop\334of\334random;n)o(um)o(b)q (er\334of\334en)o(tries;n)o(um)o(b)q(er\334of\334margin\334cells;dmrd;p)q (erm)196 569 y Fx(See)11 b(also)g(sections)f(52)h(and)f(54.)113 681 y FI(49.)42 b FG(Using)9 b(a)g(lo)q(op)g(w)o(e)h(will)e(construct)j(a)e (picture)h(consisting)g(of)e(sev)o(eral)i(plots)g(dra)o(wn)f(b)o(y)g FH(dm\334random\334test)p FG(.)113 730 y(Some)14 b(functions)h(of)g(the)h (graphics)f(group)g(will)f(b)q(e)h(needed.)23 b FH(coun)o(ter)17 b FG(is)e(the)h(lo)q(op)e(v)n(ariable)g(coun)o(ting)h(these)113 780 y(plots.)j FH(dm)13 b FG(is)h(a)g(lo)q(cal)f(data)g(matrix.)196 842 y FF(h)7 b FG(p)q(erform)14 b(the)g(exp)q(erimen)o(t)g(and)f(sho)o(w)h (the)h(result)84 b(49)7 b FF(i)22 b(\021)196 908 y(h)7 b FG(initialize)13 b(graphics)h(device)h(and)e FH(coun)o(ter)85 b FG(51)7 b FF(i)176 969 y FH(lo)q(op:)196 1031 y FF(h)g FG(construct)16 b(data)e(matrix)e 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FF(h)7 b FG(initialize)13 b(graphics)h(device)h(and)e FH(coun)o(ter)85 b FG(51)7 b FF(i)22 b(\021)196 1882 y FH(n\334viewp)q (ort\012\255\(\006prop\334of\334random\)\210.5)196 1944 y(n\334viewp)q (ort\012n\334viewp)q(ort,\254\(\006prop\334of\334random\)\016n\334viewp)q (ort)196 2006 y(coun)o(ter\0121)196 2067 y(G\334b)q(egin)196 2143 y Fx(This)12 b(co)q(de)e(is)i(used)e(in)i(section)d(49.)113 2254 y FI(52.)196 2316 y FF(h)e FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(dm\334random\334test\334DEMO)p FG(\(44\))83 b(48)7 b FF(i)k FG(+)g FF(\021)196 2382 y FH(n\334viewp)q(ort;coun)o(ter)113 2493 y FI(53.)42 b FG(Steps)19 b(to)f(realize)g(non-randomness:)25 b(1.)30 b(Select)19 b(ro)o(ws)f(of)f FH(dmrd)h FG(de\014ned)h(b)o(y)f(the)g (\014rst)h(elemen)o(ts)f(of)113 2543 y FH(p)q(erm)p FG(.)g(\(The)13 b(selected)i(ro)o(ws)e(are)h(k)o(ept)f(b)o(y)f FH(ro)o(w\334marks)p FG(.\))18 b(2.)f(Sort)c(these)i(ro)o(ws)e(according)g(to)f(their)i(columns.) 196 2604 y FF(h)7 b FG(construct)16 b(data)e(matrix)e 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FH(n\334batc)o(hes)j FG(30{31)1099 908 y FH(n\334ij)e FG(28{29)1099 972 y FH(n\334i\334)g FG(28{29)1099 1036 y FH(n\334k)g FG(28)1099 1101 y FH(n\334runs)i FG(30{31,)12 b(40{41)1099 1165 y FH(n\334viewp)q(ort)42 b FG(51{53)1099 1229 y FH(n\334\334j)f FG(28{29)1099 1294 y FH(o)g FG(10)1099 1358 y FH(o)q(cc\334n)o(um)g FG(22{24)1099 1422 y FH(OO)h FG(10)1099 1487 y FH(Oo)f FG(10)1099 1551 y FH(oO)g FG(10)1099 1615 y FH(o)q(o)g FG(10)1099 1680 y FH(Oo\334o)g FG(10)1099 1744 y FH(orig\334x)g FG(17{19)1099 1808 y FH(orig\334y)g FG(17{18)1099 1873 y FH(Ox)h FG(10)1099 1937 y FH(o)o(x)f FG(10)1099 2001 y FH(Oy)h FG(10)1099 2066 y FH(o)o(y)f FG(10)1099 2130 y FH(O0x)h FG(10)1099 2194 y FH(o0x)f FG(10)1099 2259 y FH(O0y)h FG(10)1099 2323 y FH(o0y)f FG(10)1099 2387 y FH(p)q(erm)g FG(47{48,)12 b(53)1099 2452 y FH(p)q(os)42 b FG(32{33,)12 b(38)1099 2516 y FH(prop\334of\334random)40 b FG(44{45,)13 b(48,)f(51,)h(53,)g(55)1099 2580 y FH(p\334ij)41 b FG(28{29,)12 b(32,)h(38)1099 2644 y FH(rank\334x)42 b FG(19{20,)12 b(22)1099 2709 y FH(rank\334y)42 b FG(19{20,)12 b(22)1099 2773 y FH(res)42 b FG(13{14,)13 b(21{22,)f(24,)h(26) 1099 2837 y FH(result)43 b FG(5{6,)12 b(41)1099 2902 y FH(res\334v)42 b FG(24{25)p eop %%Page: 20 21 20 20 bop 113 183 a FD(P)o(art)14 b(6:)g(Index)1489 b FG(20)113 366 y FH(ro)o(w\334marks)42 b FG(53{54)113 431 y FH(run\334coun)o(t)h FG(35{36,)12 b(40)113 495 y FH(Shap)q(e)43 b FG(22)113 559 y FH(SYNT)m(AX)d FG(22)113 623 y FH(T)i FG(4,)13 b(6,)g(35{36,)f(40{41)113 688 y FH(Tk)42 b FG(32{33,)12 b(38{39)113 752 y FH(T\334dm)41 b FG(32{33,)12 b(38,)h(41)113 816 y FH(T\334k)42 b FG(28)1099 366 y FH(T\334run)g FG(34,)13 b(38{40)1099 431 y FH(v)41 b FG(19)1099 495 y FH(x)g FG(10,)13 b(17{19)1099 559 y FH(y)41 b FG(10,)13 b(17{19)1099 623 y FH(\222NC)41 b FG(10,)13 b(26,)g(30,)g(41)1099 688 y FH(\222RL)42 b FG(56)196 978 y FF(h)7 b FG(Add)15 b(the)f(margins)e(if) h(a)h(left)g(argumen)o(t)e(is)i(giv)o(en!)41 b Fx(26)6 b FF(i)41 b Fx(Used)12 b(in)f(section)f(16.)196 1042 y FF(h)d FG(Build)14 b(a)f(protot)o(yp)q(e)i(of)e(the)i(result!)41 b Fx(21)7 b FF(i)41 b Fx(Used)12 b(in)f(section)f(16.)196 1106 y FF(h)d FG(Coun)o(t)14 b(the)h(n)o(um)o(b)q(er)e(of)g(app)q(earances)j(of)d(eac)o(h)h FE(xy)q FG(-pair!)41 b Fx(22)6 b FF(i)42 b Fx(Used)11 b(in)h(section)d(16.) 196 1171 y FF(h)e FG(Do)14 b(the)g(\014nal)g(assignmen)o(t!)39 b Fx(24)7 b FF(i)41 b Fx(Used)12 b(in)f(section)f(16.)196 1235 y FF(h)d FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(con)o(tab)43 b Fx(18,)11 b(20,)g(23,)g(25)6 b FF(i)41 b Fx(Used)12 b(in)f(section)f(14.) 196 1299 y FF(h)d FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH (dm\334random\334test)41 b Fx(29,)11 b(31,)g(33,)g(36,)g(39)6 b FF(i)41 b Fx(Used)12 b(in)f(section)f(5.)196 1364 y FF(h)d FG(Lo)q(cal)14 b(V)m(ariables)f(of)g FH(dm\334random\334test\334DEMO)41 b Fx(48,)11 b(52,)g(54)6 b FF(i)42 b Fx(Used)11 b(in)g(section)f(44.)196 1428 y FF(h)d FG(Remo)o(v)o(e)13 b(duplicated)h(elemen)o(ts)f(and)h(compute)f (the)i(\\ranks")f(of)f FH(x)h FG(and)g FH(y)q FG(!)40 b Fx(19)7 b FF(i)41 b Fx(Used)12 b(in)f(section)f(16.)196 1492 y FF(h)d FG(Sort)15 b FH(m)d FG(in)i(ascending)g(order!)42 b Fx(17)6 b FF(i)42 b Fx(Used)11 b(in)g(section)f(16.)196 1557 y FF(h)d FG(calculate,)14 b(sa)o(v)o(e)g(the)g FH(T)p FG(-statistic)h FH(T\334run)f FG(of)f(the)i(sim)o(ulation)c(run)42 b Fx(38)6 b FF(i)41 b Fx(Used)12 b(in)f(section)f(34.)196 1621 y FF(h)d FG(close)15 b(graphics)f(device)42 b Fx(50)7 b FF(i)41 b Fx(Used)12 b(in)f(section)f(49.)196 1685 y FF(h)d FG(compute)14 b(the)g(statistic)h FH(T)41 b Fx(32)6 b FF(i)42 b Fx(Used)11 b(in)h(section)d(8.)196 1750 y FF(h)e FG(construct)16 b(data)e(matrix)e FH(dm)h FG(for)g FH(dm\334random\334test)g FG(call)41 b Fx(53)6 b FF(i)42 b Fx(Used)11 b(in)g(section)f(49.)196 1814 y FF(h)d FG(construct)16 b(the)e(con)o(tingency)h(table)f(from)e(the)i(input)g(data)f(matrix)40 b Fx(28)6 b FF(i)42 b Fx(Used)11 b(in)h(section)d(8.)196 1878 y FF(h)e FG(\014nd)14 b(a)g(new)g(p)q(erm)o(utation)f(of)g FH(dm)41 b Fx(37)6 b FF(i)42 b Fx(Used)11 b(in)g(section)f(34.)196 1943 y FF(h)d FG(\014nd)14 b(an)g(appro)o(ximate)e(distribution)h(of)h FH(T)41 b Fx(34)6 b FF(i)42 b Fx(Used)11 b(in)h(section)d(8.)196 2007 y FF(h)e FG(goto)14 b FH(lo)q(op)f FG(if)g(another)i(plot)e(is)h(to)f(b) q(e)i(made)40 b Fx(55)7 b FF(i)41 b Fx(Used)12 b(in)f(section)f(49.)196 2071 y FF(h)d FG(initialize)13 b FH(dm\334random\334test\334DEMO)41 b Fx(47)6 b FF(i)42 b Fx(Used)11 b(in)g(section)f(46.)196 2135 y FF(h)d FG(initialize)13 b(graphics)h(device)h(and)e FH(coun)o(ter)43 b Fx(51)7 b FF(i)41 b Fx(Used)12 b(in)f(section)f(49.)196 2200 y FF(h)d FG(initialize)13 b(lo)q(op)g(o)o(v)o(er)h(sim)o(ulation)d(runs)42 b Fx(35)6 b FF(i)42 b Fx(Used)11 b(in)h(section)d(34.)196 2264 y FF(h)e FG(p)q(erform)14 b(the)g(exp)q(erimen)o(t)g(and)f(sho)o(w)h(the)h (result)42 b Fx(49)6 b FF(i)42 b Fx(Used)11 b(in)h(section)d(46.)196 2328 y FF(h)e FG(sa)o(v)o(e)14 b(result,)h(incremen)o(t)e(the)i FH(run\334coun)o(t)g FG(and)f(jump)e(bac)o(k)i(to)g FH(lo)q(opsim)40 b Fx(40)6 b FF(i)42 b Fx(Used)11 b(in)g(section)f(34.)196 2393 y FF(h)d FG(set)15 b(default)f(v)n(alues,)f(initialize)f FH (dm\334random\334test)41 b Fx(30)6 b FF(i)42 b Fx(Used)11 b(in)h(section)d (7.)196 2457 y FF(h)e FG(sho)o(w)14 b(the)h(result)42 b Fx(41)6 b FF(i)42 b Fx(Used)11 b(in)h(section)d(8.)196 2521 y FF(h)e FG(test)15 b(non-randomness)f(of)f(a)h(data)f(matrix)f(for)i(a)f(con)o (tingency)i(table)41 b Fx(8)7 b FF(i)41 b Fx(Used)12 b(in)f(section)f(7.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF