SI

US

卡方检验在线计算

卡方检验： 所需要的研究人员共同分析是两组数据的比较，结果可以分为只有几种类型的结果

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总计

数据1:

数据2:

数据3:

数据4:

数据5:

数据6:

数据7:

数据8:

数据9:

数据10:

总计:

自由度 (df)

=

卡方检验 (χ ²)

=

P 值

=

卡方检验 P 值计算器

卡方检验： 所需要的研究人员共同分析是两组数据的比较，结果可以分为只有几种类型的结果

function normsinv(pp){

var x,y;

var q = 1 - pp;

bb = [1.570796288,0.03706987906,-0.0008364353589,-0.0002250947176,

0.000006841218299,0.000005824238515,-0.00000104527497,8.360937017e-8,-3.231081277e-09,

3.657763036e-11,6.936233982e-13];

if (q == 0.5) return 0;

var p;

if (q > 0.5) p = 1 - q;

else p = q;

var b;

y =-Math.log(4 * p * (1 - p));

b = y * bb[10];

var i;

for (i = 9; i >= 0; i--)

{

b = y * (bb[i] + b);

}

x = Math.sqrt(b);

if (q > 0.5) x = -x;

return x;

}

function dtos(d){

var s,i,j;

s=d.toPrecision(6);

j=s.indexOf(".");

if(j<0) return s;

if(j==s.length-1)return s.substr(0,j); // 如果小数点后面什么也没有，就不要小数点

for(i=s.length-1;i>j;i--){ // 删去末尾的字符0

if(s.substr(i,1)!="0"){

return s.substr(0,i+1);

}

}

return s.substr(0,j);

}

function geta(){

if(Radio1.checked){

return parseFloat(Radio1.value);

}

else if(Radio2.checked){

return parseFloat(Radio2.value);

}

else if(Radio3.checked){

return parseFloat(Radio3.value);

}

else if(Radio4.checked){

return parseFloat(Radio4.value);

}

return 0.05;

}

function doest(n,m)

{

var alpha, p, z, f;

f = (1.0 * m) / n;

alpha = geta();

p = 1 - alpha;

z = normsinv(1 - alpha / 2);

z *= z;

var a, b, c;

a = n + z;

b = -(2 * n * f + z);

c = n * f * f;

var p12;

p12=new Array();

p12[0] = (-b - Math.sqrt(b * b - 4 * a * c)) / (2 * a);

p12[1] = (-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a);

return p12;

}

function Button1_onclick() {

var n,m,p12;

if(Text1.value=="" || Text1.value==null) return;

if(Text2.value=="" || Text2.value==null) return;

n=parseInt(Text1.value);

m=parseInt(Text2.value);

if(n>0 && m>=0 && m<=n){

spanwarn.innerHTML="";

divresult.style.display="block";

p12=doest(n,m);

span1.innerHTML=dtos(1-geta());

span2.innerHTML=p12[0].toFixed(6);

span3.innerHTML=p12[1].toFixed(6);

}

else{

spanwarn.innerHTML="输入数据不合要求！";

divresult.style.display="none";

}

}

function Radio1_onclick() {

Button1_onclick();

}

// JavaScript Document

function calculate() {

var x = document.getElementById("inputs").value;

x = x.replace(' ', '');

var arr = x.split(',');

var lcm = 0;

var flag = false;

var total = 0;

for (var j = 0; j < arr.length; j++) {

arr[j] = parseFloat(arr[j]);

total += arr[j];

}

var mean = total / arr.length;

mean = Math.round(mean * 10000) / 10000;

var xm2 = 0;

for (var j = 0; j < arr.length; j++) {

xm2 += Math.pow((arr[j] - mean), 2);

}

var sd = xm2 / (arr.length - 1);

sd = Math.sqrt(sd);

var cv = sd / mean;

sd = Math.round(sd * 10000) / 10000;

document.getElementById("res_area").style.visibility = "visible";

document.getElementById("result1").value = arr.length;

document.getElementById("result2").value = mean;

document.getElementById("result3").value = sd;

document.getElementById("result4").value = cv;

}

function normsinv(pp){

var x,y;

var q = 1 - pp;

bb = [1.570796288,0.03706987906,-0.0008364353589,-0.0002250947176,

0.000006841218299,0.000005824238515,-0.00000104527497,8.360937017e-8,-3.231081277e-09,

3.657763036e-11,6.936233982e-13];

if (q == 0.5) return 0;

var p;

if (q > 0.5) p = 1 - q;

else p = q;

var b;

y =-Math.log(4 * p * (1 - p));

b = y * bb[10];

var i;

for (i = 9; i >= 0; i--)

{

b = y * (bb[i] + b);

}

x = Math.sqrt(b);

if (q > 0.5) x = -x;

return x;

}

function gamma( x)

{

var i;

var y, t, s, u;

var a = [ 0.0000677106,-0.0003442342,

0.0015397681,-0.0024467480,0.0109736958,

-0.0002109075,0.0742379071,0.0815782188,

0.4118402518,0.4227843370,1.0];

if (x <= 0.0)

throw "x不能小于0";

y = x;

if (y <= 1.0)

{ t = 1.0 / (y * (y + 1.0)); y += 2.0; }

else if (y <= 2.0)

{ t = 1.0 / y; y += 1.0; }

else if (y <= 3.0) t = 1.0;

else

{

t = 1.0;

while (y > 3.0)

{ y -= 1.0; t = t * y; }

}

s = a[0]; u = y - 2.0;

for (i = 1; i <= 10; i++)

s = s * u + a[i];

s *= t;

return s;

}

function betacf(a, b, x)

{

var MAXIT = 1000;

var EPS = 1e-10;

var FPMIN = 1e-8;

var m, m2;

var aa, c, d, del, h, qab, qam, qap;

qab = a + b;

qap = a + 1;

qam = a - 1;

c = 1;

d = 1 - qab * x / qap;

if (Math.abs(d) < FPMIN) d = FPMIN;

d = 1 / d;

h = d;

for (m = 1; m <= MAXIT; m++)

{

m2 = 2 * m;

aa = m * (b - m) * x / ((qam + m2) * (a + m2));

d = 1 + aa * d;

if (Math.abs(d) < FPMIN) d = FPMIN;

c = 1 + aa / c;

if (Math.abs(c) < FPMIN) c = FPMIN;

d = 1 / d;

h *= d * c;

aa = -(a + m) * (qab + m) * x / ((a + m2) * (qap + m2));

d = 1 + aa * d;

if (Math.abs(d) < FPMIN) d = FPMIN;

c = 1 + aa / c;

if (Math.abs(c) < FPMIN) c = FPMIN;

d = 1 / d;

del = d * c;

h *= del;

if (Math.abs(del - 1) <= EPS) break;

}

if (m > MAXIT) throw "a or b too big, or MAXIT too small in betacf";

return h;

}

function gammln(xx)

{

var j;

var x, y, tmp, ser;

var cof = [76.18009172947146,-86.50532032941677,24.01409824083091,-1.231739572450155,

0.1208650973866179e-2,-0.5395239384953e-5];

y = x = xx;

tmp = x + 5.5;

tmp -= (x + 0.5) * Math.log(tmp);

ser = 1.000000000190015;

for (j = 0; j < 6; j++) ser += cof[j] / ++y;

return -tmp + Math.log(2.5066282746310005 * ser / x);

}

function betai(a, b, x)

{

var bt;

if (x < 0 || x > 1) throw "Bad x in routine batai";

if (x == 0 || x == 1) bt = 0;

else

bt = Math.exp(gammln(a + b) - gammln(a) - gammln(b) + a * Math.log(x) + b * Math.log(1 - x));

if (x < (a + 1) / (a + b + 2))

return bt * betacf(a, b, x) / a;

else

return 1 - bt * betacf(b, a, 1 - x) / b;

}

function tdist2(t, free)

{

if (free < 1) throw "free must biger than 0";

var f;

f = free;

var p;

p = 1 - betai(f / 2.0, 0.5, f / (f + t * t));

return p;

}

function tdist(t, free)

{

if (t == 0)

{

return 0.5;

}

if (t > 0)

{

return 0.5 + tdist2(t, free) / 2;

}

return (1 - tdist2(-t, free)) / 2;

}

var outpp;

function t_dist(n, t)

{

var sign, ibi, n2, i;

var tt, x, p, u, ga1, ga2,dd;

if (t == 0)

{

ga1 = gamma(n / 2.0);

ga2 = gamma(0.5 + n / 2.0);

outpp = 0.5;

return ga2 / (Math.sqrt(n * Math.PI) * ga1);

}

if (t < 0)

{

sign = -1;

}

else sign = 1;

tt = t * t;

x = tt / (n + tt);

if (n % 2 == 0)

{

p = Math.sqrt(x);

u = p * (1 - x) / 2.0;

ibi = 2;

}

else

{

u = Math.sqrt(x * (1 - x)) / Math.PI;

p = 1 - 2 * Math.atan(Math.sqrt((1 - x) / x)) / Math.PI;

ibi = 1;

}

if (ibi == n)

{

dd = u / Math.abs(t);

outpp = 0.5 + sign * p / 2.0;

return dd;

}

else

{

n2 = n - 2;

}

for (i = ibi; i <= n2; i += 2)

{

p += 2.0 * u / i;

u = u * (1 + i) / i * (1 - x);

}

dd = u / Math.abs(t);

outpp = 0.5 + sign * p / 2.0;

return dd;

}

function tdistinv(pvar, n)

{

var q;

q = 1 - pvar;

var t=0.0;

var pis, dfr2, c, q2, p, yq, e, ga1, ga2, ga3, t0, pp, d;

var k;

pis = Math.sqrt(Math.PI);

dfr2 = n / 2.0;

if (n == 1) return Math.tan(Math.PI * (0.5 - q));

if (n == 2)

{

if (q > 0.5) c = -1;

else c = 1;

q2 = (1 - 2 * q);

q2 *= q2;

return Math.sqrt(2.0 * q2 / (1.0 - q2)) * c;

}

p = 1 - q;

yq = normsinv(p);

e = 1.0 - 1.0 / (4.0 * n);

e = e * e - yq * yq / (2.0 * n);

if (e > 0.5) t0 = yq / Math.sqrt(e);

else

{

ga1 = gammln(dfr2);

ga2 = gammln(dfr2 + 0.5);

ga3 = Math.exp((ga1 - ga2) / n);

t0 = Math.pow(Math.sqrt(n) / (pis * q * n), (1.0 / n) / ga3);

}

for (k = 1; k <= 30; k++)

{

d = t_dist(n, t0);

pp=outpp;

if (d == 0) return t0;

t = t0 - (pp - p) / d;

if (Math.abs(t0 - t) < 0.000001 * Math.abs(t))

{

return t;

}

else t0 = t;

}

return t;

}

function tdist2inv(p, free)

{

var x2;

x2 = 300;

if (p > 1 - 1e-8) return x2;

if (p == 0) return 0;

var x1 = 0;

var xacc = 1e-12;

var JMAX = 400;

var j;

var dx, f, fmid, xmid, rtb;

f = tdist2(x1, free) - p;

fmid = tdist2(x2, free) - p;

if (f * fmid >= 0) throw "faild in tdist2inv";

if (f < 0)

{

dx = x2 - x1;

rtb = x1;

}

else

{

dx = x1 - x2;

rtb = x2;

}

for (j = 0; j < JMAX; j++)

{

dx *= 0.5;

xmid = rtb + dx;

fmid = tdist2(xmid, free) - p;

if (fmid <= 0) rtb = xmid;

if (Math.abs(dx) < xacc || fmid == 0) return rtb;

}

return 0;

}

var outgamser, outgln;

function gser(a, x)

{

var gamser,gln;

var ITMAX = 10000;

var EPS = 1e-10;

var n;

var sum, del, ap;

gamser = 0;

gln = gammln(a);

outgln=gln;

if (x <= 0)

{

if (x < 0) throw "x less than 0";

outgamser = 0;

return;

}

else

{

ap = a;

del = sum = 1.0 / a;

for (n = 0; n < ITMAX; n++)

{

ap++;

del *= x / ap;

sum += del;

if (Math.abs(del) < Math.abs(sum) * EPS)

{

outgamser = sum * Math.exp(-x + a * Math.log(x) - gln);

return;

}

}

}

}

var outgammcf;

function gcf(a, x)

{

var gammcf, gln;

var ITMAX = 10000;

var EPS = 1e-10;

var FPMIN = 1e-10;

var i;

var an, b, c, d, del, h;

gln = gammln(a);

outgln=gln;

gammcf = 0;

outgammcf=gammcf;

b = x + 1 - a;

c = 1 / FPMIN;

d = 1 / b;

h = d;

for (i = 1; i <= ITMAX; i++)

{

an = -i * (i - a);

b += 2;

d = an * d + b;

if (Math.abs(d) < FPMIN) d = FPMIN;

c = b + an / c;

if (Math.abs(c) < FPMIN) c = FPMIN;

d = 1 / d;

del = d * c;

h *= del;

if (Math.abs(del - 1) <= EPS) break;

}

if (i > ITMAX) throw "a too large, ITMAX too small in gcf";

outgammcf = Math.exp(-x + a * Math.log(x) - gln) * h;

}

function gammp(a, x)

{

var gamser, gammcf, gln;

if (x < 0 || a <= 0) throw "invalid arguments in gammp";

if (x < a + 1)

{

gser(a, x);

return outgamser;

}

else

{

gcf(a, x);

return 1.0 - outgammcf;

}

}

function chidist(x2, free)

{

var f;

f = free;

if (free < 1)

{

throw "自由度必须大于0";

}

if (x2 <= 0) return 0;

return gammp(f / 2, x2 / 2);

}

function erf(x){

var t,z,ans;

z=Math.abs(x);

t=1.0/(1.0+0.5*z);

ans = t*Math.exp(-z * z - 1.26551223 + t * (1.00002368 + t * (0.37409196 + t * (0.09678418 +

t * (-0.18628806 + t * (0.27886807 + t * (-1.13520398 + t * (1.48851587 +

t * (-0.82215223 + t * 0.17087277)))))))));

return (x >= 0.0 ? ans : 2.0 - ans);

}

function normsdist(x){

return 0.5 + (1 - erf(x /Math.sqrt(2))) / 2;

}

var outf;

function cx2(n, x2)

{

var f;

var i, n2, iai;

var pis, x, chs, u, pp;

outf = f = 0;

if (x2 == 0) return 0;

pis = Math.sqrt(Math.PI);

x = x2 / 2;

chs = Math.sqrt(x2);

if (n % 2 == 0)

{

u = x * Math.exp(-x);

outf = f = 1 - Math.exp(-x);

iai = 2;

}

else

{

u = Math.sqrt(x) * Math.exp(-x) / pis;

pp = normsdist(chs);

outf=f = 2 * (pp - 0.5);

iai = 1;

}

if (iai == n) return u / x2;

n2 = n - 2;

for (i = iai; i <= n2; i += 2)

{

f = f - 2 * u / i;

u = x2 * u / i;

}

outf=f;

return u / x2;

}

function chiinv(varp, n)

{

var q;

q = 1 - varp;

var i;

var xx;

var x, p, w, x0, pp, d;

if (n == 1)

{

x = normsinv(1 - q / 2);

return x * x;

}

if (n == 2)

{

return -2.0 * Math.log(q);

}

p = 1 - q;

x = normsinv(p);

w = 2.0 / (9.0 * n);

x0 = n * Math.pow(1 - w + x * Math.sqrt(w), 3);

xx = x0;

for (i = 1; i <= 30; i++)

{

d = cx2(n, x0);

pp=outf;

if (d == 0) return x0;

xx = x0 - (pp - p) / d;

if (Math.abs(xx - x0) < 1e-6 * Math.abs(xx)) return xx;

x0 = xx;

}

return xx;

}

function fdist(x, free1, free2)

{

var m, n;

if (x <= 0) return 0;

if (free1 <= 0 || free2 <= 0) throw "freedegree must >0";

m = free1;

n = free2;

var p;

p = 1 - betai(n / 2, m / 2, n / (n + m * x));

return p;

}

function fdistinv(p, free1, free2)

{

if (free1 < 1 || free2 < 1) throw "free must >0 in fdistinv!";

if (p < 0 || p > 1) throw "p must be probability in fdistinv!";

if (p == 0) return 0;

var xup;

var n1, n2;

n1 = free1;

n2 = free2;

var e, dev;

if (n2 <= 4)

{

xup = 500000;

}

else

{

e = n2 / (n2 - 2);

dev = 2 * n2 * n2 * (n1 + n2 - 2) / (n1 * (n2 - 2) * (n2 - 2) * (n2 - 4));

dev = Math.sqrt(dev);

xup = e + 20 * dev;

}

var x2;

x2 = xup;

if (p > 1 - 1e-8) return x2;

var x1 = 0;

var xacc = 1e-12;

var JMAX = 400;

var j;

var dx, f, fmid, xmid, rtb;

f = fdist(x1, free1, free2) - p;

fmid = fdist(x2, free1, free2) - p;

if (f * fmid >= 0) throw "faild in fdist2inv";

if (f < 0)

{

dx = x2 - x1;

rtb = x1;

}

else

{

dx = x1 - x2;

rtb = x2;

}

for (j = 0; j < JMAX; j++)

{

dx *= 0.5;

xmid = rtb + dx;

fmid = fdist(xmid, free1, free2) - p;

if (fmid <= 0) rtb = xmid;

if (Math.abs(dx) < xacc || fmid == 0) return rtb;

}

return 0;

}

function tobias(s)

{

if(s.substr(0,1)=="q")

{

s1=s.substring(1);

b=parseFloat(s1);

if(b<=0){

alert("输入数据无效！");

return -1;

}

else

return Math.sqrt(b);

}

else

{

b=parseFloat(s);

if (b<=0)

{

alert("输入格式不对！");

return -1;

}

return b;

}

}

function dtos(d){

var s,i,j;

s=d.toPrecision(6);

j=s.indexOf(".");

if(j<0) return s;

if(j==s.length-1)return s.substr(0,j); // 如果小数点后面什么也没有，就不要小数点

for(i=s.length-1;i>j;i--){ // 删去末尾的字符0

if(s.substr(i,1)!="0"){

return s.substr(0,i+1);

}

}

return s.substr(0,j);

}

function intervalt1(alpha,n,mean,ovar)

{

if (ovar <= 0) throw "var must larger than 0 in intervalt1";

var minc;

minc = tdist2inv(1 - alpha, n - 1) * Math.sqrt(ovar / n);

var x12=new Array();

x12[0] = mean - minc;

x12[1] = mean + minc;

return x12;

}

function intervalt1low(alpha,n,mean,ovar)

{

if (alpha <= 0 || alpha >= 1) "alpha must be probability in intervalt1low";

if (ovar <= 0) throw "var must larger than 0 in intervalt1low";

var minc;

minc = tdistinv(1 - alpha, n - 1) * Math.sqrt(ovar / n);

var x1;

x1 = mean - minc;

return x1;

}

function intervalt1high(alpha,n,mean,ovar)

{

if (alpha <= 0 || alpha >= 1) throw "alpha must be probability in intervalt1high";

if (ovar <= 0) throw "var must larger than 0 in intervalt1high";

var minc;

minc = tdistinv(1 - alpha, n - 1) * Math.sqrt(ovar / n);

var x2;

x2 = mean + minc;

return x2;

}

var outs1,outs2

function intervalx1(alpha,n,s2)

{

if (alpha <= 0 || alpha >= 1) throw "alpha must be probability in intervalx1!";

if (s2 <= 0) throw "var must larger than 0 in intervalx1";

var s12=new Array();

s12[0] = chiinv(1 - alpha / 2, n - 1);

s12[1] = chiinv(alpha / 2, n - 1);

s12[0] = s2 * (n - 1) / s12[0];

s12[1] = s2 * (n - 1) / s12[1];

return s12;

}

function intervalx1low(alpha,n,s2)

{

if (alpha <= 0 || alpha >= 1) throw "alpha must be probability in intervalx1low!";

if (s2 <= 0) throw "var must larger than 0 in intervalx1low!";

var s1;

s1 = chiinv(1 - alpha, n - 1);

s1 = s2 * (n - 1) / s1;

return s1;

}

function intervalx1high(alpha,n,s2)

{

if (alpha <= 0 || alpha >= 1) throw "alpha must be probability in intervalx1high!";

if (s2 <= 0) throw "var must larger than 0 in intervalx1high!";

var s22;

s22 = chiinv(alpha,n-1);

s22 = s2 * (n - 1) / s22;

return s2;

}

function intervalz1(alpha,n,bias,mean)

{

var x12;

if(bias<0) return;

if (alpha <= 0 || alpha >= 1) throw "alpha must be probability in intervalz1";

var minc;

minc = normsinv(1 - alpha / 2) *bias / Math.sqrt(n);

x12=new Array();

x12[0] = mean - minc;

x12[1] = mean + minc;

return x12;

}

function intervalz1low(alpha,n,bias,mean)

{

if(bias<=0) return;

if (alpha <= 0 || alpha >= 1) throw "alpha must be probability in intervalz1low";

var minc;

minc = normsinv(1 - alpha) *bias / Math.sqrt(n);

var x1;

x1 = mean - minc;

return x1;

}

function intervalz1high(alpha,n,bias,mean)

{

if(bias<=0) return;

if (alpha <= 0 || alpha >= 1) throw "alpha must be probability in intervalz1high";

var minc;

minc = normsinv(1 - alpha) * bias / Math.sqrt(n);

var x2;

x2 = mean + minc;

return x2;

}

function intervalz2(alpha,n1,xm,bs1,n2,ym,bs2)

{

var m,x12;

x12=new Array();

m =xm-ym;

var s1, s2;

s1 = bs1 * bs1;

s2 = bs2 * bs2;

var xinc;

xinc = normsinv(1 - alpha / 2) * Math.sqrt((s1 / n1) + (s2 / n2));

x12[0] = m - xinc;

x12[1] = m + xinc;

return x12;

}

function intervalz2low(alpha,n1,xm,bs1,n2,ym,bs2)

{

var m,x1;

m =xm-ym;

var s1, s2;

s1 = bs1 * bs1;

s2 = bs2 * bs2;

var xinc;

xinc = normsinv(1 - alpha) * Math.sqrt((s1 / n1) + (s2 / n2));

x1 = m - xinc;

return x1;

}

function intervalz2high(alpha,n1,xm,bs1,n2,ym,bs2)

{

var m,x2;

m = xm-ym;

var s1, s2;

s1 = bs1 * bs1;

s2 = bs2 * bs2;

var xinc;

xinc = normsinv(1 - alpha) * Math.sqrt((s1 / n1) + (s2 / n2));

x2 = m + xinc;

return x2;

}

function intervalt2(alpha,n1,mean1,var1,n2,mean2,var2)

{

var sw;

sw = ((n1 - 1) * var1*var1 + (n2 - 1) * var2*var2) / (n1 + n2 - 2);

sw = Math.sqrt(sw);

var xinc;

xinc=tdist2inv(1-alpha,n1+n2-2);

xinc *= sw * Math.sqrt((1.0 / n1) + (1.0 / n2));

var x12=new Array();

x12[0] = mean1 - mean2 - xinc;

x12[1] = mean1 - mean2 + xinc;

return x12;

}

function intervalt2low(alpha,n1,mean1,var1,n2,mean2,var2)

{

var sw,x1;

sw = ((n1 - 1) * var1*var1 + (n2 - 1) * var2*var2) / (n1 + n2 - 2);

sw = Math.sqrt(sw);

var xinc;

xinc = tdistinv(1 - alpha, n1 + n2 - 2);

xinc *= sw * Math.sqrt((1.0 / n1) + (1.0 / n2));

x1 = mean1 - mean2 - xinc;

return x1;

}

function intervalt2high(alpha,n1,mean1,var1,n2,mean2,var2)

{

var sw;

sw = ((n1 - 1) * var1*var1 + (n2 - 1) * var2*var2) / (n1 + n2 - 2);

sw = Math.sqrt(sw);

var xinc;

xinc = tdistinv(1 - alpha, n1 + n2 - 2);

xinc *= sw * Math.sqrt((1.0 / n1) + (1.0 / n2));

x2 = mean1 - mean2 + xinc;

return x2;

}

function intervalf2(alpha,n1,var1,n2,var2)

{

var v,f12;

v = (var1*var1) / (var2*var2);

f12=new Array();

f12[0] = v / fdistinv(1 - alpha / 2, n1 - 1, n2 - 1);

f12[1] = v / fdistinv(alpha / 2, n1 - 1, n2 - 1);

return f12;

}

function intervalf2low(alpha,n1,var1,n2,var2)

{

var v,f1;

v = (var1*var1) / (var2*var2);

f1 = v / fdistinv(1 - alpha, n1 - 1, n2 - 1);

return f1;

}

function intervalf2high(alpha,n1,var1,n2,var2)

{

var v,f2;

v = (var1*var1) / (var2*var2);

f2 = v / fdistinv(alpha, n1 - 1, n2 - 1);

return f2;

}

function geta(){

if(Radio1.checked){

return parseFloat(Radio1.value);

}

else if(Radio2.checked){

return parseFloat(Radio2.value);

}

else if(Radio3.checked){

return parseFloat(Radio3.value);

}

else if(Radio4.checked){

return parseFloat(Radio4.value);

}

return 0.05;

}

function gotoview(n){

view1.style.display="none";

view2.style.display="none";

view3.style.display="none";

view4.style.display="none";

view5.style.display="none";

view6.style.display="none";

switch (n){

case 1:

view1.style.display="block";

Button1_onclick();

break;

case 2:

view2.style.display="block";

Button2_onclick();

break;

case 3:

view3.style.display="block";

Button3_onclick();

break;

case 4:

view4.style.display="block";

Button4_onclick();

break;

case 5:

view5.style.display="block";

Button5_onclick();

break;

case 6:

view6.style.display="block";

Button6_onclick();

break;

}

}

function Radioa_onclick() {

if(Radioa1.checked){

diva.style.display="block";

divb.style.display="none";

if(Radiob1.checked)

gotoview(1);

else if(Radiob2.checked)

gotoview(2);

else if(Radiob3.checked)

gotoview(3);

}

else if(Radioa2.checked){

diva.style.display="none";

divb.style.display="block";

if(Radioc1.checked)

gotoview(4);

else if(Radioc2.checked)

gotoview(5);

else if(Radioc3.checked)

gotoview(6);

}

}

function Button1_onclick() {

var alpha,p,n,mean,bias;

alpha=geta();

p=1-alpha;

n=parseInt(Text1.value);

mean=parseFloat(Text2.value);

bias=tobias(Text3.value);

var x1,x2,x12;

label1.innerHTML="";

if(n>0 && mean<1e20 && bias>0){

x12=intervalz1(alpha,n,bias,mean);

label1.innerHTML+="双侧置信区间：

";

label1.innerHTML+="以置信概率" + dtos(p) + "肯定μ落在区间(" +dtos(x12[0]) + ", " +dtos(x12[1]) + ")中";

x1=intervalz1low(alpha,n,bias,mean);

label1.innerHTML+="单侧置信下限：

";

label1.innerHTML+="以置信概率" +dtos(p) + "肯定μ大于" +dtos(x1);

x2=intervalz1high(alpha,n,bias,mean);

label1.innerHTML+="单侧置信上限：

";

label1.innerHTML+="以置信概率" +dtos(p) + "肯定μ小于" +dtos(x2);

}

}

function Button2_onclick() {

var alpha,p,n,mean,ovar;

alpha=geta();

p=1-alpha;

n=parseInt(Text4.value);

mean=parseFloat(Text5.value);

ovar=tobias(Text6.value);

var x1,x2,x12;

label2.innerHTML="";

if(n>0 && mean<1e20 && ovar>0){

ovar*=ovar;

x12=intervalt1(alpha,n,mean,ovar);

label2.innerHTML+="双侧置信区间：

";

label2.innerHTML+="以置信概率" +dtos(p) + "肯定μ落在区间(" +dtos(x12[0]) + ", " +dtos(x12[1]) + ")中";

x1=intervalt1low(alpha,n,mean,ovar);

label2.innerHTML+="单侧置信下限：

";

label2.innerHTML+="以置信概率" +dtos(p) + "肯定μ大于" +dtos(x1);

x2=intervalt1high(alpha,n,mean,ovar);

label2.innerHTML+="单侧置信上限：

";

label2.innerHTML+="以置信概率" +dtos(p) + "肯定μ小于" +dtos(x2);

}

}

function Button3_onclick() {

var alpha,p,n,ovar;

alpha=geta();

p=1-alpha;

n=parseInt(Text7.value);

ovar=tobias(Text8.value);

var s1,s2,s12;

label3.innerHTML="";

if(n>0 && ovar>0){

ovar*=ovar;

s12=intervalx1(alpha,n,ovar);

label3.innerHTML+="双侧置信区间：

";

label3.innerHTML+="以置信概率" +dtos(p) + "肯定σ2落在区间(" +dtos(s12[0]) + ", " +dtos(s12[1]) + ")中";

label3.innerHTML+="

或者肯定σ落在区间(" +dtos(Math.sqrt(s12[0])) + ", " +dtos(Math.sqrt(s12[1])) + ")中";

s1=intervalx1low(alpha,n,ovar);

label3.innerHTML+="单侧置信下限：

";

label3.innerHTML+= "以置信概率" +dtos(p) + "肯定σ2大于" +dtos(s1);

label3.innerHTML+="

或者肯定σ大于" +dtos(Math.sqrt(s1));

s2=intervalx1high(alpha,n,ovar);

label3.innerHTML+="单侧置信上限：

";

label3.innerHTML+="以置信概率" +dtos(p) + "肯定σ2小于" + dtos(s2);

label3.innerHTML+="

或者肯定σ小于" +dtos(Math.sqrt(s2));

}

}

function Button4_onclick() {

var n,xm,sig1,m,ym,sig2,alpha,p;

alpha=geta();

p=1-alpha;

n=parseInt(Text9.value);

xm=parseFloat(Text10.value);

sig1=tobias(Text11.value);

m=parseInt(Text12.value);

ym=parseFloat(Text13.value);

sig2=tobias(Text14.value);

var x1,x2,x12;

label4.innerHTML="";

if(n>0 && m>0 && xm<1e30 && ym<1e30 && sig1>0 && sig2>0){

x12=intervalz2(alpha,n,xm,sig1,m,ym,sig2);

label4.innerHTML+="双侧置信区间：

";

label4.innerHTML+="以置信概率" +dtos(p) + "肯定μ1-μ2落在区间("

+dtos(x12[0]) + ", " +dtos(x12[1]) + ")中";

x1=intervalz2low(alpha,n,xm,sig1,m,ym,sig2);

label4.innerHTML+="单侧置信下限：

";

label4.innerHTML+="以置信概率" +dtos(p) + "肯定μ1-μ2大于" +dtos(x1);

x2=intervalz2high(alpha,n,xm,sig1,m,ym,sig2);

label4.innerHTML+="单侧置信上限：

";

label4.innerHTML+="以置信概率" +dtos(p) + "肯定μ1-μ2小于" +dtos(x2);

}

}

function Button5_onclick() {

var n,xm,sig1,m,ym,sig2,alpha,p;

alpha=geta();

p=1-alpha;

n=parseInt(Text15.value);

xm=parseFloat(Text16.value);

sig1=tobias(Text17.value);

m=parseInt(Text18.value);

ym=parseFloat(Text19.value);

sig2=tobias(Text20.value);

var x1,x2,x12;

label5.innerHTML="";

if(n>0 && m>0 && xm<1e30 && ym<1e30 && sig1>0 && sig2>0){

x12=intervalt2(alpha,n,xm,sig1,m,ym,sig2);

label5.innerHTML+="双侧置信区间：

";

label5.innerHTML+= "以置信概率" +dtos(p) + "肯定μ1-μ2落在区间("

+dtos(x12[0]) + ", " +dtos(x12[1]) + ")中";

x1=intervalt2low(alpha,n,xm,sig1,m,ym,sig2);

label5.innerHTML+="单侧置信下限：

";

label5.innerHTML+="以置信概率" +dtos(p) + "肯定μ1-μ2大于" +dtos(x1);

x2=intervalt2high(alpha,n,xm,sig1,m,ym,sig2);

label5.innerHTML+="单侧置信上限：

";

label5.innerHTML+="以置信概率" +dtos(p) + "肯定μ1-μ2小于" +dtos(x2);

}

}

function Button6_onclick() {

var n,sig1,m,sig2,alpha,p;

alpha=geta();

p=1-alpha;

n=parseInt(Text21.value);

sig1=tobias(Text22.value);

m=parseInt(Text23.value);

sig2=tobias(Text24.value);

var f1,f2,f12;

label6.innerHTML="";

if(n>0 && m>0 && sig1>0 && sig2>0){

f12=intervalf2(alpha,n,sig1,m,sig2);

label6.innerHTML+= "双侧置信区间：

";

label6.innerHTML+="以置信概率" +dtos(p) + "肯定σ12/σ22落在区间("

+dtos(f12[0]) + ", " +dtos(f12[1]) + ")中";

f1=intervalf2low(alpha,n,sig1,m,sig2);

label6.innerHTML+= "单侧置信下限：

";

label6.innerHTML+="以置信概率" +dtos(p) + "肯定σ12/σ22大于" +dtos(f1);

f2=intervalf2high(alpha,n,sig1,m,sig2);

label6.innerHTML+= "单侧置信上限：

";

label6.innerHTML+="以置信概率" +dtos(p) + "肯定σ12/σ22小于"

+dtos(f2);

}

}// JavaScript Document

// 以下是计算t分布及线性回归等程序

function normsinv(pp){

var x,y;

var q = 1 - pp;

bb = [1.570796288,0.03706987906,-0.0008364353589,-0.0002250947176,

0.000006841218299,0.000005824238515,-0.00000104527497,8.360937017e-8,-3.231081277e-09,

3.657763036e-11,6.936233982e-13];

if (q == 0.5) return 0;

var p;

if (q > 0.5) p = 1 - q;

else p = q;

var b;

y =-Math.log(4 * p * (1 - p));

b = y * bb[10];

var i;

for (i = 9; i >= 0; i--)

{

b = y * (bb[i] + b);

}

x = Math.sqrt(b);

if (q > 0.5) x = -x;

return x;

}

function gamma( x)

{

var i;

var y, t, s, u;

var a = [ 0.0000677106,-0.0003442342,

0.0015397681,-0.0024467480,0.0109736958,

-0.0002109075,0.0742379071,0.0815782188,

0.4118402518,0.4227843370,1.0];

if (x <= 0.0)

throw "x不能小于0";

y = x;

if (y <= 1.0)

{ t = 1.0 / (y * (y + 1.0)); y += 2.0; }

else if (y <= 2.0)

{ t = 1.0 / y; y += 1.0; }

else if (y <= 3.0) t = 1.0;

else

{

t = 1.0;

while (y > 3.0)

{ y -= 1.0; t = t * y; }

}

s = a[0]; u = y - 2.0;

for (i = 1; i <= 10; i++)

s = s * u + a[i];

s *= t;

return s;

}

function betacf(a, b, x)

{

var MAXIT = 1000;

var EPS = 1e-10;

var FPMIN = 1e-8;

var m, m2;

var aa, c, d, del, h, qab, qam, qap;

qab = a + b;

qap = a + 1;

qam = a - 1;

c = 1;

d = 1 - qab * x / qap;

if (Math.abs(d) < FPMIN) d = FPMIN;

d = 1 / d;

h = d;

for (m = 1; m <= MAXIT; m++)

{

m2 = 2 * m;

aa = m * (b - m) * x / ((qam + m2) * (a + m2));

d = 1 + aa * d;

if (Math.abs(d) < FPMIN) d = FPMIN;

c = 1 + aa / c;

if (Math.abs(c) < FPMIN) c = FPMIN;

d = 1 / d;

h *= d * c;

aa = -(a + m) * (qab + m) * x / ((a + m2) * (qap + m2));

d = 1 + aa * d;

if (Math.abs(d) < FPMIN) d = FPMIN;

c = 1 + aa / c;

if (Math.abs(c) < FPMIN) c = FPMIN;

d = 1 / d;

del = d * c;

h *= del;

if (Math.abs(del - 1) <= EPS) break;

}

if (m > MAXIT) throw "a or b too big, or MAXIT too small in betacf";

return h;

}

function gammln(xx)

{

var j;

var x, y, tmp, ser;

var cof = [76.18009172947146,-86.50532032941677,24.01409824083091,-1.231739572450155,

0.1208650973866179e-2,-0.5395239384953e-5];

y = x = xx;

tmp = x + 5.5;

tmp -= (x + 0.5) * Math.log(tmp);

ser = 1.000000000190015;

for (j = 0; j < 6; j++) ser += cof[j] / ++y;

return -tmp + Math.log(2.5066282746310005 * ser / x);

}

function betai(a, b, x)

{

var bt;

if (x < 0 || x > 1) throw "Bad x in routine batai";

if (x == 0 || x == 1) bt = 0;

else

bt = Math.exp(gammln(a + b) - gammln(a) - gammln(b) + a * Math.log(x) + b * Math.log(1 - x));

if (x < (a + 1) / (a + b + 2))

return bt * betacf(a, b, x) / a;

else

return 1 - bt * betacf(b, a, 1 - x) / b;

}

function tdist2(t, free)

{

if (free < 1) throw "free must biger than 0";

var f;

f = free;

var p;

p = 1 - betai(f / 2.0, 0.5, f / (f + t * t));

return p;

}

function tdist(t, free)

{

if (t == 0)

{

return 0.5;

}

if (t > 0)

{

return 0.5 + tdist2(t, free) / 2;

}

return (1 - tdist2(-t, free)) / 2;

}

var outpp;

function t_dist(n, t)

{

var sign, ibi, n2, i;

var tt, x, p, u, ga1, ga2,dd;

if (t == 0)

{

ga1 = gamma(n / 2.0);

ga2 = gamma(0.5 + n / 2.0);

outpp = 0.5;

return ga2 / (Math.sqrt(n * Math.PI) * ga1);

}

if (t < 0)

{

sign = -1;

}

else sign = 1;

tt = t * t;

x = tt / (n + tt);

if (n % 2 == 0)

{

p = Math.sqrt(x);

u = p * (1 - x) / 2.0;

ibi = 2;

}

else

{

u = Math.sqrt(x * (1 - x)) / Math.PI;

p = 1 - 2 * Math.atan(Math.sqrt((1 - x) / x)) / Math.PI;

ibi = 1;

}

if (ibi == n)

{

dd = u / Math.abs(t);

outpp = 0.5 + sign * p / 2.0;

return dd;

}

else

{

n2 = n - 2;

}

for (i = ibi; i <= n2; i += 2)

{

p += 2.0 * u / i;

u = u * (1 + i) / i * (1 - x);

}

dd = u / Math.abs(t);

outpp = 0.5 + sign * p / 2.0;

return dd;

}

function tdistinv(pvar, n)

{

var q;

q = 1 - pvar;

var t=0.0;

var pis, dfr2, c, q2, p, yq, e, ga1, ga2, ga3, t0, pp, d;

var k;

pis = Math.sqrt(Math.PI);

dfr2 = n / 2.0;

if (n == 1) return Math.tan(Math.PI * (0.5 - q));

if (n == 2)

{

if (q > 0.5) c = -1;

else c = 1;

q2 = (1 - 2 * q);

q2 *= q2;

return Math.sqrt(2.0 * q2 / (1.0 - q2)) * c;

}

p = 1 - q;

yq = normsinv(p);

e = 1.0 - 1.0 / (4.0 * n);

e = e * e - yq * yq / (2.0 * n);

if (e > 0.5) t0 = yq / Math.sqrt(e);

else

{

ga1 = gammln(dfr2);

ga2 = gammln(dfr2 + 0.5);

ga3 = Math.exp((ga1 - ga2) / n);

t0 = Math.pow(Math.sqrt(n) / (pis * q * n), (1.0 / n) / ga3);

}

for (k = 1; k <= 30; k++)

{

d = t_dist(n, t0);

pp=outpp;

if (d == 0) return t0;

t = t0 - (pp - p) / d;

if (Math.abs(t0 - t) < 0.000001 * Math.abs(t))

{

return t;

}

else t0 = t;

}

return t;

}

function relhold(freedom, alpha)

{

var t;

t = tdistinv(1 - alpha / 2, freedom);

return t / Math.sqrt(freedom + t * t);

}

// 线性回归的核心程序

function linehuigui(data, alpha)

{

var a,b,sig2,sigx2,r,ra,t,ta,xmean;

var n;

n = data.length / 2;

var i;

var sumx = 0, sumy = 0, sumxx = 0, sumyy = 0, sumxy = 0;

var x, y;

for (i = 0; i < n; i++)

{

x = data[2 * i];

y = data[2 * i + 1];

sumx += x;

sumy += y;

sumxx += x * x;

sumyy += y * y;

sumxy += x * y;

}

xmean = sumx / n;

var sxx, syy, sxy;

sxx = sumxx - sumx * sumx / n;

syy = sumyy - sumy * sumy / n;

sxy = sumxy - sumx * sumy / n;

b = sxy / sxx;

a = (sumy / n) - (sumx / n) * b;

sig2 = (syy - b * sxy) / (n - 2.0);

sigx2 = sxx;

t = b * Math.sqrt(sxx / sig2);

ta = tdistinv(1 - alpha / 2, n - 2);

r = sxy / Math.sqrt(sxx * syy);

ra = relhold(n - 2, alpha);

var out=new Array();

out[0]=a;

out[1]=b;

out[2]=sig2;

out[3]=sigx2;

out[4]=r;

out[5]=ra;

out[6]=t;

out[7]=ta;

out[8]=xmean;

return out;

}

// 以下是绘制曲线程序

function updown(a){// 将给定的数分离成两个数相乘，一个是数的部分，另一个是指数部分，利用函数toExponential来做

var r=new Array(2);

var s,s1,s2;

s=a.toExponential(4);

var i,j,c,b;

i=s.indexOf("e");

j=s.length;

s1=s.substring(0,i);

s2=s.substring(i+1,j);

c=parseFloat(s1);

b=parseFloat(s2);

r[0]=c;

r[1]=b;

return r;

}

function getscals(low, high)// 根据最低值low和最高值high计算刻度的数量和刻度，返回一个实数矩阵，维数就是刻度，内容就是各个刻度的值

{

var l=high-low;

if(low>0)l=high;

if(high<0){

l=-low;

high=0;

}

var llow=low;

var lhigh=high;

var bs=new Array();

var bbb=new Array();

var bbb=updown(l/4);

var a=bbb[0];

var index=bbb[1];

llow/=Math.pow(10,index);

lhigh/=Math.pow(10,index);

var ascale;

if(a<=2)

ascale=2;

else if(a<=5){

ascale=5;

}

else ascale=10;

var abegin=0;

var i,d,dd,s;

if(llow<0){

for(i=1;i<1000;i++){

abegin=-i*ascale;

if(abegin<=llow)

break;

}

}

else abegin=0;

for(i=0;i<50;i++){

d=abegin+i*ascale;

dd=d*Math.pow(10,index);

s=dd.toPrecision(8);

bs[i]=parseFloat(s);

//bs[i]=d*Math.pow(10,index);

if(d>=lhigh || Math.abs(d-lhigh)<1e-5)break;

}

return bs;

}

var ctx;

var width=600,hight=400;//图像的宽度和高度

var xbegin,ybegin,xlength,ylength;//曲线的绘制范围，x和y的起始点和宽高度

var axmin,aymin,axwidth,aywidth;

function drawaxis(xl,xh,yl,yh){//绘制xy坐标轴，xl,xh,yl,yh是x和y取值的最小值和最大值

var yofx,xofy;//,ybegin,xbegin;//x轴的y坐标和y轴的x坐标及曲线的x和y的起始点

var xscalelength,yscalelength;//两个刻度之间的距离

//var xlength,ylength;//曲线的x和y的幅度

var xscals,yscals; // 是数组，存放x和y的刻度

var iyofx,ixofy;//y刻度的第几个数是0，x刻度的第几个数是0

xscals=getscals(xl,xh);

axmin=xscals[0];

axwidth=xscals[xscals.length-1]-xscals[0];

yscals=getscals(yl,yh);

aymin=yscals[0];

aywidth=yscals[yscals.length-1]-yscals[0];

yofx=ybegin=hight-30;

ylength=hight-70-30;

yscalelength=ylength/(yscals.length-1);

var i;

for(i=0;ij;i--){ // 删去末尾的字符0

if(s.substr(i,1)!="0"){

return s.substr(0,i+1);

}

}

return s.substr(0,j);

}

function strtodouble(s)

{

var index=s.search(/\//);

if(index<0){

return parseFloat(s);

}

var ss="abc";

ss=s.substring(index+1,s.length);

var a,b;

var sss;

sss=s.substring(0,index);

a=parseFloat(ss);

b=parseFloat(sss);

//return (0.0+sss)/(0.0+ss);

return b/a;

}

function stringstodouble(s)

{

var reg_pattern=/[0123456789.\-\/]+/g;

var arr=s.match(reg_pattern);

var a=new Array();

var i;

if(arr!=null)

for(i=0;ixmax)xmax=datax[i];

if(datay[i]ymax)ymax=datay[i];

}

var canvas=document.getElementById('my_canvas');

if(canvas.getContext)

{

ctx=canvas.getContext('2d');

ctx.globalCompositeOperation="source-over";

ctx.clearRect(0,0,600,400);

ctx.lineWidth=1;

// 在下面开始绘制曲线

drawaxis(xmin,xmax,ymin,ymax);

ctx.closePath();

ctx.beginPath();

var ix,iy;

for(i=0;i";

spanresult.innerHTML+="从t检验的角度看：t检验统计量为t=" +dtos(t) + ",而t" +dtos(alpha/2) +

"(" + (n - 2).toString() + ")=" +dtos(ta)+"

";

if (Math.abs(t) > ta) {

spanresult.innerHTML += "因为|t|>tα/2, 所以拒绝b=0的原假设，回归效果显著。";

divpre.style.display="block";

}

else

{

spanresult.innerHTML += "因为|t|≤tα/2, 所以接受b=0的原假设，回归效果不好。";

}

spanresult.innerHTML+= "

从相关系数检验法的角度看：r=" + dtos(r) + ",r" +dtos(alpha) + "=" + dtos(ra)+"

";

if (Math.abs(r) > ra)

{

spanresult.innerHTML += "因为|r|>rα, 所以拒绝b=0的原假设，回归效果显著。";

}

else

{

spanresult.innerHTML += "因为|r|≤rα, 所以接受b=0的原假设，回归效果不好。";

}

ctx.lineWidth=1;

ctx.beginPath();//注意，从此开始的四句毫无意义，但是如果不加，就会有重叠

ctx.moveTo(1,1);

ctx.lineTo(2,1);

ctx.closePath();

ctx.stroke();

}

}

function Button2_onclick() {

var yinc, x0, y0;

if(Text1.value=="" || Text1.value==null){

spanr2.innerHTML="请输入x0的值";

return;

}

x0=parseFloat(Text1.value);

if(isNaN(x0)){

spanr2.innerHTML="输入x0的格式错误！";

return;

}

y0 = a + b * x0;

yinc = ta * Math.sqrt(sig2 * (((n + 1.0) / n) + (x0 - xmean) * (x0 - xmean) / sigx2));

spanr2.innerHTML="y0的预测区间是："+dtos(y0)+"±"+dtos(yinc)+",

";

spanr2.innerHTML += "也就是：(" + dtos(y0 - yinc) + ", " + dtos(y0 + yinc) + ")";

}

function Button3_onclick() {

var s;

s="6,31,10,58,21,124,40,220,62,299,62,190,90,320,100,406,120,380";

TextArea1.value=s;

spanresult.innerHTML="";

spanr2.innerHTML="";

divpre.style.display="none";

}

function Button4_onclick() {

var s;

s="100,45,110,51,120,54,130,61,140,66,150,70,160,74,170,78,180,85,190,89";

TextArea1.value=s;

spanresult.innerHTML="";

spanr2.innerHTML="";

divpre.style.display="none";

}

function Radio1_onclick() {

spanresult.innerHTML="";

spanr2.innerHTML="";

divpre.style.display="none";

}

// JavaScript Document