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September 18, 2018 19:29
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Save cryptorick/f33ca7af382713c4b649a9702592d4c1 to your computer and use it in GitHub Desktop.
I stole some stat functions from the newLISP (C) source code; so I could compute a confidence interval in awk. :D
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BEGIN { | |
ITMAX = 100 | |
EPS7 = 3.0e-7 | |
} | |
function fatalError(msg, errcode) { | |
print msg > "/dev/null" | |
exit(errcode+0) | |
} | |
function gammaln(xx, | |
x,y,tmp,ser,cof,j) { | |
cof[0] = 76.18009172947146 | |
cof[1] = -86.50532032941677 | |
cof[2] = 24.01409824083091 | |
cof[3] = -1.231739572450155 | |
cof[4] = 0.1208650973866179e-2 | |
cof[5] = -0.5395239384953e-5 | |
if(xx == 0.0) | |
fatalError("gammaln: ERR_INVALID_PARAMETER_0, parameter was: " xx, 2) | |
y = x = xx | |
tmp = x + 5.5 | |
tmp -= (x+0.5) * log(tmp) | |
ser = 1.000000000190015 | |
for (j=0;j<=5;j++) ser += cof[j]/++y | |
return -tmp + log(2.5066282746310005*ser/x); | |
} | |
function fabs(x) { | |
return x >= 0.0 ? x : -x | |
} | |
function betacf(a, b, x, | |
qap,qam,qab,em,tem,d, | |
bz,bm,bp,bpp, | |
az,am,ap,app,aold, | |
m) | |
{ | |
bm = az = am = 1.0 | |
qab=a+b | |
qap=a+1.0 | |
qam=a-1.0 | |
bz=1.0-qab*x/qap | |
for (m=1;m<=ITMAX;m++) | |
{ | |
em=m | |
tem=em+em | |
d=em*(b-em)*x/((qam+tem)*(a+tem)) | |
ap=az+d*am | |
bp=bz+d*bm | |
d = -(a+em)*(qab+em)*x/((qap+tem)*(a+tem)) | |
app=ap+d*az | |
bpp=bp+d*bz | |
aold=az | |
am=ap/bpp | |
bm=bp/bpp | |
az=app/bpp | |
bz=1.0 | |
if (fabs(az-aold) < (EPS7 * fabs(az))) return az | |
} | |
return(paramError = 1) | |
} | |
function betai(a, b, x, | |
bt) { | |
if (x < 0.0 || x > 1.0) | |
{ | |
paramError = 1 # TODO: find out what this is for. | |
return(0.0) | |
} | |
if (x == 0.0 || x == 1.0) | |
bt = 0.0 | |
else | |
bt = exp(gammaln(a+b)-gammaln(a)-gammaln(b)+a*log(x)+b*log(1.0-x)) | |
if (x < (a+1.0)/(a+b+2.0)) | |
return (bt * betacf(a,b,x) / a) | |
else | |
return (1.0 - bt * betacf(b,a,1.0-x) / b) | |
} | |
function probT(t, df, | |
bta) | |
{ | |
bta = betai(df/2.0, 0.5, 1.0/(1.0 + t*t/df)); | |
if(t > 0.0) return(1.0 - 0.5 * bta); | |
else if(t < 0.0) return(0.5 * bta); | |
return(0.5); | |
} | |
function critical_value(p, df1, df2, max_val, type, | |
NEWTON_EPSILON, minval, | |
maxval, critval, prob) | |
{ | |
NEWTON_EPSILON = 0.000001 # Accuracy of Newton approximation | |
minval = 0.0; | |
maxval = max_val; | |
critval; | |
prob = 0.0; | |
if (p <= 0.0) return 0.0; | |
else if (p >= 1.0) return maxval; | |
critval = (df1 + df2) / sqrt(p); # fair first value | |
while ((maxval - minval) > NEWTON_EPSILON) | |
{ | |
prob = probT(critval, df1); | |
if (prob < p) minval = critval; | |
else maxval = critval; | |
critval = (maxval + minval) * 0.5; | |
} | |
return critval; | |
} | |
function criticalX(p, df1, | |
df2, x) | |
{ | |
df2 = 0; | |
x = critical_value((1.0 - p), df1, df2, 99999.0, type); | |
if(x < NEWTON_EPSILON) x = 0.0; | |
return(x); | |
} | |
function criticalT(p, df) { | |
return criticalX(p, df) | |
} | |
function confidenceT(alpha, stdev, samplesize) { | |
return sqrt(stdev/samplesize) * criticalT(alpha/2, samplesize-1) | |
} |
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Usage example
Output is