The code below can be used to generate half normal probability paper. The erfinv function is a bit inaccurate (2 sig figs) so it could be improved with a better approximation. Update: I modified this with the code from Wikipedia to give better accuracy. Create a blank file first. Mine was 1500 by 2000. The code is Python. I had to install Pillow for this.
from PIL import Image,ImageDraw,ImageFont
from math import *
def halfnormal(z,s):
return erf(z/sqrt(2)/s)
def erfinv(z):
a = .147
x=sqrt(sqrt((2/pi/a+log(1-z**2)/2)**2-log(1-z**2)/a)-(2/pi/a+log(1-z**2)/2))
#print z,z-erf(x)
return x
def invhalfnorm(z,s):
return erfinv(z)*sqrt(2)
def halfnormalgraph():
im = Image.open("blank_graph.png")
draw = ImageDraw.Draw(im)
font1 = ImageFont.truetype("arial.ttf", 16)
font2 = ImageFont.truetype("arial.ttf", 28)
j=30.0
k=700.0
xmax=46
xshift=30
gridfill = (180,180,250)
draw.text((550,10), "Half Normal Probability Paper", font=font2, fill=256)
for i in range(xmax):
x1=j*i+j*2+xshift
y1=im.size[1]-j*2
y2=j*2
draw.line((x1, y1, x1, y2), fill=gridfill)
x1=j*2+xshift
x2=j*xmax+j+xshift
for i in range(10):
iv=i/20.0+0
y1=im.size[1]-invhalfnorm(iv,1.0)*k-j*2
draw.line((x1, y1, x2, y1 ), fill=gridfill)
draw.text((2+xshift,y1-8), "{:10.0f}".format(iv*100), font=font1, fill=256)
for i in range(20):
iv=i/50.0+.5
y1=im.size[1]-invhalfnorm(iv,1.0)*k-j*2
draw.line((x1, y1, x2, y1 ), fill=gridfill)
draw.text((2+xshift,y1-8), "{:10.0f}".format(iv*100), font=font1, fill=256)
for i in range(10):
iv=i/100.0+.90
y1=im.size[1]-invhalfnorm(iv,1.0)*k-j*2
draw.line((x1, y1, x2, y1 ), fill=gridfill)
draw.text((2+xshift,y1-8), "{:10.0f}".format(iv*100), font=font1, fill=256)
im.save("halfnormgraph.png")
Here is another program that makes the desired number of divisions and an example of the output. This would be useful for plotting full factorial designed experiments, DOE, with 2 levels and 3 factors. Included are sheets for 7, 15, and 31 divisions which are the ones most useful for full factorial experiments.
def hng2(bins=7):
im = Image.open("blank_graph.png")
draw = ImageDraw.Draw(im)
font1 = ImageFont.truetype("arial.ttf", 16)
font2 = ImageFont.truetype("arial.ttf", 28)
j=30.0
k=700.0
xmax=46
xshift=30
gridfill = (180,180,250)
draw.text((550,10), "Half Normal Probability Paper", font=font2, fill=256)
for i in range(xmax):
x1=j*i+j*2+xshift
y1=im.size[1]-j*2
y2=j*2
draw.line((x1, y1, x1, y2), fill=gridfill)
x1=j*2+xshift
x2=j*xmax+j+xshift
iv=0.0
y1=im.size[1]-invhalfnorm(iv,1.0)*k-j*2
draw.line((x1, y1, x2, y1 ), fill=gridfill)
draw.text((-2+xshift,y1-8), "{:10.2f}".format(iv*100), font=font1, fill=256)
for i in range(bins):
iv=1.0*i/bins+1.0/2.0/bins
y1=im.size[1]-invhalfnorm(iv,1.0)*k-j*2
draw.line((x1, y1, x2, y1 ), fill=gridfill)
draw.text((-2+xshift,y1-8), "{:10.2f}".format(iv*100), font=font1, fill=256)
im.save("hng2.png")
hng2(7)
