Sunday, February 7, 2010

Confidence intervals in matplotlib


This plot comes from the same place as the previous one (Cumming 2007 PMID 17420288 ).

It shows the influence of sample size on the standard error and confidence interval, and compares these values to the standard deviation. Standard error (se) is calculated as sd / √n, and the confidence interval is calculated as the t statistic * se, where t is hard coded in the script. The value approaches 1.96 (for p-value of 0.05) as n gets large. I have to investigate more how to determine this with numpy or PyCogent.


import numpy as np
from pylab import *

data1 = [53,38,29]
data2 = [16,29,32,34,40,44,49,51,52,53]
data3 = np.random.normal(loc=39,scale=10,size=30)
data = [data1,np.abs(data2),data3]

def do_error_bar(x,e,lw=2,w=2):
o = plot([x,x],[m+e,m-e],color='k',lw=lw)
o = plot([x-w,x+w],[m+e,m+e],color='k',lw=lw)
o = plot([x-w,x+w],[m-e,m-e],color='k',lw=lw)

#layout from 1 to 100
N = len(data)
total = 100
margin = 5
space = 15
fig_width = total - margin*2
all_spaces = (N-1)*space
total_group_width = fig_width - all_spaces
group_width = total_group_width * 1.0 / N

dx = group_width/3.0 # 4 elements per group
x = margin # start
tD = {3:3.182, 10:2.228, 30:2.042}
S = 50 # large circle size
s = 10 # small circle size
y = 17 # y pos for text

for group in data:
for g in group:
scatter(x,g,s=s,color='k')

x += dx
n = len(group)
m = np.mean(group)
sd = np.std(group)
scatter(x,m,s=S,color='k')
do_error_bar(x,sd)
text(x-1.5,y,'std')
text(x,y-5,'n = ' + str(n))

x += dx
se = sd/np.sqrt(n)
t = tD[n]
ci = t * se
scatter(x,m,s=S,color='k')
do_error_bar(x,ci)
text(x-1.5,y,'CI')

x += dx
scatter(x,m,s=S,color='k')
do_error_bar(x,se)
text(x-1.5,y,'se')
x += space

ax = axes()
ax.xaxis.set_visible(False)
show()

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