Using timeit() and hypothesis test for means

Question

I've had some problems using timeit() as an accurate benchmark when comparing longer (> 1 lines) code snippets for SL4A on Android. I get a pretty high variation when comparing times. (Possibly something to do with the way android/dalvik vm allocates cpu time?).

Anyway, I wrote a script that uses a hypothesis test for means to analyse large (~1000) samples of times. Is there anything wrong with this approach?

from math import sqrt
import timeit

#statistics stuff

mean = lambda x: sum(x) / float(len(x))

def stdev (mean, dataset):
    variance = ((x - mean)**2 for x in dataset)
    deviation = sqrt(sum(variance) / float(len(dataset) - 1))
    return deviation / sqrt(len(dataset))

def interval(mean, sampleDeviation, defaultZ = 1.57):
    margin = sampleDeviation * defaultZ
    return (mean - margin, mean + margin)

def testnull(dataset1, dataset2, defaultZ = 1.57):
    mean1, mean2 = mean(dataset1), mean(dataset2)
    sd1, sd2 = stdev(mean1, dataset1), stdev(mean2, dataset2)
    interval1, interval2 = interval(mean1, sd1, defaultZ), interval(mean2, sd2, defaultZ)
    inside = lambda x, y: y >= x[0] and y <= x[1]
    if inside(interval1, interval2[0]) or inside(interval1, interval2[1]):
        return True
    return False

#timer setup

t1 = timeit.Timer('sum(x)', 'x = (i for i in range(1000))')
t2 = timeit.Timer('sum(x)', 'x = list(range(1000))')

genData, listData = [], []

for i in range(10000):
    genData.append(t1.timeit())
    listData.append(t2.timeit())

# testing the interval
    print('The null hypothesis is {0}'.format(testnull(genData, listData)))

Answer 1

I think that's sensible. What you want is to compare the confidence intervals of both versions of the code for overlap. Georges et al (2007) has a complete description of the technique you are trying to use.