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Wald-Wolfowitz Runs Test demonstration in python
# Wald-Wolfowitz Runs Test (Actual)
# *** For educational purposes only,
# use more robust code for actual analysis
import math
import scipy.stats as st # for pvalue
# Example data (Current script only works for binary ints)
L = [1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1]
# Finds runs in data: counts and creates a list of them
# TODO: There has to be a more pythonic way to do this...
def getRuns(l):
runsList = []
tmpList = []
for i in l:
if len(tmpList) == 0:
tmpList.append(i)
elif i == tmpList[len(tmpList)-1]:
tmpList.append(i)
elif i != tmpList[len(tmpList)-1]:
runsList.append(tmpList)
tmpList = [i]
runsList.append(tmpList)
return len(runsList), runsList
# define the WW runs test described above
def WW_runs_test(R, n1, n2, n):
# compute the standard error of R if the null (random) is true
seR = math.sqrt( ((2*n1*n2) * (2*n1*n2 - n)) / ((n**2)*(n-1)) )
# compute the expected value of R if the null is true
muR = ((2*n1*n2)/n) + 1
# test statistic: R vs muR
z = (R - muR) / seR
return z
# Gather info
numRuns, listOfRuns = getRuns(L) # Grab streaks in the data
# Define parameters
R = numRuns # number of runs
n1 = sum(L) # number of 1's
n2 = len(L) - n1 # number of 0's
n = n1 + n2 # should equal len(L)
# Run the test
ww_z = WW_runs_test(R, n1, n2, n)
# test the pvalue
p_values_one = st.norm.sf(abs(ww_z)) #one-sided
p_values_two = st.norm.sf(abs(ww_z))*2 #twosided
# Print results
print('Wald-Wolfowitz Runs Test')
print('Number of runs: %s' %(R))
print('Number of 1\'s: %s; Number of 0\'s: %s ' %(n1,n2))
print('Z value: %s' %(ww_z))
print('One tailed P value: %s; Two tailed P value: %s ' %(p_values_one, p_values_two))
@shadiakiki1986

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@shadiakiki1986 shadiakiki1986 commented Nov 26, 2020

The more pythonic way for getRuns is:

def getRuns(l):
  import itertools
  return len([sum(1 for _ in r) for _, r in itertools.groupby(l)])

and then drop the listOfRuns variable since you don't use it anyway

Ref: https://aaronschlegel.me/wald-wolfowitz-two-sample-runs-test.html

@kwcooper

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@kwcooper kwcooper commented Dec 4, 2020

Ha! I love it. Good eye @shadiakiki1986. Got to love itertools.

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