Wald-Wolfowitz Runs Test demonstration in python

Wald-Wolfowitz_Runs_Test.py

# 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))

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

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