start with Kruskal-Wallis test

analysis/test-difference-between-distributions.py

@@ -1,27 +1,55 @@
 # test whether travel times are drawn from the same distribution
 
-import requests
+import requests, scipy
 
-backend = 'http://localhost:8072/aggregate-travel-times'
+sig_level = 0.05
 
-# get data for the same corridor and month, one year apart
-tt1 = requests.get(f'{backend}/30345882/30357505/16/19/2022-04-01/2022-05-01/false/12345').json()
-tt2 = requests.get(f'{backend}/30345882/30357505/16/19/2023-04-01/2023-05-01/false/12345').json()
-# major complete-street rebuild took place between tt2 and tt3
-tt3 = requests.get(f'{backend}/30345882/30357505/16/19/2024-04-01/2024-05-01/false/12345').json()
+backend = 'http://localhost:8072'
 
-tt1_obs = [ tt['seconds'] for tt in tt1['results']['observations'] ]
-tt2_obs = [ tt['seconds'] for tt in tt2['results']['observations'] ]
-tt3_obs = [ tt['seconds'] for tt in tt3['results']['observations'] ]
+# define a range of years to query data for
+years = [ y for y in range(2018, 2025) ]
 
-import scipy.stats as stats
-# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ranksums.html
-# aka
+# get data for the same corridor and month, for each year in the range
+def getObs(responseData):
+    return [ tt['seconds'] for tt in responseData['results']['observations'] ]
+
+data = [
+    getObs(
+        requests.get(f'{backend}/aggregate-travel-times/30345882/30357505/16/19/{year}-04-01/{year}-05-01/false/12345').json()
+    ) for year in years
+]
+
+# now test whether any of these sets of observations differ significantly
+# from the others
+# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kruskal.html
+(stat, pvalue) = scipy.stats.kruskal(*data)
+
+print(
+    f'One or more of the distributions is different with a P-value of {pvalue}'
+    if pvalue < sig_level else
+    f'We fail to reject the hypothesis that observations are drawn from the same distribution' 
+)
+
+if pvalue > sig_level:
+    # if this test doesn't reject the null hypothesis
+    # there's no need to go further
+    raise SystemExit
+
+# now let's find out which years saw significant differences from their
+# preceding year. We'll use a Mann-Whitney U test
 # https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test
-statistic1, pvalue1 = stats.ranksums(tt1_obs, tt2_obs,'two-sided')
-statistic2, pvalue2 = stats.ranksums(tt2_obs, tt3_obs,'two-sided')
+# available in scipy as
+# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ranksums.html
 
-sig_level = 0.05
+for t1_year, data_t1, data_t2 in zip(years, data, data[1:]):
+    stat, pvalue = scipy.stats.ranksums(data_t1, data_t2, 'two-sided')
+    print(
+        f'Travel time distributions differ between {t1_year} and {t1_year+1} with a P-value of {pvalue}'
+        if pvalue < sig_level else
+        f'Travel times between {t1_year} and {t1_year+1} are not significantly different' 
+    )
 
-print(f'P = {pvalue1}', 'not different' if pvalue1 > sig_level else 'different')
-print(f'P = {pvalue2}', 'not different' if pvalue2 > sig_level else 'different')
+# This is an interesting period. COVID happened, and then for this particular
+# corridor, after things settled down for a year between 2022-2023, there was 
+# a major road-diet / complete-street installed which greatly changed motor
+# vehicle travel times