Sign test

In this tutorial we demonstrate how to check equal size of two samples using the sign test. To do so, we provide an example in which we check if Heung-Min Son shoots with both feet the same number of times.

import pandas as pd
import numpy as np
import json
# plotting
import matplotlib.pyplot as plt
#opening data
import os
import pathlib
import warnings

pd.options.mode.chained_assignment = None
warnings.filterwarnings('ignore')

Opening the dataset

First we open the data. For this example we will use WyScout data from 2017/18 Premier League season. To meet file size requirements of Github, we have to open it from different files, but you can open the file locally from the directory you saved it in. Also, we open the file containing all players in WyScout database.

#open event data
train = pd.DataFrame()
for i in range(13):
    file_name = 'events_England_' + str(i+1) + '.json'
    path = os.path.join(str(pathlib.Path().resolve()), 'data', 'Wyscout', file_name)
    with open(path) as f:
        data = json.load(f)
    train = pd.concat([train, pd.DataFrame(data)])

    path = os.path.join(str(pathlib.Path().resolve()),"data", 'Wyscout', 'players.json')

#open dataset with players
with open(path) as f:
    players = json.load(f)
player_df = pd.DataFrame(players)

Preparing the dataset

First, we filter the events to only keep shots. Then, we check for Son’s id in the player database. As the next step, we keep shots made by him. Then, we look for the shots made with his left (ones with id = 401) and right (ones with id = 401) foot. In the end, we create a list with ones for shots with his left foot and -1 for shots with his right foot.

#take shots only
shots = train.loc[train['subEventName'] == 'Shot']
#look for son's id
son_id = player_df.loc[player_df["shortName"] == "Son Heung-Min"]["wyId"].iloc[0]
#get son's shot
son_shots = shots.loc[shots["playerId"] == son_id]

#left leg shots
lefty_shots = son_shots.loc[son_shots.apply (lambda x:{'id':401} in x.tags, axis = 1)]
#right leg shots
righty_shots = son_shots.loc[son_shots.apply (lambda x:{'id':402} in x.tags, axis = 1)]

#create list with ones for left foot shots and -1 for right foot shots
l = [1] * len(lefty_shots)
l.extend([-1] * len(righty_shots))

Testing the hypothesis

Now we can test the hypothesis that Heung-Min Son is indeed ambidextrous. To do so, a sign test is used. We set the significance level at 0.05. After conducting the hypothesis, there’s no reason to reject the null hypothesis. Therefore, we claim that Son shoots with his right and left foot the same number of times.

from statsmodels.stats.descriptivestats import sign_test
test = sign_test(l, mu0 = 0)
pvalue = test[1]

if pvalue < 0.05:
    print("P-value amounts to", str(pvalue)[:5], "- We reject null hypothesis - Heung-Min Son is not ambidextrous")
else:
    print("P-value amounts to", str(pvalue)[:5], " - We do not reject null hypothesis - Heung-Min Son is ambidextrous")

P-value amounts to 0.142  - We do not reject null hypothesis - Heung-Min Son is ambidextrous