T.Test

Data Science Day 20:

When we are watching Soccer games, at the beginning of the match, the screen will show the basic info for each team. Suppose we want to know is there any difference between the average age between Real Madrid and Barcelona players, What statistical test should we use?

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Answer:

We can use T-test to determine whether there is a significant difference between the means of two groups.

T-test assumptions:

• The dependent variable is Normally distributed
  Note, identify the probability of a particular outcome
• Independent observations
• The dependent variable is Continuous.  
• No outliers

Example: Kaggle FIFA 2018 dataset

Null Hypothesis H0: There is NO significant difference between the age of  Real Madrid and Barcelona’s players.

1. We choose the variable Age and Club (Real Madrid, Barcelona).
   

   # import packages
   import numpy as np
   from scipy import stats
   import pandas as pd
   import matplotlib.pyplot as plt
   import statistics as st
   import seaborn as sns
   
   data1= data[["club","age"]]
   data2=data1.loc[data1["club"].isin(["Real Madrid CF", "FC Barcelona"])
   

    

2. Histogram Graph for Age 

data3=data1.loc[data1["club"].isin(["Real Madrid CF"])]
data4=data1.loc[data1["club"].isin(["FC Barcelona"])]

plt.hist(data3.age, bins="auto", color="c" ,edgecolor="k",alpha=0.5)
plt.hist(data4.age, bins="auto", color="r", alpha=0.5)
plt.xlabel('Age')
plt.ylabel('Frequency')
plt.title('Age Distribution in Barcelona vs MFC')

plt.show()

3. Density Plot of Age

#kde plot
df=pd.DataFrame({"mfc": data3.age, "barcelona":data4.age,})
ax=df.plot.kde()
plt.title("Density Plot for Players' Age in Barcelona vs MFC")
plt.show()

       4. Statistical T-test 

stats.ttest_ind(data3.age,data4.age, equal_var=False)
Ttest_indResult(statistic=-1.9061510499479299, pvalue=0.062416380021536121)

Conclusion:

Although the Histogram graph does not show a normal distribution, the Density Plot represents some feature of the Normality for Age Distribution. Since the P-value= 0.06, we will Accept the Null Hypothesis: 
There is No significant difference in players age between Real Madrid and Barcelona. 

Additional Info:

We used Non-direction (two sided) Ttest to generate the results,  but one question we can ask ourselves is how sure are we about the results?

1. Type 1 error, Reject a null hypothesis that is True
   Predict there is a difference while in reality there’s no.
   p=0.05,  there is  a 5% chance we are making type 1 error
2. Type 2 error, Accept a null hypothesis that is false
   Predict there  is no difference when the reality has one

In the previous example, we have a 2-level independent variable Club (Barcelona, Real Madrid), and one dependent variable age.

What if we have an independent variable more than 2 levels?
AC Milan, Barcelona, and Real Madrid ? 

That will be ANOVA’s show!

Happy Studying! 🍉