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https://github.com/billgewrgoulas/hypothesis-testing-on-37-seasons-of-nba

First assignment for the course Data Mining @CSE.UOI
https://github.com/billgewrgoulas/hypothesis-testing-on-37-seasons-of-nba

data-analysis data-science numpy scipy seaborn statistics

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First assignment for the course Data Mining @CSE.UOI

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# Hypothesis Testing on 37 Seasons of NBA



## Introduction



The purpose of this project is to analyze the NBA statistics Dataset from Kaggle and extract usefull information by applying various statistical analysis and hypothesis testing methods.



## Objectives



* Apply data pre-processing on the Data

* Extract usefull conclusions by creating various plots of the Data

* Apply hypothesis testing methods.






## Part 1 Statistical Analysis



#### Step 1 - Data Pre-Processing

* Keep only seasons from 1980 to 2017.

* Keep only the players of age 18 to 40 years old.

* Focus only on the main positions PG, SG, SF, PF, C.



#### Step 2 - Create the hist plots of the points of each player per season.

* We observe that the points of the players follow the chi-squere distribution.

* Use the log-scale method to better visualize the plots.



#### Step 3 Analyze how age affects player performance.

* For each player calculate the metrics: PPG, APG, BPG, TS%, PER, RPG for each season.

* Create a line plot for each metric.

* Observe that the age factor has a direct correlation with player performance and affects each metric differently.



#### Step 4 Analyze if player performance with the age is affected by the position.

* Create lineplots for the metrics using the position as the grouping variable

* Observe that there is a correlation between the player performance metrics and the age and position.

* Some metrics in certain positions are affected more as time passes.



#### Step 5 In this step we are interested in investigating whether there is a correlation between the metrics PPG, APG, RPG, BPG.

* Calculate the statistics for each player but using the data from all the seasons the player has participated.

* Create the scatter plots for all pairs of the metrics in order to find any linear relationships.

* To extract more accurate results perform the Pearson Correlation Test on the Data.

* From the results of the test we can tell that there are statistical significant relationships between the metrics.

* Do the same for the positions and extract more specific correlations.



#### Step 6 In this part we want to study if there is a difference between the performance of players who play in a different position.

* Use the metrics from the previous step and create barplots with the average values for different positions, with 95% -confidence intervals.

* Observe that the players perform differently when playing in different positions.



## Part 2 Hypothesis Testing



#### Question 1 In this part we want to find which position is the best for a player, by studying the PER metric in different positions.

* First create the corresponding barplot PER-Position similary to step 6.

* Observe that all positions seem equal in terms of Player Efficiency Rate.

* In order to decide which position is the most efficient we will make the following assumptions:

*  -H0 Null hypothesis: There is no significant difference between the PER in different positions.

*  -H1 Alternate hypothesis: There is significant difference between the PER in different positions.

* Using the Student T-Test we conclude that there are some significant differences of the means in different positions.



#### Question 2 In this part we will focus our attention on player Russell Westbrook, who has achieved a significant number of Triple-Doubles.

* First using the data we will find the chance of his team winning when he has achieved triple-double and compare it to the probability of his team winning regardless if he has achiaved a tripple double, in order to understand if this is beneficial for his team.

* Subsequently we will assume the following:

*  -H0: There is no dependence between a victory and the triple-double Of Russel

*  -H1: There is a correlation between a victory and the triple-double Of Russel

* In this case we will apply the Chi-Squere Test of Independence to test the Hypothesis.

* From the results we find that the H0 is rejected thus there is correlation between a victory and the triple-doubles Of Russel.



#### Question 3 In this part we will study if there is a correlation between the number of assists peripheral players give to one team (the backcourt - PG, SG) and the points scored by the tall ones in the team (the frontcourt - SF, PF).

* To test this we are going to use the  Pearson Correlation Coefficient.

* First we will calculate the observations for each team and for each Season and then apply the test.

* From the results we can conclude that there is positive linear relationship between the metrics with coefficient = 0.58.



#### Question 4 In this part we will find out if teams score an average of more points at home vs away.

* We will examine the teams: Boston Celtics and Minnesota Timberwolves and assume the following:

*  -H0: There is no significant difference between points at home vs away.

*  -H1: There is a significant difference between points at home vs away.

* In order to test these assumptions we will perform two experiments:

* First we will use the Student T-Test and afterwords we will do a permutation test

* From the results of the two tests we can reject the H0 for Boston Celtics but not for Minnesota Timberwolves.