Intro to R:Data Dive 7

Dataset:English Premier League

#importing libraries
library(tidyverse)
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library(ggrepel)

Loading Dataset

data <-read.csv('C:/Downloads/final_dataset.csv')
colnames(data)
##  [1] "X"             "Date"          "HomeTeam"      "AwayTeam"     
##  [5] "FTHG"          "FTAG"          "FTR"           "HTGS"         
##  [9] "ATGS"          "HTGC"          "ATGC"          "HTP"          
## [13] "ATP"           "HM1"           "HM2"           "HM3"          
## [17] "HM4"           "HM5"           "AM1"           "AM2"          
## [21] "AM3"           "AM4"           "AM5"           "MW"           
## [25] "HTFormPtsStr"  "ATFormPtsStr"  "HTFormPts"     "ATFormPts"    
## [29] "HTWinStreak3"  "HTWinStreak5"  "HTLossStreak3" "HTLossStreak5"
## [33] "ATWinStreak3"  "ATWinStreak5"  "ATLossStreak3" "ATLossStreak5"
## [37] "HTGD"          "ATGD"          "DiffPts"       "DiffFormPts"

Hypothesis 1: Does the Home Team Score More Goals on Average than the Away Team.

Null Hypothesis : The mean number of goals scored by the Home Team (FTHG) is equal to or less than the mean number of goals scored by the Away Team (FTAG).

Alternative Hypothesis : The mean number of goals scored by the Home Team (FTHG) is greater than the mean number of goals scored by the Away Team (FTAG).

Alpha Level (α)=0.05 (common significance level).

Power Level (1 - β)=0.80 (common power level).

Minimum Effect Size: Let’s assume a minimum effect size of 0.5 goals per game.

data<- data %>%
  select(FTAG,FTHG)
# Calculate mean 
home_team_mean <- mean(data$FTHG)
away_team_mean <- mean(data$FTAG)
home_team_mean
## [1] 1.527485

The average number of goals scored by the home team is 1.52

away_team_mean
## [1] 1.130263

The average number of goals scored by the away team is 1.13

Conducting t-test

t_test_result1 <- t.test(data$FTHG, data$FTAG, alternative = "two.sided")
t_test_result1
## 
##  Welch Two Sample t-test
## 
## data:  data$FTHG and data$FTAG
## t = 19.13, df = 13406, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.3565204 0.4379240
## sample estimates:
## mean of x mean of y 
##  1.527485  1.130263

  • The p-value (2.2e-16) is significantly smaller than the alpha level (0.05). This indicates an extremely undefined

  • Since the p-value is less than alpha, we reject the null hypothesis.

#Visualization 
ggplot(data, aes(x = factor(1), y = FTHG)) +
  geom_boxplot(fill = "blue", alpha = 0.5) +
  geom_boxplot(aes(x = factor(2), y = FTAG), fill = "red", alpha = 0.5) +
  labs(x = "", y = "Goals") +
  theme_minimal() +
  scale_x_discrete(labels = c("Home Team", "Away Team"))

conclusion:

Based on the analysis and the small p-value, we can conclude the following:

There is extremely strong statistical evidence to suggest that the Home Team scores more goals on average than the Away Team.

Hypothesis 2-Home Team’s win streak

Null Hypothesis : The Home Team’s win streak over the last 3 games (HTWinStreak3) is not significantly different from the Away Team’s win streak over the last 3 games (ATWinStreak3).

Alternative Hypothesis:The Home Teams win streak over the last 3 games is significantly different from the Away teams win streak over the last 3 games.

alpha level= 0.05(common significance level)

power level = 0.80(common power level)

effect_size = 1 Lets assume effective size as 1

data <-read.csv('C:/Downloads/final_dataset.csv')
data<- data %>%
  select(HTWinStreak3,ATWinStreak3)

Conducting the t-test

t_test_result2 <- t.test(data$HTWinStreak3, data$ATWinStreak3, alternative = "two.sided")
t_test_result2
## 
##  Welch Two Sample t-test
## 
## data:  data$HTWinStreak3 and data$ATWinStreak3
## t = -0.1412, df = 13678, p-value = 0.8877
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.008703139  0.007533549
## sample estimates:
## mean of x mean of y 
## 0.0622807 0.0628655

Since the p-value (0.8877) is significantly greater than the alpha level we fail to reject the null hypothesis .

This means that there is not enough evidence to conclude that the Home Team’s win streak (HTWinStreak3) is significantly different from the Away Team’s win streak (ATWinStreak3).

#Visualization
ggplot(data, aes(x = HTWinStreak3)) +
  geom_histogram(binwidth = 1, fill = "yellow", alpha = 0.5) +
  geom_histogram(data = data, aes(x = ATWinStreak3), binwidth = 1, fill = "red", alpha = 0.5) +
  labs(title = "Distribution of Home Team and Away Team Win Streaks (Last 3 Games)",
       x = "Win Streak",
       y = "Frequency") +
  theme_minimal()

In summary, based on the results of the t-test there is no significant difference in win streaks between the Home Team and the Away Team.