week7

library(tidyverse)

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library(ggplot2)
library(dbplyr)

## 
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##     ident, sql

library(ggthemes)
library(ggrepel)

week3_dataset <- read.csv("baseball.csv",header = TRUE)

Hypothesis 1 is to compare AL and NL SLG Hypothesis 1 is to OBP of the playoffs and non-playoffs team

avg_by_league <- week3_dataset %>% 
  group_by(League)%>%
  summarize(avg = mean(SLG))

playoff_vs_nonPlayoff <- week3_dataset %>%
  group_by(Playoffs)%>%
  summarise(OBP = mean(OBP))

avg_diff <- (avg_by_league$avg[1] -
             avg_by_league$avg[2])
playoff_diff <- (playoff_vs_nonPlayoff$OBP[2] -
                 playoff_vs_nonPlayoff$OBP[1])

paste(avg_diff, playoff_diff)

## [1] "0.010586038961039 0.0137022632242649"

Alpha level (significance level): 0.05 Power level: 0.80 Choose these alpha level as 0.05 and power level as 0.8 just for common defaults hypothesis testing. effect size:

sd <- sd(week3_dataset$SLG)
Hypothesis1_D <- avg_diff/sd
Hypothesis2_D <- playoff_diff/sd
Hypothesis1_D

## [1] 0.3182154

Hypothesis2_D

## [1] 0.4118888

Hypothesis1

AL_teams <- subset(week3_dataset, League == "AL")
NL_teams <- subset(week3_dataset, League == "NL")
alpha <- 0.05

mean_al_slg <- mean(AL_teams$SLG)
mean_nl_slg <- mean(NL_teams$SLG)
var_al_slg <- var(AL_teams$SLG)
var_nl_slg <- var(NL_teams$SLG)

numerator <- (mean_al_slg - mean_nl_slg)^2
denominator <- (var_al_slg / length(mean_al_slg)) + (var_nl_slg / length(mean_nl_slg))

lr_statistic <- numerator / denominator
critical_value <- qnorm(1 - alpha)

lr_statistic

## [1] 0.05190443

critical_value

## [1] 1.644854

Fail to reject the null hypothesis since the likelihood ratio is less then critical value

Fisher

contingency_table <- table(week3_dataset$SLG, week3_dataset$League)
fisher_test_result_hypothesis1 <- chisq.test(contingency_table)

## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect

print(fisher_test_result_hypothesis1)

## 
##  Pearson's Chi-squared test
## 
## data:  contingency_table
## X-squared = 183.17, df = 161, p-value = 0.1113

since the P-value is greater then 0.05 there is no significant association between making the playoffs and the league.

Hypothesis2

playoff_teams <- subset(week3_dataset, Playoffs == 1)
non_playoff_teams <- subset(week3_dataset, Playoffs == 0)
alpha <- 0.05

mean_playoff_obp <- mean(playoff_teams$OBP)
mean_non_playoff_obp <- mean(non_playoff_teams$OBP)
var_playoff_obp <- var(playoff_teams$OBP)
var_non_playoff_obp <- var(non_playoff_teams$OBP)

numerator <- (mean_playoff_obp - mean_non_playoff_obp)^2
denominator <- (var_playoff_obp / length(playoff_teams)) + (var_non_playoff_obp / length(non_playoff_teams))

lr_statistic <- numerator / denominator
critical_value <- qnorm(1 - alpha)

lr_statistic

## [1] 7.260359

critical_value

## [1] 1.644854

Reject null hypothesis since likelihood ratio is greater then critical value

fisher

contingency_table <- table(week3_dataset$SLG, week3_dataset$Playoffs)
fisher_test_result_hypothesis1 <- chisq.test(contingency_table)

## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect

print(fisher_test_result_hypothesis1)

## 
##  Pearson's Chi-squared test
## 
## data:  contingency_table
## X-squared = 282.11, df = 161, p-value = 1.166e-08

Visualizations1

week3_dataset %>%
  ggplot() +
    geom_boxplot(mapping = aes(x = as.factor(League), y = SLG), fill = "lightblue") +
    labs(title = "Distribution of On-Base Percentage (OBP) by Playoff Status",
         x = "Playoff Status",
         y = "OBP") +
    theme_minimal()

Visualizations2

week3_dataset %>%
  ggplot() +
    geom_boxplot(mapping = aes(x = as.factor(Playoffs), y = OBP), fill = "lightblue") +
    labs(title = "Distribution of On-Base Percentage (OBP) by Playoff Status",
         x = "Playoff Status",
         y = "OBP") +
    theme_minimal()