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library(readr)
library(dplyr)
library(ggplot2) 
library(rmarkdown) 

library(readxl)
alos <- read_excel("C:/Users/thyagu/rmit/applied analytics/Assign2/average-length-of-stay-multilevel-data (2).xlsx",skip=12,col_names = TRUE)

Expecting logical in O30023 / R30023C15: got '‡'Expecting logical in O30024 / R30024C15: got '‡'Expecting logical in O30025 / R30025C15: got '‡'Expecting logical in O30026 / R30026C15: got '‡'Expecting logical in O30027 / R30027C15: got '‡'Expecting logical in O30028 / R30028C15: got '‡'New names:
* `` -> ...9
* `` -> ...11
* `` -> ...13
* `` -> ...15
* `` -> ...17
* ... and 1 more problem

alos <- alos %>% rename(Peer_group = `Peer group`)
alos <- alos %>% rename(Avg_len_stay = `Average length of stay (days)`)
alos$Avg_len_stay <- as.numeric(alos$Avg_len_stay)

NAs introduced by coercion

alos_df <- alos %>% select(Peer_group,Avg_len_stay)
alos_df <- alos_df %>% filter(Peer_group %in% c("Large hospitals","Medium hospitals"))
alos_df <- na.omit(alos_df)
alos_df$Peer_group <- factor(alos_df$Peer_group,ordered = FALSE)
knitr::kable(head(alos_df[52:58,])) 

Peer_group	Avg_len_stay
Large hospitals	5.0
Large hospitals	4.8
Large hospitals	4.9
Medium hospitals	3.5
Medium hospitals	3.2
Medium hospitals	2.7

#outliers
summary(alos_df$Avg_len_stay)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   2.400   3.500   3.894   4.800  13.200 

boxplot(alos_df$Avg_len_stay)
benchmark <- 4.800 + 1.5*IQR(alos_df$Avg_len_stay) #benchmark is 8.4
benchmark 

[1] 8.4

dim(alos_df)

[1] 6593    2

head(alos_df,5)

class(alos_df$Avg_len_stay)

[1] "numeric"

alos_clean <- alos_df %>% filter(Avg_len_stay < benchmark)
alos_clean

dim(alos_clean)  

[1] 6335    2

#Descriptive Statistics and Visualization
alos_Largehosp <- alos_clean %>% filter(Peer_group == "Large hospitals")
dim(alos_Largehosp)

[1] 4225    2

alos_Mediumhosp <- alos_clean %>% filter(Peer_group == "Medium hospitals")
dim(alos_Mediumhosp)

[1] 2110    2

hist(alos_Largehosp$Avg_len_stay,main = "Avg length of stay in days for Large hospitals",col = "green",xlab = "Avg length of stay",breaks = 20,xlim=c(0,10))

hist(alos_Mediumhosp$Avg_len_stay,main = "Avg length of stay in days for Medium hospitals",col = "blue",xlab = "Avg length of stay",breaks = 20,xlim=c(0,10))

summary_table <- alos_clean %>% group_by(Peer_group)  %>% summarise(Mean=mean(Avg_len_stay,na.rm=TRUE),
                                                                    Median=median(Avg_len_stay,na.rm=TRUE),
                                                                    IQR=IQR(Avg_len_stay,na.rm=TRUE),
                                                                    SD=sd(Avg_len_stay,na.rm=TRUE),
                                                                    Var=var(Avg_len_stay,na.rm=TRUE),
                                                                    Min=min(Avg_len_stay,na.rm=TRUE),
                                                                    Max=max(Avg_len_stay,na.rm=TRUE),
                                                                    Q1=quantile(Avg_len_stay,probs=.25,na.rm=TRUE),
                                                                    Q3=quantile(Avg_len_stay,probs=.75,na.rm=TRUE),
                                                                    n = n(),
                                                                    Missing = sum(is.na(Avg_len_stay)))
knitr::kable(summary_table,digits=round(1))  

Peer_group	Mean	Median	IQR	SD	Var	Min	Max	Q1	Q3	n	Missing
Large hospitals	3.7	3.4	2.3	1.6	2.6	1.2	8.3	2.4	4.7	4225	0
Medium hospitals	3.5	3.3	1.9	1.5	2.2	1.0	8.3	2.4	4.3	2110	0

#Hypothesis testing(Normality test)

qqnorm(alos_Largehosp$Avg_len_stay)
qqline(alos_Largehosp$Avg_len_stay) 

qqnorm(alos_Mediumhosp$Avg_len_stay)
qqline(alos_Mediumhosp$Avg_len_stay)

install.packages("car")

Error in install.packages : Updating loaded packages

library(car)
leveneTest(Avg_len_stay~Peer_group,data=alos_clean)

Levene's Test for Homogeneity of Variance (center = median)
        Df F value    Pr(>F)    
group    1  18.416 1.802e-05 ***
      6333                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#0.00001802 

# unequal variance t-test
res <- t.test(Avg_len_stay~Peer_group,data=alos_clean,var.equal = FALSE, alternative = "two.sided")
res 

    Welch Two Sample t-test

data:  Avg_len_stay by Peer_group
t = 5.9202, df = 4545.1, p-value = 3.453e-09
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.1623117 0.3230370
sample estimates:
 mean in group Large hospitals mean in group Medium hospitals 
                      3.742864                       3.500190 

# t value
round(res$statistic,2)

   t 
5.92 

# df` degree of freedom
round(res$parameter) 

  df 
4545 

# p-value
(res$p.value)

[1] 3.453018e-09

# conf.int
round(res$conf.int,2) 

[1] 0.16 0.32
attr(,"conf.level")
[1] 0.95

# sample estimates
round(res$estimate,2)

 mean in group Large hospitals mean in group Medium hospitals 
                          3.74                           3.50 

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