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library(readr)
library(dplyr)

Registered S3 method overwritten by 'dplyr':
  method           from
  print.rowwise_df     

Attaching package: 㤼㸱dplyr㤼㸲

The following objects are masked from 㤼㸱package:stats㤼㸲:

    filter, lag

The following objects are masked from 㤼㸱package:base㤼㸲:

    intersect, setdiff, setequal, union

library(ggplot2) 
library(rmarkdown) 

Registered S3 methods overwritten by 'htmltools':
  method               from         
  print.html           tools:rstudio
  print.shiny.tag      tools:rstudio
  print.shiny.tag.list tools:rstudio

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

w chunk by clicking the Insert Chunk button on the toolbar or by pressing Ctrl+Alt+I.

sum(is.na(alos_df))

[1] 0

boxplot(alos_df$Avg_len_stay)

benchmark <- 4.800 + 1.5*IQR(alos_df$Avg_len_stay) #benchmark is 8.4
alos_clean <- alos_df %>% filter(Avg_len_stay < benchmark) 
dim(alos_clean)

[1] 6335    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

NA

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")

WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:

https://cran.rstudio.com/bin/windows/Rtools/
Installing package into 㤼㸱C:/Users/thyagu/Documents/R/win-library/3.6㤼㸲
(as 㤼㸱lib㤼㸲 is unspecified)
trying URL 'https://cran.rstudio.com/bin/windows/contrib/3.6/car_3.0-7.zip'
Content type 'application/zip' length 1556318 bytes (1.5 MB)
downloaded 1.5 MB

package ‘car’ successfully unpacked and MD5 sums checked

The downloaded binary packages are in
    C:\Users\thyagu\AppData\Local\Temp\RtmpCwdM8h\downloaded_packages

library(car)

Loading required package: carData
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     

Attaching package: 㤼㸱car㤼㸲

The following object is masked from 㤼㸱package:dplyr㤼㸲:

    recode

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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