Importing data

We need to import the dataset first. The dataset can be downloaded from here. (If using windows, press “control” button and click here it will open in your default browser)

setwd("D:/Pilot_Study/Descriptive-statistics-Mann-Whitney-U-test-and-Chi-squared-test")

library(readxl)

LathamPark <- read_excel("D:/Pilot_Study/Data.xlsx", 
                   sheet = "LathamPark")


LakeDanielPark <- read_excel("D:/Pilot_Study/Data.xlsx", 
                         sheet = "LakeDanielPark")

Auduban <- read_excel("D:/Pilot_Study/Data.xlsx", 
                             sheet = "Auduban")

Installing packages

# install.packages("tidyverse")
library(tidyverse)
# install.packages("devtools")
# devtools::install_github("thomasp85/patchwork")
library(patchwork)
# install.packages("gdata")
library(gdata)
# install.packages("flextable")
library(flextable)
#install.packages("leaflet")
library(leaflet)

library(readxl)
data <- read_excel("Data_for_map.xlsx")




m <- leaflet() %>% 
  addTiles() %>% 
  addMarkers( data = data, lng = ~Long, lat = ~lat, 
              popup = ~ Name)
m

hybrd.ifelse <- function(x) {
  mutate_all(x, ~ifelse(is.na(.), 0, .)) 
}

LathamPark <- hybrd.ifelse(LathamPark)
Auduban <- hybrd.ifelse(Auduban)
LakeDanielPark <- hybrd.ifelse(LakeDanielPark)

Volume_Calc <- function(dataframe, 
                   Zone1, Zone2, Zone3, Zone4, PieceD) {
  length <-  (Zone1 + Zone2 + Zone3+ Zone4)
  diameter_m <- (PieceD/100) # Converting diameter into meter
  radius <- diameter_m/2     # Radius = d/2
  volume <- (length*pi*(radius^2))  # L*pi*r^2
  a <- cbind(dataframe, length, diameter_m, radius, volume)
}

LathamPark <- Volume_Calc(LathamPark, LathamPark$Zone1, LathamPark$Zone2, 
         LathamPark$Zone3, LathamPark$Zone4, LathamPark$PieceD)



Auduban <- Volume_Calc(Auduban, Auduban$Zone1, Auduban$Zone2, 
                         Auduban$Zone3, Auduban$Zone4, Auduban$PieceD)

LakeDanielPark <- Volume_Calc(LakeDanielPark, LakeDanielPark$Zone1, 
                                LakeDanielPark$Zone2, 
                                LakeDanielPark$Zone3, LakeDanielPark$Zone4, 
                                LakeDanielPark$PieceD)

Auduban_V <- mutate (Auduban, "Auduban Volume" = volume) %>% 
  select("Auduban Volume")
LakeDanielPark_V <- mutate(LakeDanielPark, "Lake Daniel Park volume" = volume) %>% 
  select("Lake Daniel Park volume")
LathamPark_V <- mutate(LathamPark, "Latham Park volume" = volume) %>% 
  select("Latham Park volume")

Volume <- gdata::cbindX(LakeDanielPark_V, Auduban_V,
       LathamPark_V)

Volume <- pivot_longer(Volume, c("Lake Daniel Park volume", "Latham Park volume", 
                       "Auduban Volume" ), names_to = "Field",
             values_to = "Volume") %>% drop_na()

ggplot(Volume, aes(x = Field, y = Volume))+
  geom_boxplot()+
  theme_bw()+
  annotate(geom="text", x=1.3, y=6.5, label="Very Large tree",
           color="red")

Volume_hist<- function(dataframe, Site){
  a <- filter(dataframe, Field == Site)
  b <- ggplot(a, aes(x = Volume, fill= Site))+
    geom_histogram()+
    labs (x = Site)+
    theme_bw()+
    theme(legend.position = "none")
}

Auduban_V_ggplot <- Volume_hist(Volume, "Auduban Volume")
LathamPark_V_ggplot <- Volume_hist(Volume, "Latham Park volume")
LakeDanielPark_V_ggplot <- Volume_hist(Volume, "Lake Daniel Park volume")

All_site_hist <- 
  ggplot(Volume, aes(x = Volume, fill = Volume))+
  geom_histogram()+
  labs (x = "All sites")+
  theme_bw()+
  theme(legend.position = "none")

(Auduban_V_ggplot | LathamPark_V_ggplot) / 
  (LakeDanielPark_V_ggplot | All_site_hist)

mean(LakeDanielPark$volume)

## [1] 0.1504215

sd(LakeDanielPark$volume)

## [1] 0.163793

median(LakeDanielPark$volume)

## [1] 0.07696902

mean(Auduban$volume)

## [1] 0.3286007

sd(Auduban$volume)

## [1] 1.04468

median(Auduban$volume)

## [1] 0.05677486

mean(LathamPark$volume)

## [1] 0.08859561

sd(LathamPark$volume)

## [1] 0.08513687

median(LathamPark$volume)

## [1] 0.04846692

a <- Volume %>% 
  group_by(Field) %>%
  summarise(
    "Volume Per 100 meters"  = (sum(Volume))/2,  # Per 100 meter
    mean = mean(Volume, na.rm = TRUE),
    sd = sd(Volume, na.rm = TRUE),
    median = median(Volume, na.rm = TRUE),
    IQR = IQR(Volume, na.rm = TRUE))

## `summarise()` ungrouping output (override with `.groups` argument)

a <- flextable(a)
autofit(a, add_w = 0.001, add_h = 0.1)

Kruskal Wallis test

Kruskal Wallis test is a non - parametric test alternative to ANOVA. This methos is useful for testing whether sample originates from the same population. The reasons for the test: • Volume is a continious data unlike total count of wood logs • The dataset is not normal (very skewed data)

boxplot(Volume~Field, data = Volume)

The result of Kurskal Wallis test is:

kruskal.test(Volume ~ Field, data = Volume)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Volume by Field
## Kruskal-Wallis chi-squared = 1.4147, df = 2, p-value = 0.493

There is no statistically significant between volume of individual pieces of Lake Daniel, Lake Latham Park and Auduban Preserve.

Frequency of Large wood per 100 meters

Field <- c("Latham Park", "Lake Daniel" , "Auduban")

Values <- c(33, 25, 60)

Pieces <- data.frame(Field, Values)

Pieces$Per100 <- Values/2

ggplot(data = Pieces, aes(x = Field, y = Per100))+
  geom_col(width = 0.5)+
  theme_bw()+
  ylab("Pieces per 100 meters")+
  xlab("")

Ho: p1 = p2= p3 Ha: At least one of the site is different from other

data <- Pieces$Per100
chisq.test(data)

## 
##  Chi-squared test for given probabilities
## 
## data:  data
## X-squared = 8.5508, df = 2, p-value = 0.01391

The difference in the frequency of Large Wood is statistically significant

Channel Orientation

CountLP <- LathamPark %>% group_by(`Channel Orient`) %>% count(name = "LathamPark") 
CountAu <- Auduban %>% group_by(`Channel Orient`) %>% count(name = "Auduban")
CountLD <- LakeDanielPark %>% group_by(`Channel Orient`) %>% count(name = "LakeDanielPark")





a <- CountLP %>% right_join(CountAu) %>% right_join(CountLD)

## Joining, by = "Channel Orient"
## Joining, by = "Channel Orient"

flextable::flextable(a)

Degradation Class

mean(Auduban$`Piece Decay`)

## [1] 2.028571

sd(Auduban$`Piece Decay`)

## [1] 0.8570028

mean(LathamPark$`Piece Decay`)

## [1] 2.142857

sd(LathamPark$`Piece Decay`)

## [1] 0.853564

mean(LakeDanielPark$`Piece Decay`)

## [1] 2.08

sd(LakeDanielPark$`Piece Decay`)

## [1] 0.8124038

Jams

Sites <- c("Auduban Preserve", "Latham Park", "Lake Daniel Park")
`No. of Jams` <- c(2, 1, 0)

data.frame(Sites, `No. of Jams`)

##              Sites No..of.Jams
## 1 Auduban Preserve           2
## 2      Latham Park           1
## 3 Lake Daniel Park           0

To find the actual length, we need to add all four zones together. The four zones are: zone 1, zone 2, zone 3, and zone 4. We can use a function to perform the task

library(readxl)

LathamPark <- read_excel("D:/Pilot_Study/Data.xlsx", 
                   sheet = "LathamPark")


LakeDanielPark <- read_excel("D:/Pilot_Study/Data.xlsx", 
                         sheet = "LakeDanielPark")

Auduban <- read_excel("D:/Pilot_Study/Data.xlsx", 
                             sheet = "Auduban")

LathamPark <- hybrd.ifelse(LathamPark)
Auduban <- hybrd.ifelse(Auduban)
LakeDanielPark <- hybrd.ifelse(LakeDanielPark)


LathamPark <- Volume_Calc(LathamPark, LathamPark$Zone1, LathamPark$Zone2, 
         LathamPark$Zone3, LathamPark$Zone4, LathamPark$PieceD)



Auduban <- Volume_Calc(Auduban, Auduban$Zone1, Auduban$Zone2, 
                         Auduban$Zone3, Auduban$Zone4, Auduban$PieceD)

LakeDanielPark <- Volume_Calc(LakeDanielPark, LakeDanielPark$Zone1, 
                                LakeDanielPark$Zone2, 
                                LakeDanielPark$Zone3, LakeDanielPark$Zone4, 
                                LakeDanielPark$PieceD)

Selecting our Length column

Auduban_Length <- mutate (Auduban, "Auduban length" = length) %>% 
  select("Auduban length")
LakeDanielPark_Lenght <- mutate(LakeDanielPark, "Lake Daniel Park length" = length) %>% 
  select("Lake Daniel Park length")
LathamPark_Length <- mutate(LathamPark, "Latham Park length" = length) %>% 
  select("Latham Park length")

Length <- gdata::cbindX(Auduban_Length, LakeDanielPark_Lenght,
       LathamPark_Length)

Length <- pivot_longer(Length, c("Lake Daniel Park length", "Latham Park length", 
                       "Auduban length" ), names_to = "Field",
             values_to = "length") %>% drop_na()

Perforning Kruskal Wallis Test on Length

ggplot(data = Length, aes(Field, y = length))+
  geom_boxplot()+
  theme_bw()

kruskal.test(length ~ Field, data = Length)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  length by Field
## Kruskal-Wallis chi-squared = 5.2773, df = 2, p-value = 0.07146

Performing Kurskal Wallis Test on Diameter

Auduban_Diameter <- Auduban %>% 
  select(diameter_m) %>% 
  rename(diameter_Audobon = diameter_m)

LakeDanielPark_Diameter <- LakeDanielPark %>% 
  select(diameter_m) %>% 
  rename(diameter_LakeDanielPark = diameter_m)


LathamPark_Diameter <- LathamPark %>% 
  select(diameter_m) %>% 
  rename(diamater_LathamPark = diameter_m)

Diameter <- gdata::cbindX(Auduban_Diameter, LakeDanielPark_Diameter,
       LathamPark_Diameter)

Diameter <- pivot_longer(Diameter, c("diameter_Audobon", "diameter_LakeDanielPark", 
                       "diamater_LathamPark" ), names_to = "Field",
             values_to = "diameter") %>% drop_na()

ggplot(data = Diameter, aes(x = diameter, fill = "red"))+
  geom_histogram()+
  theme_bw()+
  theme(legend.position = "none")+
  facet_wrap(~Field)

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

kruskal.test(diameter ~ Field, data = Diameter)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  diameter by Field
## Kruskal-Wallis chi-squared = 5.3667, df = 2, p-value = 0.06833