RPubs link information

• RPubs link: http://rpubs.com/VaishRajaraman/statsAssignment3

Introduction

• Deforestation refers to the act of clearing wide areas of forest which is then used for non - forest purposes
• Approximately 18 million acres of forest area are lost every year according to the United Nations’ Food and Agriculture Organization (FAO)
• The loss of trees cause climate change, soil erosion, increase in green house gases and a lot of other problems
• Deforestation is considered to be one of the contributing factors to global climate change, because of which many countries are taking measures to increase their forest cover

Problem Statement

• The aim of this report is to investigate if there is a decrease in forest land area. The data was collected for east-asia and pacific regions for the years 2010 and 2015.

• The sample was measured twice, in 2010 and in 2015. This makes it dependent or paired samples.

• Since these two are dependent samples, paired sample t-test is used to determine if there was any statistically significant change in the forest land area in these regions.

Data

• The data was collected from worldbank website using world development indicators database https://databank.worldbank.org/source/world-development-indicators#

• Countries under the region East asia and Pacific were selected for the investigation and the forest area(in sq km) of these countries were considered for the years 2010 and 2015

Data Cont.

• The dataset has four vaiables - Series Name , Country Name, 2010, 2015 and 42 observations.
• We are going to deal with variables ‘2010’ and ‘2015’
• Country Name - Unique name of countries
• ‘2010’ - forest area in sq km in the year 2010
• ‘2015’ - forest area in sq km in the year 2015

ForestArea<- eastAsia_Pacific
head(ForestArea)

Descriptive Statistics

• Detailed summary statistics are obtained from summarise() function

For year ‘2010’

ForestArea %>% summarise(Min = min(`2010`,na.rm = TRUE),
Q1 = quantile(`2010`,probs = .25,na.rm = TRUE),
Median = median(`2010`, na.rm = TRUE),
Q3 = quantile(`2010`,probs = .75,na.rm = TRUE),
Max = max(`2010`,na.rm = TRUE),
Mean = mean(`2010`, na.rm = TRUE),
SD = sd(`2010`, na.rm = TRUE),
n = n(),
Missing = sum(is.na(`2010`))) -> table1
knitr::kable(table1)

Decsriptive Statistics Cont.

For year ‘2015’

ForestArea %>% summarise(Min = min(`2015`,na.rm = TRUE),
Q1 = quantile(`2015`,probs = .25,na.rm = TRUE),
Median = median(`2015`, na.rm = TRUE),
Q3 = quantile(`2015`,probs = .75,na.rm = TRUE),
Max = max(`2015`,na.rm = TRUE),
Mean = mean(`2015`, na.rm = TRUE),
SD = sd(`2015`, na.rm = TRUE),
n = n(),
Missing = sum(is.na(`2015`))) -> table2
knitr::kable(table2)

Decsriptive Statistics Cont.

• side-by-side box plot is created for ‘2010’ and ‘2015’ for better visualisation of data
• we have omitted the missing data, this is because the values were not recorded for few countries. After omittion we now have 35 observations (n=35)
• from the box plot, we can observe presence of few outliers. These values are genuine values and not outliers as few countries have very high forest cover. Hence they are not dealt with as outliers and considered as normal data.

ForestArea<- na.omit(ForestArea)
ForestArea %>% select(`2010`:`2015`) %>% boxplot(horizontal = TRUE)

Visualisation

• In order to check for a statistically significant difference in forest area, we apply paired sample t-test. We first determine the normality of the distribution using histogram with normal distribution overlay. For 2010:

Visualisation Cont

For 2015:

Assumptions:

• From the histogram with normal distribution overlay we can observe that for both the years the distribution is right skewed and is not normally distributed.
• But using the central limit theorem, since we have n = 35, we can proceed with the two-sample t-test even though the normality assumption is violated when the sample size is greater than 30.

Hypthesis Testing

• Paired two sample t-test is used to test if there was any statistically significant reduction in forest area.
• The difference in forest areas in the year 2010 and 2015 is denoted by μΔ.
• The statistical hypotheses for paired sample t-test are as follows:

\[H_0: \mu_\Delta= 0 \]

\[H_A: \mu_\Delta \ne 0\] - For paired sample t-test we use C.I.= 95% and α=0.05

Hypothesis Testing Cont.

• Performing t-test for year ‘2010’ and ‘2015’ , note that since it is paired t-test we have paired = TRUE and alternative = two.sided as per the alternative hypothesis assumption.

#paired t-test:
t.test(
ForestArea$`2010`, ForestArea$`2015`,
paired = TRUE,
alternative = "two.sided"
)

## 
##  Paired t-test
## 
## data:  ForestArea$`2010` and ForestArea$`2015`
## t = -0.45411, df = 34, p-value = 0.6526
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -6618.576  4200.919
## sample estimates:
## mean of the differences 
##               -1208.828

Discussion

• From the paired sample t-test the t value is t = -0.45411 and p value reported is 0.6526. The p value is greater than α=0.05, so we fail to reject H0. Also the 95% CI is [-6618.576 , 4200.919] which captures the null hypothesis H0, so we fail to reject H0.

• From the above results, it was found that there was no statistically significant difference in the forest area from the year 2010 to 2015 in east asia and pacific region countries.

• We can say that these countries were sucessfull in maintaining their forest area over a period of 5 years and it has neither increased nor decreased.

Further Scope

• This investigation was performed only for the countries in east asia and pacific region. It can further be extended to countries of other regions or even all the countries in the world.

References

• https://www.ul.com/news/four-reasons-keep-focus-deforestation-supply-chains