RPubs link information

• R-Pubs Link- http://rpubs.com/tenzingsangay0/434110

Introduction

• Link: https://catalog.data.gov/dataset/new-york-city-leading-causes-of-death-ce97f
• Death is indeed inevitable.
• Hence, in this report we check if the difference in death rate for male and female is equal.
• Data represents number of deaths and death rates for the top causes of all deaths from 2007 to 2014 in the city of New York, by selected characteristics such as gender, age, and race/ethnicity.
• Age adjusted death rate in our analysis to free our analysis from a biased sample.

Problem Statement

• The statistical analysis aims to check whether the death rate in the case of male and female is the same.
• Data visualization is provided to invesigate and the compare the age-adjusted death rate in both the sex.
• The Levene’s test of homogeneity of variance was then undergone.
• As the data being compared here were independent we went forward with the Two-sample t-test.

Data

• The open-dataset was collected form “https://catalog.data.gov/dataset/new-york-city-leading-causes-of-death-ce97f” website.
• Our Dataset consist of 7 variables and 1094 observations.
• Death, Death Rates and Age Ajusted death rates are given for 7 years from 2007 to 2014.
• The variables included in the dataset are:
  • Year (Data_Type: Integer)
  • Leading Causes (Data_Type: Charcter)
  • Sex (Data_Type: factor Levels: Male, Female)
  • Race (Data_Type: Charcter)
  • Deaths (Data_Type: Numeric)
  • Death Rate (Data_Type: Numeric)
  • Age Adjusted Dead Rate (Data_Type: Numeric)

Data Cont.

• As the dataset was untidy, certain data preprocessing steps were taken. Some of the steps included:
• Sex variable was factorized and better labelling was added.
• Deaths, Death Rates and Age adjusted Death Rate intially represented as charcters were converted to numeric datatype.
• Age adjusted death rate include a method that accounts for differences in age structure or age composition so that populations of different age distributions can be compared. We considered this variable to undergo our investigation to prevent any biased sampling.

Descriptive Statistics and Visualisation

• For visualization of data we plotted a box plot to investigate the age adjusted death rate in male and female.
• Missing values and Outliers were observed in the box plot and neccessary measures were taken to handle these data issues.
• Missing values were imputed to zero and outliers were handled using the capping method.

boxplot(CauseOfDeath$`Age Adjusted Death Rate`~ CauseOfDeath$Sex,
        main="Boxplot of Age Adjusted Death Rate After Handling Outlier", 
        ylab="Age Adjusted Death",xlab="Sex")

CauseOfDeath$`Age Adjusted Death Rate`[is.na(CauseOfDeath$`Age Adjusted Death Rate`)]<-0

Descriptive Statistics and Visualisation Cont..

cap <- function(x){
  quantiles <- quantile(x, c(.05, .25, .75, .95), na.rm = TRUE)
  x[ x< quantiles[2] - 1.5 * IQR(x) ] <- quantiles[1]
  x[ x> quantiles[3] + 1.5 * IQR(x) ] <- quantiles[4]
  x}
CauseOfDeath$`Age Adjusted Death Rate` <- CauseOfDeath$`Age Adjusted Death Rate` %>% cap()
boxplot(CauseOfDeath$`Age Adjusted Death Rate`~CauseOfDeath$Sex,
        main="Boxplot of Age Adjusted Death Rate After Handling Outlier",
        ylab="Age Adjusted Death Rate",xlab="Sex")

Decsriptive Statistics Cont.

• A summary of the variable being compared is shown.

CauseOfDeath %>% group_by(Sex) %>% summarise(Min = min(`Age Adjusted Death Rate`,na.rm = TRUE),
                                           Q1 = quantile(`Age Adjusted Death Rate`,probs = .25,na.rm = TRUE),
                                           Median = median(`Age Adjusted Death Rate`, na.rm = TRUE),
                                           Q3 = quantile(`Age Adjusted Death Rate`,probs = .75,na.rm = TRUE),
                                           Max = max(`Age Adjusted Death Rate`,na.rm = TRUE),
                                           Mean = mean(`Age Adjusted Death Rate`, na.rm = TRUE),
                                           SD = sd(`Age Adjusted Death Rate`, na.rm = TRUE),
                                           Missing = sum(is.na(`Age Adjusted Death Rate`)))->table1




knitr::kable(table1)

Levene Test

• Thanks to CLT, we know that the sampling distribution of the mean will be normally distributed when the sample size is large(i.e n>30).
• Homogeneity of variance, is tested using Levene’s test.
• Here we compare the variance of male and female age adjusted death rate.
• We find p-value = 0.2945
• Hence Levene’s test shows that we fail to reject null hypothesis and the test is statistically insignificant. i.e p>0.05 hence equal variance can be assured.
• Thereafter we undergo the Two sample t-test for Equal Variance.

leveneTest(`Age Adjusted Death Rate` ~ Sex, data = CauseOfDeath,na.rm=TRUE)

Hypothesis Testing

t.test(
  `Age Adjusted Death Rate` ~ Sex,
  data = CauseOfDeath,
  var.equal = FALSE,
  alternative = "two.sided")

## 
##  Welch Two Sample t-test
## 
## data:  Age Adjusted Death Rate by Sex
## t = -1.4938, df = 1090.4, p-value = 0.1355
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -12.91705   1.75050
## sample estimates:
## mean in group Female   mean in group Male 
##             34.57639             40.15967

• The following results were observed: Degree of freedom = 1090.4, p-value = 0.1355.
• According to p-value method as p-value >0.05, we fail to reject Ho.
• Hence it is not statistically significant.

\[H_0: \mu_1 = \mu_2 \] - The Null hypothesis states that the Age adjusted Death Rate is equal in the case of Male and Female \[H_A: \mu_1 \ne \mu_2\] - The Alternate hypothesis states that the age adjusted death rate is not equal in the case of Male and Female.

Discussion

• The hypothesis testing resulted with a p-value of 0.1355 which is greater than 0.05 so we can state that the test statistically insignificant.
• Hence, we conclude that the age adjusted death rate in the case of male and female is the same.
• Our dataset was limited in this analysis as only a death rate for a single city was taken into consideration.
• In the dataset more data can be taken into consideration to get a more precise analysis.

References

• https://catalog.data.gov/dataset/new-york-city-leading-causes-of-death-ce97f
• RMIT Course Material.
• //data.cityofnewyork.us/Health/New-York-City-Leading-Causes-of-Death/jb7j-dtam