RPubs link information

RPubs Link: http://rpubs.com/Nikitha/StatisticsAssignment3

Introduction

• The body mass index (BMI) has been a steadfast measurement of health and wellness discussions for decades.
• Body mass index (BMI) measures body fat based on your height and weight.
• It’s a quick way to know whether you’re at a healthy weight, underweight, overweight, or obese.
• In general, the higher your BMI, the greater your risk of developing serious weight-related health problems.
• Some common conditions related to overweight and obesity include: premature death, cardiovascular diseases, high blood pressure, osteoarthritis, some cancers and diabetes.
• Determining the body type based on BMI index is help us to keep maintain healthy diet and body

Introduction Cont.

• A pattern may be observed based on the sex of the individual and the type of the body shape they possess.
• The determination of such kinds of pattern in the early stages may prevent the future fatalities by spreading awareness among the people and hence lead them to a healthier diet.
• This analysis is for understanding such pattern if existing.

Problem Statement

• The goal of this analysis is to determine whether the different body type has any relationship with the gender variation.
• Hence a null hypothesis test states that there is no correlation between the gender and the different body type.
• A Chi-square Test of Assosciation is to be applied on the data to verify the acceptance of the Null Hypothesis
• While performing the chi-square test, the value obtained is to be compared with the critical value to accept or reject the hypothesis

Data

• The data that is being used for the analysis is obtained from the below link: https://www.kaggle.com/yersever/500-person-gender-height-weight-bodymassindex/download
• This dataset is an open data hence can be used by others for the academic purposes.

Data Cont.

• Variables of the selected data set are: Gender, Height, Weight, Index
• We are considering the Gender and the index of the above variables for the analysis of the problem statement.
• Gender gives the gender of the different people with different height and weight whereas index implies on the different type of body type
• Both Gender and Index variables have been converted to factor.
• Gender variable is given labels of 2 levels with “MALE” and “FEMALE” levels
• Index variable is given labels of 6 levels with “Extremely Weak”,“Weak”,“Normal”,“Overweight”,“Obesity”,“Extreme Obesity”.

Descriptive Statistics and Visualisation

• Data is imported using readr function.
• Summary of the compete data is obtained using summary().
• Appropriate variable converion is applied for gender and index.
• The data is cleaned in the gender column for filtering the unknown value befor chi-square test.
• The function colSums() is used for viewing any missing values

BODY_MEASUREMENTS <- read.csv("C:/Users/Niki/Desktop/Statistics/Assignment3/500-person-gender-height-weight-bodymassindex/500_Person_Gender_Height_Weight_Index.csv",stringsAsFactors = FALSE)
head(BODY_MEASUREMENTS)

summary(BODY_MEASUREMENTS)

##     Gender              Height          Weight        Index      
##  Length:500         Min.   :140.0   Min.   : 50   Min.   :0.000  
##  Class :character   1st Qu.:156.0   1st Qu.: 80   1st Qu.:3.000  
##  Mode  :character   Median :170.5   Median :106   Median :4.000  
##                     Mean   :169.9   Mean   :106   Mean   :3.748  
##                     3rd Qu.:184.0   3rd Qu.:136   3rd Qu.:5.000  
##                     Max.   :199.0   Max.   :160   Max.   :5.000

BODY_MEASUREMENTS= BODY_MEASUREMENTS %>% filter(BODY_MEASUREMENTS$Gender!='unknown') 
BODY_MEASUREMENTS$Gender <- factor(BODY_MEASUREMENTS$Gender, levels=c("Male","Female"), 
                            labels = c("MALE","FEMALE"))
BODY_MEASUREMENTS

BODY_MEASUREMENTS$Index <- factor(BODY_MEASUREMENTS$Index, levels=c("0","1","2","3","4","5"), 
                                   labels = c("Extremely Weak","Weak","Normal","Overweight","Obesity","Extreme Obesity"))
colSums(is.na(BODY_MEASUREMENTS))

## Gender Height Weight  Index 
##      0      0      0      0

Decsriptive Statistics Cont.

• The next step is to plot a table with the different body type that is levelled in the above section with the gender.
• A proportion table of the above obtained distribution is calculated.
• A visual summary for for explaining any possible association is obtained using barplot

table(BODY_MEASUREMENTS$Index,BODY_MEASUREMENTS$Gender)

##                  
##                   MALE FEMALE
##   Extremely Weak     6      7
##   Weak              15      7
##   Normal            28     41
##   Overweight        32     36
##   Obesity           59     71
##   Extreme Obesity  105     93

BODYTYPE = table(BODY_MEASUREMENTS$Index,BODY_MEASUREMENTS$Gender) %>% prop.table()
barplot(BODYTYPE,main="Gender with BodyType",ylab="Different Body Type proportion With Gender",
        ylim=c(0,.6),
        legend=rownames(BODYTYPE),beside=TRUE,
        args.legend=c(x = "topright",horiz=FALSE,title="BODY TYPE"),xlab="Gender", col = brewer.pal(5, name = "Blues"))

Hypothesis Testing

• The statistical Null hypothesis for the test is stated as H0 : There is no association with the body type and the gender variables.
• To test for the above hypothesis Chi-square test is applied on the gender and index variable.
• To obtain the difference between the values before and after test expected and observed values are taken.
• According to the Chi-square test of association,it is assumed that no more than 25% of the cells have expected counts below 5.
• The χ2 value obtained is 7.3085.The degree of freedom or df obtained is .
• The value α=0.05 is taken defaultively for the Chi=Square test.

CHI <- chisq.test(table(BODY_MEASUREMENTS$Index,BODY_MEASUREMENTS$Gender)) 
CHI

## 
##  Pearson's Chi-squared test
## 
## data:  table(BODY_MEASUREMENTS$Index, BODY_MEASUREMENTS$Gender)
## X-squared = 7.3085, df = 5, p-value = 0.1987

CHI$observed

##                  
##                   MALE FEMALE
##   Extremely Weak     6      7
##   Weak              15      7
##   Normal            28     41
##   Overweight        32     36
##   Obesity           59     71
##   Extreme Obesity  105     93

CHI$expected

##                  
##                    MALE FEMALE
##   Extremely Weak   6.37   6.63
##   Weak            10.78  11.22
##   Normal          33.81  35.19
##   Overweight      33.32  34.68
##   Obesity         63.70  66.30
##   Extreme Obesity 97.02 100.98

qchisq(p = .95,df = 5)

## [1] 11.0705

pchisq(q = 7.3085,df = 5,lower.tail = FALSE)

## [1] 0.1986891

Hypthesis Testing Cont.

• We apply a one-tailed hypothesis test ,since the chi-square distribution is a positive distribution.
• The one tailed critical value χ2crit, associated with α=0.05 and df= can be calculated using the qchisq().
• We obtain the value χ2crit = 11.0705 which is greater than χ2
• Since χ2 < χ2crit, we fail to reject H0.
• As R does not report the critical value, the easiest method to test H0 is to use the p-value
• To calculate the p-value, we need to find the probability of observing the sample χ2, or one more extreme, assuming there is no association in the population. We use the pchisq()
• The p-value obtained is 0.1986891. We observe that p > 0.05. Hence failed to reject H0.

Discussion

• We have deduct from the above results that statistically,there is no association with the body type and the gender variables.
• The chi-square test of association is applied to prove the above conclusion where we received the values χ2=7.3085,p>0.001
• The final goal of this analysis was to verify whether there is any relation between gender and body type which we found that non- existing.
• Hence a healthy diet is to be maintained irrespective of gender for a fit body type.

References

• [1]Data collection from Kaggle: https://www.kaggle.com/yersever/500-person-gender-height-weight-bodymassindex/download