HOMEWORK2
2024-01-18
#Research Question1: Is there a association between physical activity level of the individual and cardiovascular disease?
#Research Quetsion2: Is there a correlation between the weight and the Systolic blood pressure (ap_hi)?
# Read the CSV file
mydata <- read.table("~/NADJA ROGANOVIC/heart_data.csv", header=TRUE, sep=",", dec=".")
#Excluding unimportant variables
mydata<- mydata[, -c(4,3,5,8,9,10,11,12)]
head(mydata)## index id weight ap_hi active cardio
## 1 0 0 62 110 1 0
## 2 1 1 85 140 1 1
## 3 2 2 64 130 0 1
## 4 3 3 82 150 1 1
## 5 4 4 56 100 0 0
## 6 5 8 67 120 0 0##Description
Unit of observation: a individual person
Sample size: 70000
Source: Kaggle databases - Risk Factors for Cardiovascular Heart Disease
weight: Weight measured in kilograms
ap_hi: Systolic blood pressure reading taken from patient
active : whether person physically active or not( Binary ;0 =No,1 = Yes )
cardio: whether person suffers from cardiovascular diseases or not(Binary ;0–no , 1‑yes )
set.seed(1)
mydata <- mydata[sample(nrow(mydata), 400), ] Now my data have 400 rows in comparison with 70000 at beginning
Data manipulation - creating factor:
mydata$activeF <- factor(mydata$active,
levels = c(0, 1),
labels = c("No", "Yes"))
mydata$cardioF <- factor(mydata$cardio,
levels = c(0, 1),
labels = c("No", "Yes"))
head(mydata)## index id weight ap_hi active cardio activeF cardioF
## 24388 24387 34842 70 140 1 1 Yes Yes
## 59521 59520 84974 53 90 1 0 Yes No
## 43307 43306 61873 86 160 1 1 Yes Yes
## 69586 69585 99392 51 110 1 0 Yes No
## 11571 11570 16539 93 120 1 0 Yes No
## 25173 25172 35941 61 130 1 0 Yes No- Descriptive statistics
mydata$weight <- as.numeric(mydata$weight)
mydata$ap_hi <- as.numeric(mydata$ap_hi)
mydata$active <- as.factor(mydata$active)
mydata$activeF <- as.factor(mydata$activeF)
mydata$cardio <- as.factor(mydata$cardio)
mydata$cardioF <- as.factor(mydata$cardioF)
summary(mydata)## index id weight ap_hi active
## Min. : 132 Min. : 177 Min. : 44.00 Min. : 11.0 0: 76
## 1st Qu.:17323 1st Qu.:24750 1st Qu.: 65.00 1st Qu.:120.0 1:324
## Median :33152 Median :47374 Median : 74.00 Median :120.0
## Mean :35427 Mean :50584 Mean : 75.65 Mean :126.4
## 3rd Qu.:55085 3rd Qu.:78579 3rd Qu.: 84.00 3rd Qu.:140.0
## Max. :69983 Max. :99974 Max. :140.00 Max. :200.0
## cardio activeF cardioF
## 0:200 No : 76 No :200
## 1:200 Yes:324 Yes:200
##
##
##
## The smallest weight in this data set is 44 kilograms, while the largest weight is 140 kilograms.
The first quartile, or 25th percentile, signifies that 25% of the weights are less than or equal to 65 kilograms.
Half (50%) of the weights are less than or equal to 74.00 kilograms.
People on average have 75.65 kilograms.
The third quartile, or 75th percentile, signifies that 75% of the weights are less than or equal to 84 kilograms.
hist(mydata$weight,
xlab = "Weight",
ylab = "Frequency",
main = "Histogram of Weight",
col = "lightblue")
hist(mydata$ap_hi,
xlab = "Systolic blood pressure",
ylab = "Frequency",
main = "Histogram of Systolic blood pressure",
col = "lightgreen")
##Research Question1: Is there a association between physical activity level of the individual and cardiovascular disease?
#Chi - Square Test
##Assumptions
- Observations must be independent.
- Check that all expected frequencies are greater than 5.
- In larger contingency tables (at least one categorical variable has more than two categories), up to 20% of the expected frequencies can be between 1 and 5, but this will reduce the power of the test.
results <- chisq.test(mydata$activeF, mydata$cardioF,
correct = TRUE)
results##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: mydata$activeF and mydata$cardioF
## X-squared = 1.9656, df = 1, p-value = 0.1609##Hypothesis:
H0: There is no association between physical activity level of the individual and cardiovascular disease.
H1: There is an association between physical activity level of the individual and cardiovascular disease
Based on sample data, we cannot reject null hypothesis, and we can say that there is no association between physical activity level of the individual and cardiovascular disease.
addmargins(results$observed)## mydata$cardioF
## mydata$activeF No Yes Sum
## No 32 44 76
## Yes 168 156 324
## Sum 200 200 400round(results$expected, 2)## mydata$cardioF
## mydata$activeF No Yes
## No 38 38
## Yes 162 162- Standardized residuals tell us whether the differences between empirical and expected frequencies are statistically significant
round(results$res, 2)## mydata$cardioF
## mydata$activeF No Yes
## No -0.97 0.97
## Yes 0.47 -0.47- There is no significant discrepancies between the actual and expected values for all categories, because all values of standardized residuals are less than 1.96 and this differences are not statistically significant at 5%.
addmargins(round(results$expected, 2))## mydata$cardioF
## mydata$activeF No Yes Sum
## No 38 38 76
## Yes 162 162 324
## Sum 200 200 400- Second and third assumptions are met, since all of the expected frequencies are greater than 1 and 5.
addmargins(round(prop.table(results$observed), 3))## mydata$cardioF
## mydata$activeF No Yes Sum
## No 0.08 0.11 0.19
## Yes 0.42 0.39 0.81
## Sum 0.50 0.50 1.00Explanation of the number 0.39 (active Yes, cardio Yes) - Out of 400 people there is 39% of people who are physically active and have cardiovascular disease
Explanation of the number 0.11 - (active No, cardio Yes) - Out of 400 people there is 11% of people who are not physically active and have cardiovascular disease
addmargins(round(prop.table(results$observed, 1), 3), 2)## mydata$cardioF
## mydata$activeF No Yes Sum
## No 0.421 0.579 1.000
## Yes 0.519 0.481 1.000Explanation of the number 0.579 (active No, cardio Yes) - Out of all people that were not physically active 57.9% of them have cardiovascular disease.
Explanation of the number 0.519 (active Yes, cardio No) - Out of all people that were physically active 51,9% of them have no cardiovascular disease.
addmargins(round(prop.table(results$observed, 2), 3), 1)## mydata$cardioF
## mydata$activeF No Yes
## No 0.16 0.22
## Yes 0.84 0.78
## Sum 1.00 1.00Explanation of the number 0.22 (active No, cardio Yes) - Out of all people who have cardiovascular disease 22% of them are not physically active
Explanation of the number 0.84 (active Yes, cardio No) - out of all people who do not have cardiovascular disease 84% of them are physically active
library(effectsize)## Warning: package 'effectsize' was built under R version 4.3.2effectsize::cramers_v(mydata$activeF, mydata$cardioF)## Cramer's V (adj.) | 95% CI
## --------------------------------
## 0.06 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].interpret_cramers_v(0.06)## [1] "very small"
## (Rules: funder2019)- The effect size is very small meaning that we found very small effect on physical activity to cardiovascular disease.
##Fisher‘s Exactxact Probability Test of Independence
*We use this non-parametric test in case any of the assumptions cannot be met.
fisher.test(mydata$activeF, mydata$cardioF)##
## Fisher's Exact Test for Count Data
##
## data: mydata$activeF and mydata$cardioF
## p-value = 0.1606
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
## 0.3933268 1.1519814
## sample estimates:
## odds ratio
## 0.6759953H0= Odds ratio is equal to 1
H1= Odds ratio is not equal to 1
Based on sample data, we cannot reject null hypothesis.In this way we have confirmed again that there is no association between physical activity and cardiovascular disease.
interpret_oddsratio(0.6759)## [1] "very small"
## (Rules: chen2010)The effect size is very small meaning we found very small effect on physical activity to cardiovascular disease.
#Research Quetsion2: Is there a correlation between the weight and the Systolic blood pressure (ap_hi)?
Assumptions
- Both variables are numeric (This assumption is met)
- Errors are normally distributed (We assume this assumption is met, since we have enough big sample)
- Linear relationship between the variables.
library(car)## Loading required package: carDatascatterplotMatrix(mydata[, c(4, 5)], smooth = FALSE)
* For this homework, we will assume linear relationship between
variables.
cor.test(mydata$ap_hi, mydata$weight,
method = "pearson",
exact = FALSE,
use ="complete.obs")##
## Pearson's product-moment correlation
##
## data: mydata$ap_hi and mydata$weight
## t = 4.2938, df = 398, p-value = 2.209e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1147251 0.3022264
## sample estimates:
## cor
## 0.2104099H0: rho (weight, ap_hi) equal to 0
H1: rho (weight, ap_hi) not equal to 0
Based on sample data, we reject null hypothesis at p<0.001, which means that there is correlation between weight and Systolic blood pressure.