Author: Milagros Ines Rodriguez Ventura

Descriptive statistics of dataset test_heart

data <- read.table("./test_heart.csv", header=TRUE, sep=",")
head(data)
##   age sex cp trestbps chol fbs restecg thalach exang oldpeak slope ca thal
## 1  63   1  3      145  233   1       0     150     0     2.3     0  0    1
## 2  37   1  2      130  250   0       1     187     0     3.5     0  0    2
## 3  41   0  1      130  204   0       0     172     0     1.4     2  0    2
## 4  56   1  1      120  236   0       1     178     0     0.8     2  0    2
## 5  57   0  0      120  354   0       1     163     1     0.6     2  0    2
## 6  57   1  0      140  192   0       1     148     0     0.4     1  0    1
##   target
## 1      1
## 2      1
## 3      1
## 4      1
## 5      1
## 6      1

1 Description of data set used in the analysis

1.2 Definition of variables
  • age: Age of the patient
  • sex: Gender of the patient. Possible values: 0 = Female, 1 = Male
  • cp: Categorical attribute indicating the type of chest pain experienced by the patient. It has four possible values
  • trestbps: Resting blood pressure of the patient
  • chol: Serum cholesterol level in mg/dl of the patient
  • fbs: Indicates whether the patient’s fasting blood sugar is greater than 120 mg/dl
  • restecg: Categorical attribute representing the results of the resting electrocardiogram. It has three possible values
  • thalach: Maximum heart rate achieved by the patient
  • exang: Indicates whether the patient experienced angina (chest pain) induced by exercise
  • oldpeak: ST depression induced by exercise relative to rest
  • slope: Slope of the peak exercise ST segment
  • ca: Number of major blood vessels colored by fluoroscopy (ranging from 0 to 3)
  • thal: Categorical attribute indicating the thalassemia type of the patient. It has three possible values: 0 for normal, 1 for fixed defect, and 2 for reversible defect
  • target: Presence of heart disease in the patient. A value of 0 signifies the absence of heart disease, while a value of 1 indicates the presence of heart disease
1.3 Unit of observation

All variables are numerical, except sex, cp, restecg and thal, that are categorical

1.4 Sample size

303 observations

2 Data manipulation

nulls_per_variable <- colSums(is.na(data))  # Nulls check per variable
# Convert categorical variables to factors
data$sexFactor <- factor(data$sex, 
                             levels = c(0, 1), 
                             labels = c("F", "M"))

data$thalFactor <- factor(data$thal, 
                             levels = c(0, 1, 2), 
                             labels = c("Normal", "Fixed defect", "Reversible defect"))
                          
# Note: I only did it with the variables sex and thal because I didn't have the references of the other categorical variables

3 Descriptive statistics

# I want to see how the cholesterol values behave depending of the gender
library(psych)
## Warning: package 'psych' was built under R version 4.3.3
describeBy(data$chol, data$sexFactor)
## 
##  Descriptive statistics by group 
## group: F
##    vars  n  mean    sd median trimmed   mad min max range skew kurtosis   se
## X1    1 96 261.3 65.09    253  255.82 60.79 141 564   423 1.31     3.71 6.64
## ------------------------------------------------------------ 
## group: M
##    vars   n   mean    sd median trimmed mad min max range skew kurtosis   se
## X1    1 207 239.29 42.78    235  238.48  43 126 353   227 0.15    -0.32 2.97

By this results, we can conclude that, on average, the women of this sample have higher cholesterol level than men. This is, 261.3 mg/dl vs. 239.29 mg/dl.

We have to take into account that the number of samples for women and men differ by over a double, so the conclusions might not be accurate, since the more samples we have, the more sure we can be of the results.

# I want to see how the maximum heart achieved behaves according to the gender
library(psych)
describeBy(data$thalach, data$sexFactor)
## 
##  Descriptive statistics by group 
## group: F
##    vars  n   mean    sd median trimmed   mad min max range  skew kurtosis   se
## X1    1 96 151.12 20.05    157  152.78 17.79  96 192    96 -0.74    -0.07 2.05
## ------------------------------------------------------------ 
## group: M
##    vars   n   mean    sd median trimmed   mad min max range  skew kurtosis   se
## X1    1 207 148.96 24.13    151  150.17 26.69  71 202   131 -0.44    -0.22 1.68

We can see that the standard deviation of the maximum heart rate achieved by the patient is higher in men than in women. This means that the values of the variable thalach are more condensed around the mean for women than for men.

Also, by looking at the median, we can conclude that for women, 50% of them have a maximum heart rate smaller than 157 and the remaining 50% have a maximum heart rate greater than 157. On the other hand, for men, the value that divides the sample is 151.

# Summary of the variables
summary(data)
##       age             sex               cp           trestbps    
##  Min.   :29.00   Min.   :0.0000   Min.   :0.000   Min.   : 94.0  
##  1st Qu.:47.50   1st Qu.:0.0000   1st Qu.:0.000   1st Qu.:120.0  
##  Median :55.00   Median :1.0000   Median :1.000   Median :130.0  
##  Mean   :54.37   Mean   :0.6832   Mean   :0.967   Mean   :131.6  
##  3rd Qu.:61.00   3rd Qu.:1.0000   3rd Qu.:2.000   3rd Qu.:140.0  
##  Max.   :77.00   Max.   :1.0000   Max.   :3.000   Max.   :200.0  
##       chol            fbs            restecg          thalach     
##  Min.   :126.0   Min.   :0.0000   Min.   :0.0000   Min.   : 71.0  
##  1st Qu.:211.0   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:133.5  
##  Median :240.0   Median :0.0000   Median :1.0000   Median :153.0  
##  Mean   :246.3   Mean   :0.1485   Mean   :0.5281   Mean   :149.6  
##  3rd Qu.:274.5   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:166.0  
##  Max.   :564.0   Max.   :1.0000   Max.   :2.0000   Max.   :202.0  
##      exang           oldpeak         slope             ca        
##  Min.   :0.0000   Min.   :0.00   Min.   :0.000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.00   1st Qu.:1.000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.80   Median :1.000   Median :0.0000  
##  Mean   :0.3267   Mean   :1.04   Mean   :1.399   Mean   :0.7294  
##  3rd Qu.:1.0000   3rd Qu.:1.60   3rd Qu.:2.000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :6.20   Max.   :2.000   Max.   :4.0000  
##       thal           target       sexFactor             thalFactor 
##  Min.   :0.000   Min.   :0.0000   F: 96     Normal           :  2  
##  1st Qu.:2.000   1st Qu.:0.0000   M:207     Fixed defect     : 18  
##  Median :2.000   Median :1.0000             Reversible defect:166  
##  Mean   :2.314   Mean   :0.5446             NA's             :117  
##  3rd Qu.:3.000   3rd Qu.:1.0000                                    
##  Max.   :3.000   Max.   :1.0000

With the summary function we can see the max and min value of each variable in the dataset, the mean (average), the median (value that is in the middle) and the 1st and 3rd quartile (the value below which 25% of the data falls and the value below which 75% of the data falls, respectively)

4 Distribution of the variables

hist(data$age,
     main = 'Distribution of age',
     xlab = 'Level of age',
     col = 'darkolivegreen3')

By the shape of the graph we can infer that the distribution of the variable age is approximately normal, because it’s somewhat symmetric, the histogram has a “bell shape” and there is an absence of significant outliers that skew the distribution.

library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.3.3
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha
ggplot(data, aes(y = age)) +
  geom_boxplot() +
  ggtitle("Boxplot - age")

From the boxplot we can also see that the distribution of the variable is quite symmetric

hist(data$trestbps,
     main = 'Distribution of trestbps',
     xlab = 'Level of trestbps',
     col = 'lightpink2')

By looking at this histogram I can say that it’s right-skewed and also that there are some outliers

library(ggplot2)
ggplot(data, aes(y=trestbps)) +
  geom_boxplot()+
  ggtitle("Boxplot - trestbps")

By looking at the boxplot I confirm the existence of outliers that might be the responsible for the skewness of the distribution

hist(data$chol,
     main = 'Distribution of chol',
     xlab = 'Level of chol',
     col = 'lightblue3')

The same as before, by looking at the histogram we can say that the distribution of the variable chol is right skewed due to the existence of outliers

library(ggplot2)
ggplot(data, aes(y=chol)) +
  geom_boxplot()+
  ggtitle("Boxplot - chol")

In the boxplot we can clearly see the existence of outliers and that if we removed them the distribution would be approximately normal

hist(data$thalach,
     main = 'Distribution of thalach',
     xlab = 'Level of thalach',
     col = 'darkorange3')

I can conclude that the distribution of the variable is left-skewed because the majority of the data points are clustered on the right side of the distribution, and the tail extends towards the left

library(ggplot2)
ggplot(data, aes(y=thalach)) +
  geom_boxplot()+
  ggtitle("Boxplot - thalach")

We can see that the median is displaced into the side of Q3 and also that here is one outlier

hist(data$oldpeak,
     main = 'Distribution of oldpeak',
     xlab = 'Level of oldpeak',
     col = 'plum4')

We can say that as the level of oldpeak increases, the frequency of appearance of the value decreases

library(ggplot2)
ggplot(data, aes(y=oldpeak)) +
  geom_boxplot()+
  ggtitle("Boxplot - oldpeak")

We see that most of the data points are concentrated in the smaller values of the variable and that there are some bigger outliers

Besides the previous analysis I was intrigued to see if there was any correlation between the age and the cholesterol levels so I did a scatterplot:

plot(x=data$age, y=data$chol, 
     main = "Correlation age-cholesterol",  
     xlab = "age",          
     ylab = "chol",          
     col = ifelse(data$sexFactor == "M", "deepskyblue3", "tomato3"),                 
     pch = 16)

legend("topright", legend = c("Female", "Male"), 
       col = c("deepskyblue3", "tomato3"), pch = 16, bty = "n")

I can conclude that there is not an apparent correlation between the variables and I can’t neither see a clear pattern between men and women