Homework 1 - MVA
Januš Grm
2025-01-17
#Importing the data
mydata <- read.table("Sleep_health_and_lifestyle_dataset.csv", header=TRUE, sep=",",check.names = FALSE)
head(mydata)## Person ID Gender Age Occupation Sleep Duration Quality of Sleep
## 1 1 Male 27 Software Engineer 6.1 6
## 2 2 Male 28 Doctor 6.2 6
## 3 3 Male 28 Doctor 6.2 6
## 4 4 Male 28 Sales Representative 5.9 4
## 5 5 Male 28 Sales Representative 5.9 4
## 6 6 Male 28 Software Engineer 5.9 4
## Physical Activity Level Stress Level BMI Category Blood Pressure Heart Rate
## 1 42 6 Overweight 126/83 77
## 2 60 8 Normal 125/80 75
## 3 60 8 Normal 125/80 75
## 4 30 8 Obese 140/90 85
## 5 30 8 Obese 140/90 85
## 6 30 8 Obese 140/90 85
## Daily Steps Sleep Disorder
## 1 4200 None
## 2 10000 None
## 3 10000 None
## 4 3000 Sleep Apnea
## 5 3000 Sleep Apnea
## 6 3000 InsomniaA data frame with 374 observations on the following 14 variables: Unit of observation: Person - Person ID: A unique number for each person.
Gender: Male or female.
Age: How old the person is.
Occupation: The person’s job.
Sleep Duration: How many hours they sleep each day.
Quality of Sleep: How good or bad they think their sleep is (from 1 to 10).
Physical Activity: How many minutes they exercise each day.
Stress Level: How stressed they feel (from 1 to 10).
BMI Category: Whether they are underweight, normal weight, or overweight.
Blood Pressure: A measure of how hard their blood is pushing against their arteries.
Heart Rate: How fast their heart beats per minute when resting.
Daily Steps: How many steps they take each day.
Sleep Disorder: Whether they have sleep problems like insomnia or sleep apnea.
Source: LAKSIKA THARMALINGAM (2023) Sleep Health and Lifestyle Dataset. Kaggle. https://www.kaggle.com/datasets/uom190346a/sleep-health-and-lifestyle-dataset
#Delete units to missing data
library(tidyr)
mydata <- mydata %>% drop_na()library(psych)
describe(mydata[ , c(-1,-2,-4,-9,-10,-13)])## vars n mean sd median trimmed mad min
## Age 1 374 42.18 8.67 43.0 41.84 10.38 27.0
## Sleep Duration 2 374 7.13 0.80 7.2 7.12 1.04 5.8
## Quality of Sleep 3 374 7.31 1.20 7.0 7.32 1.48 4.0
## Physical Activity Level 4 374 59.17 20.83 60.0 58.97 22.24 30.0
## Stress Level 5 374 5.39 1.77 5.0 5.36 2.97 3.0
## Heart Rate 6 374 70.17 4.14 70.0 69.74 2.97 65.0
## Daily Steps 7 374 6816.84 1617.92 7000.0 6732.67 1482.60 3000.0
## max range skew kurtosis se
## Age 59.0 32.0 0.26 -0.92 0.45
## Sleep Duration 8.5 2.7 0.04 -1.29 0.04
## Quality of Sleep 9.0 5.0 -0.21 -0.77 0.06
## Physical Activity Level 90.0 60.0 0.07 -1.27 1.08
## Stress Level 8.0 5.0 0.15 -1.33 0.09
## Heart Rate 86.0 21.0 1.22 2.21 0.21
## Daily Steps 10000.0 7000.0 0.18 -0.42 83.66- Stress Level - the median is 5.0, indicating that half of the sample reports stress levels below 5 and the other half above 5 on a scale of 1–10.
- The Age mean is 42.18 years, meaning the average age of individuals in the sample is approximately 42 years.
- The skewness value of -0.21 for Quality of Sleep indicates that the distribution is slightly skewed to the left.
1. RQ1
- Research question : Does the Female on average sleeps longer than Male?
- H0: The average sleep duration for females is equal to or less than that for males.
- H1: The average sleep duration for females is greater than that for males.
library(psych)
describeBy(mydata$`Sleep Duration`, g = mydata$Gender)##
## Descriptive statistics by group
## group: Female
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 185 7.23 0.88 7.2 7.23 1.33 5.8 8.5 2.7 0.07 -1.48 0.06
## ------------------------------------------------------------
## group: Male
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 189 7.04 0.69 7.2 7.06 0.89 5.9 8.1 2.2 -0.27 -1.53 0.05library(ggplot2)##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphaggplot(mydata, aes(x = `Sleep Duration`)) +
geom_histogram(binwidth = 0.2, colour="gray") +
facet_wrap(~Gender, ncol = 1) +
ylab("Frequency")
shapiro.test(mydata$`Sleep Duration`[mydata$Gender == "Female"])##
## Shapiro-Wilk normality test
##
## data: mydata$`Sleep Duration`[mydata$Gender == "Female"]
## W = 0.89858, p-value = 6.361e-10- H₀ : Distrubtion of Sleep Duration is normal.
- H₁ : Distrubtion of Sleep Duration is not normal.
- We can reject the null hypothesis at p<0.001
shapiro.test(mydata$`Sleep Duration`[mydata$Gender == "Male"])##
## Shapiro-Wilk normality test
##
## data: mydata$`Sleep Duration`[mydata$Gender == "Male"]
## W = 0.87248, p-value = 1.513e-11H₀ : Distrubtion of Sleep Duration is normal.
H₁ : Distrubtion of Sleep Duration is not normal.
We can reject the null hypothesis at p<0.001
Non - Parametric test
wilcox.test(mydata$`Sleep Duration` ~ mydata$Gender,
correct = FALSE,
exact = FALSE,
alternative = "greater")##
## Wilcoxon rank sum test
##
## data: mydata$`Sleep Duration` by mydata$Gender
## W = 20036, p-value = 0.007211
## alternative hypothesis: true location shift is greater than 0- Parametric test
t.test(mydata$`Sleep Duration` ~ mydata$Gender,
alternative = "greater",
var.equal = TRUE)##
## Two Sample t-test
##
## data: mydata$`Sleep Duration` by mydata$Gender
## t = 2.3624, df = 372, p-value = 0.009334
## alternative hypothesis: true difference in means between group Female and group Male is greater than 0
## 95 percent confidence interval:
## 0.05835527 Inf
## sample estimates:
## mean in group Female mean in group Male
## 7.229730 7.036508library(effectsize)##
## Attaching package: 'effectsize'## The following object is masked from 'package:psych':
##
## phieffectsize(wilcox.test(mydata$`Sleep Duration` ~ mydata$Gender,
correct = FALSE,
exact = FALSE,
alternative = "two.sided"))## r (rank biserial) | 95% CI
## --------------------------------
## 0.15 | [0.03, 0.26]interpret_rank_biserial(0.15)## [1] "small"
## (Rules: funder2019)Conclusion: Using the sample data, we find that there is a difference in the average sleep duration between females and males ( p = 0.007 for the Wilcoxon test). Sleep duration is higher for females. The effect size is small ( r = 0.15 ).The variable Sleep Duration is numeric, but the Shapiro-Wilk test showed that the data is not normally distributed ( p < 0.001 ). Because of this, a non-parametric test was more suitable. In conclusion, females sleep longer on average than males.
2. RQ2
Research question : There is a correlation between Age and Sleep Duration
- H0: There is no correlation between Age and Sleep Duration.
- H1: There is a correlation between Age and Sleep Duration.
library(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2ggpairs(mydata[ ,c(3,5)])
library(Hmisc)##
## Attaching package: 'Hmisc'## The following object is masked from 'package:psych':
##
## describe## The following objects are masked from 'package:base':
##
## format.pval, unitsrcorr(as.matrix(mydata[ ,c(3,5)]),
type = "spearman")## Age Sleep Duration
## Age 1.00 0.31
## Sleep Duration 0.31 1.00
##
## n= 374
##
##
## P
## Age Sleep Duration
## Age 0
## Sleep Duration 0Conclusion: We found out there is a correlation between Age and Sleep Duration. Using Spearman correlation, we found a semi strong positive correlation (ρ=0.31) between Age and Sleep Duration. The choice of Spearman was appropriate because the variables were not normally distributed. We would use Pearson if variables would be normally distributed.
3. RQ3
Research Question: Is there an association between Gender and the type of Sleep Disorder?
- H0: There is no association between Gender and the type of Sleep Disorder
- H1: There is association between Gender and the type of Sleep Disorder.
results <- chisq.test(mydata$Gender, mydata$`Sleep Disorder`,
correct = TRUE)
results##
## Pearson's Chi-squared test
##
## data: mydata$Gender and mydata$`Sleep Disorder`
## X-squared = 54.306, df = 2, p-value = 1.613e-12- Based on the Chi-Square test, there is a statistically significant association between Gender and the type of Sleep Disorder (p<0.001)
addmargins(results$observed)## mydata$`Sleep Disorder`
## mydata$Gender Insomnia None Sleep Apnea Sum
## Female 36 82 67 185
## Male 41 137 11 189
## Sum 77 219 78 374Explanation of Observed/Empirical Variables:
The observed value of 36 means that, in the sample, there are 36 Females with Insomnia. Similarly, the observed value of 11 means that there are 11 Males with Sleep Apnea. These values represent the actual counts recorded in the data.
round(results$expected, 2)## mydata$`Sleep Disorder`
## mydata$Gender Insomnia None Sleep Apnea
## Female 38.09 108.33 38.58
## Male 38.91 110.67 39.42Explanation of Expected/Theoretical Variables:
If there was no association between Gender and the type of Sleep Disorder, the expected number of Females with Insomnia would be 38.09, and the expected number of Males with Sleep Apnea would be 39.42.
round(results$res, 2)## mydata$`Sleep Disorder`
## mydata$Gender Insomnia None Sleep Apnea
## Female -0.34 -2.53 4.57
## Male 0.33 2.50 -4.53Explanation of Standardized Residual:
There is less Males with Sleep Apnea than expected at a significance level of α = 0.1%
There is more Female with Sleep Apnea than expected at a significance level of α = 0.1%
library(effectsize)
effectsize::cramers_v(mydata$Gender, mydata$`Sleep Disorder`)## Cramer's V (adj.) | 95% CI
## --------------------------------
## 0.37 | [0.28, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].interpret_cramers_v(0.37)## [1] "large"
## (Rules: funder2019)Based on the Chi-Square test, there is a statistically significant association between Gender and the type of Sleep Disorder (p<0.001) with a large effect size (V=0.37).