We use the data from https://www.lock5stat.com/datapage3e.html
I propose the following 10 questions based on my understanding of the data.
Is there a significant difference in the average GPA between male and female college students?
Is there a significant difference in the average number of early classes between the first two class years and other class years?
Do students who identify as “larks” have significantly better cognitive skills (cognition z-score) compared to “owls”?
Is there a significant difference in the average number of classes missed in a semester between students who had at least one early class (EarlyClass=1) and those who didn’t (EarlyClass=0)?
Is there a significant difference in the average happiness level between students with at least moderate depression and normal depression status?
Is there a significant difference in average sleep quality scores between students who reported having at least one all-nighter (AllNighter=1) and those who didn’t (AllNighter=0)?
Do students who abstain from alcohol use have significantly better stress scores than those who report heavy alcohol use?
Is there a significant difference in the average number of drinks per week between students of different genders?
Is there a significant difference in the average weekday bedtime between students with high and low stress (Stress=High vs. Stress=Normal)?
Is there a significant difference in the average hours of sleep on weekends between first two year students and other students?
We will explore the questions in detail.
# call in data set
data <- read.csv("https://www.lock5stat.com/datasets3e/SleepStudy.csv")
# display first six rows
head(data)## Gender ClassYear LarkOwl NumEarlyClass EarlyClass GPA ClassesMissed
## 1 0 4 Neither 0 0 3.60 0
## 2 0 4 Neither 2 1 3.24 0
## 3 0 4 Owl 0 0 2.97 12
## 4 0 1 Lark 5 1 3.76 0
## 5 0 4 Owl 0 0 3.20 4
## 6 1 4 Neither 0 0 3.50 0
## CognitionZscore PoorSleepQuality DepressionScore AnxietyScore StressScore
## 1 -0.26 4 4 3 8
## 2 1.39 6 1 0 3
## 3 0.38 18 18 18 9
## 4 1.39 9 1 4 6
## 5 1.22 9 7 25 14
## 6 -0.04 6 14 8 28
## DepressionStatus AnxietyStatus Stress DASScore Happiness AlcoholUse Drinks
## 1 normal normal normal 15 28 Moderate 10
## 2 normal normal normal 4 25 Moderate 6
## 3 moderate severe normal 45 17 Light 3
## 4 normal normal normal 11 32 Light 2
## 5 normal severe normal 46 15 Moderate 4
## 6 moderate moderate high 50 22 Abstain 0
## WeekdayBed WeekdayRise WeekdaySleep WeekendBed WeekendRise WeekendSleep
## 1 25.75 8.70 7.70 25.75 9.50 5.88
## 2 25.70 8.20 6.80 26.00 10.00 7.25
## 3 27.44 6.55 3.00 28.00 12.59 10.09
## 4 23.50 7.17 6.77 27.00 8.00 7.25
## 5 25.90 8.67 6.09 23.75 9.50 7.00
## 6 23.80 8.95 9.05 26.00 10.75 9.00
## AverageSleep AllNighter
## 1 7.18 0
## 2 6.93 0
## 3 5.02 0
## 4 6.90 0
## 5 6.35 0
## 6 9.04 0## Question 1: Is there a significant difference in the average GPA between male and female college students?
# perform t-test
t_test_1 <- t.test(GPA ~ Gender, data = data, alternative = "two.sided")
# display t-test results
print(t_test_1)##
## Welch Two Sample t-test
##
## data: GPA by Gender
## t = 3.9139, df = 200.9, p-value = 0.0001243
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## 0.09982254 0.30252780
## sample estimates:
## mean in group 0 mean in group 1
## 3.324901 3.123725## Question 2: Is there a significant difference in the average number of early classes between the first two class years and other class years?
# define data group
data$ClassGroup <- ifelse(data$ClassYear %in% c(1, 2), "FirstTwoYears", "OtherYears")
# perform t-test
t_test_2 <- t.test(NumEarlyClass ~ ClassGroup, data = data)
# display t-test results
print(t_test_2)##
## Welch Two Sample t-test
##
## data: NumEarlyClass by ClassGroup
## t = 4.1813, df = 250.69, p-value = 4.009e-05
## alternative hypothesis: true difference in means between group FirstTwoYears and group OtherYears is not equal to 0
## 95 percent confidence interval:
## 0.4042016 1.1240309
## sample estimates:
## mean in group FirstTwoYears mean in group OtherYears
## 2.070423 1.306306## Question 3: Do students who identify as “larks” have significantly better cognitive skills (cognition z-score) compared to “owls”?
# define data subset
data_subset <- subset(data, LarkOwl %in% c("Lark", "Owl"))
# perform t-test
t_test_3 <- t.test(CognitionZscore ~ LarkOwl, data = data_subset, alternative = "greater")
# display t-test results
print(t_test_3)##
## Welch Two Sample t-test
##
## data: CognitionZscore by LarkOwl
## t = 0.80571, df = 75.331, p-value = 0.2115
## alternative hypothesis: true difference in means between group Lark and group Owl is greater than 0
## 95 percent confidence interval:
## -0.1372184 Inf
## sample estimates:
## mean in group Lark mean in group Owl
## 0.09024390 -0.03836735## Question 4: Is there a significant difference in the average number of classes missed in a semester between students who had at least one early class and those who didn’t?
# perform t-test
t_test_4 <- t.test(ClassesMissed ~ EarlyClass, data = data, alternative = "two.sided")
# display t-test results
print(t_test_4)##
## Welch Two Sample t-test
##
## data: ClassesMissed by EarlyClass
## t = 1.4755, df = 152.78, p-value = 0.1421
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.2233558 1.5412830
## sample estimates:
## mean in group 0 mean in group 1
## 2.647059 1.988095## Question 5: Is there a significant difference in the average happiness level between students with at least moderate depression and normal depression status?
# define data group
data$DepressionGroup <- ifelse(data$DepressionScore >= 10, "ModerateOrHigher", "Normal")
# perform t-test
t_test_5 <- t.test(Happiness ~ DepressionGroup, data = data)
# display t-test results
print(t_test_5)##
## Welch Two Sample t-test
##
## data: Happiness by DepressionGroup
## t = -5.6339, df = 55.594, p-value = 6.057e-07
## alternative hypothesis: true difference in means between group ModerateOrHigher and group Normal is not equal to 0
## 95 percent confidence interval:
## -7.379724 -3.507836
## sample estimates:
## mean in group ModerateOrHigher mean in group Normal
## 21.61364 27.05742## Question 6: Is there a significant difference in average sleep quality scores between students who reported having at least one all-nighter and those who didn’t?
# preform t-test
t_test_6 <- t.test(AverageSleep ~ AllNighter, data = data)
# display t-test results
print(t_test_6)##
## Welch Two Sample t-test
##
## data: AverageSleep by AllNighter
## t = 4.4256, df = 42.171, p-value = 6.666e-05
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## 0.4366603 1.1685667
## sample estimates:
## mean in group 0 mean in group 1
## 8.073790 7.271176## Question 7: Do students who abstain from alcohol use have significantly better stress scores than those who report heavy alcohol use?
# define data subset
data_subset <- subset(data, AlcoholUse %in% c("Abstain", "Heavy"))
# perform t-test
t_test_7 <- t.test(StressScore ~ AlcoholUse, data = data_subset, alternative = "less")
# display t-test results
print(t_test_7)##
## Welch Two Sample t-test
##
## data: StressScore by AlcoholUse
## t = -0.62604, df = 28.733, p-value = 0.2681
## alternative hypothesis: true difference in means between group Abstain and group Heavy is less than 0
## 95 percent confidence interval:
## -Inf 2.515654
## sample estimates:
## mean in group Abstain mean in group Heavy
## 8.970588 10.437500## Question 8: Is there a significant difference in the average number of drinks per week between students of different genders?
# perform t-test
t_test_8 <- t.test(Drinks ~ Gender, data = data)
# display t-test results
print(t_test_8)##
## Welch Two Sample t-test
##
## data: Drinks by Gender
## t = -6.1601, df = 142.75, p-value = 7.002e-09
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -4.360009 -2.241601
## sample estimates:
## mean in group 0 mean in group 1
## 4.238411 7.539216## Question 9: Is there a significant difference in the average weekday bedtime between students with high and low stress?
# define data group
data$StressGroup <- ifelse(data$StressScore >= 15, "HighStress", "LowStress")
# perform t-test
t_test_9 <- t.test(WeekdayBed ~ StressGroup, data = data, alternative = "two.sided")
# display t-test results
print(t_test_9)##
## Welch Two Sample t-test
##
## data: WeekdayBed by StressGroup
## t = -1.0746, df = 87.048, p-value = 0.2855
## alternative hypothesis: true difference in means between group HighStress and group LowStress is not equal to 0
## 95 percent confidence interval:
## -0.4856597 0.1447968
## sample estimates:
## mean in group HighStress mean in group LowStress
## 24.71500 24.88543## Question 10: Is there a significant difference in the average hours of sleep on weekends between first two year students and other students?
# define data group
data$YearGroup <- ifelse(data$ClassYear %in% c(1, 2), "FirstTwoYears", "OtherYears")
# perform t-test
t_test_10 <- t.test(WeekendSleep ~ YearGroup, data = data)
# display t-test results
print(t_test_10)##
## Welch Two Sample t-test
##
## data: WeekendSleep by YearGroup
## t = -0.047888, df = 237.36, p-value = 0.9618
## alternative hypothesis: true difference in means between group FirstTwoYears and group OtherYears is not equal to 0
## 95 percent confidence interval:
## -0.3497614 0.3331607
## sample estimates:
## mean in group FirstTwoYears mean in group OtherYears
## 8.213592 8.221892