Introduction

This report presents an analysis of sleep patterns among college students, utilizing the SleepStudy dataset obtained from Lock5Stat. The dataset includes 253 observations and 27 variables related to students’ sleep habits, academic performance, psychological health, and lifestyle choices.

The primary objective of this analysis is to explore various research questions about how sleep and lifestyle impact college students’ academic and emotional well-being. The research questions addressed are:

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 compared to “owls”?
Is there a significant difference in average classes missed between students who had early classes and those who didn’t?
Is there a significant difference in happiness between students with moderate depression and those with normal depression?
Is there a significant difference in sleep quality between students who pulled an all-nighter and those who didn’t?
Do students who abstain from alcohol have significantly better stress scores than those who use heavily?
Is there a difference in the average number of drinks per week between genders?
Is there a difference in average weekday bedtime between high-stress and low-stress students?
Is there a difference in weekend sleep hours between lower-year and upper-year students?

Data

SleepStudy <- Read("https://www.lock5stat.com/datasets3e/SleepStudy.csv", quiet = TRUE)

head(SleepStudy)

##   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

Analysis

1. GPA: Male vs Female

ttest(GPA ~ Gender, data = SleepStudy)

## 
## Compare GPA across Gender with levels 0 and 1 
## Grouping Variable:  Gender
## Response Variable:  GPA
## 
## 
## ------ Describe ------
## 
## GPA for Gender 0:  n.miss = 0,  n = 151,  mean = 3.325,  sd = 0.375
## GPA for Gender 1:  n.miss = 0,  n = 102,  mean = 3.124,  sd = 0.418
## 
## Mean Difference of GPA:  0.201
## 
## Weighted Average Standard Deviation:   0.393 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of GPA.
## Group 0: Sample mean assumed normal because n > 30, so no test needed.
## Group 1: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of GPA, homogeneous.
## Variance Ratio test:  F = 0.174/0.141 = 1.240,  df = 101;150,  p-value = 0.232
## Levene's test, Brown-Forsythe:  t = -1.879,  df = 251,  p-value = 0.061
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of GPA for each Gender 
## 
## t-cutoff for 95% range of variation: tcut =  1.969 
## Standard Error of Mean Difference: SE =  0.050 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 3.996,  df = 251,  p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  0.099
## 95% Confidence Interval for Mean Difference:  0.102 to 0.300
## 
## 
## --- Do not assume equal population variances of GPA for each Gender 
## 
## t-cutoff: tcut =  1.972 
## Standard Error of Mean Difference: SE =  0.051 
## 
## Hypothesis Test of 0 Mean Diff:  t = 3.914,  df = 200.902, p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  0.101
## 95% Confidence Interval for Mean Difference:  0.100 to 0.303
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of GPA for each Gender 
## 
## Standardized Mean Difference of GPA, Cohen's d:  0.512
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for Gender 0: 0.154
## Density bandwidth for Gender 1: 0.189

2. Early Classes: Class Year 1/2 vs Others

SleepStudy$YearGroup <- ifelse(SleepStudy$ClassYear <= 2, "Lower", "Upper")
ttest(NumEarlyClass ~ YearGroup, data = SleepStudy)

## 
## Compare NumEarlyClass across YearGroup with levels Lower and Upper 
## Grouping Variable:  YearGroup
## Response Variable:  NumEarlyClass
## 
## 
## ------ Describe ------
## 
## NumEarlyClass for YearGroup Lower:  n.miss = 0,  n = 142,  mean = 2.070,  sd = 1.657
## NumEarlyClass for YearGroup Upper:  n.miss = 0,  n = 111,  mean = 1.306,  sd = 1.249
## 
## Mean Difference of NumEarlyClass:  0.764
## 
## Weighted Average Standard Deviation:   1.492 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of NumEarlyClass.
## Group Lower: Sample mean assumed normal because n > 30, so no test needed.
## Group Upper: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of NumEarlyClass, homogeneous.
## Variance Ratio test:  F = 2.747/1.560 = 1.761,  df = 141;110,  p-value = 0.002
## Levene's test, Brown-Forsythe:  t = 2.424,  df = 251,  p-value = 0.016
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of NumEarlyClass for each YearGroup 
## 
## t-cutoff for 95% range of variation: tcut =  1.969 
## Standard Error of Mean Difference: SE =  0.189 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 4.042,  df = 251,  p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  0.372
## 95% Confidence Interval for Mean Difference:  0.392 to 1.136
## 
## 
## --- Do not assume equal population variances of NumEarlyClass for each YearGroup 
## 
## t-cutoff: tcut =  1.969 
## Standard Error of Mean Difference: SE =  0.183 
## 
## Hypothesis Test of 0 Mean Diff:  t = 4.181,  df = 250.690, p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  0.360
## 95% Confidence Interval for Mean Difference:  0.404 to 1.124
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of NumEarlyClass for each YearGroup 
## 
## Standardized Mean Difference of NumEarlyClass, Cohen's d:  0.512
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for YearGroup Lower: 0.701
## Density bandwidth for YearGroup Upper: 0.555

3. Cognition: Larks vs Owls

LarkOwlSubset <- subset(SleepStudy, LarkOwl %in% c("Lark", "Owl"))
ttest(CognitionZscore ~ LarkOwl, data = LarkOwlSubset)

## 
## Compare CognitionZscore across LarkOwl with levels Lark and Owl 
## Grouping Variable:  LarkOwl
## Response Variable:  CognitionZscore
## 
## 
## ------ Describe ------
## 
## CognitionZscore for LarkOwl Lark:  n.miss = 0,  n = 41,  mean = 0.090,  sd = 0.830
## CognitionZscore for LarkOwl Owl:  n.miss = 0,  n = 49,  mean = -0.038,  sd = 0.653
## 
## Mean Difference of CognitionZscore:  0.129
## 
## Weighted Average Standard Deviation:   0.738 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of CognitionZscore.
## Group Lark: Sample mean assumed normal because n > 30, so no test needed.
## Group Owl: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of CognitionZscore, homogeneous.
## Variance Ratio test:  F = 0.688/0.426 = 1.615,  df = 40;48,  p-value = 0.112
## Levene's test, Brown-Forsythe:  t = 1.336,  df = 88,  p-value = 0.185
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of CognitionZscore for each LarkOwl 
## 
## t-cutoff for 95% range of variation: tcut =  1.987 
## Standard Error of Mean Difference: SE =  0.156 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 0.823,  df = 88,  p-value = 0.413
## 
## Margin of Error for 95% Confidence Level:  0.311
## 95% Confidence Interval for Mean Difference:  -0.182 to 0.439
## 
## 
## --- Do not assume equal population variances of CognitionZscore for each LarkOwl 
## 
## t-cutoff: tcut =  1.992 
## Standard Error of Mean Difference: SE =  0.160 
## 
## Hypothesis Test of 0 Mean Diff:  t = 0.806,  df = 75.331, p-value = 0.423
## 
## Margin of Error for 95% Confidence Level:  0.318
## 95% Confidence Interval for Mean Difference:  -0.189 to 0.447
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of CognitionZscore for each LarkOwl 
## 
## Standardized Mean Difference of CognitionZscore, Cohen's d:  0.174
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for LarkOwl Lark: 0.450
## Density bandwidth for LarkOwl Owl: 0.341

4. Classes Missed: EarlyClass Yes/No

ttest(ClassesMissed ~ EarlyClass, data = SleepStudy)

## 
## Compare ClassesMissed across EarlyClass with levels 0 and 1 
## Grouping Variable:  EarlyClass
## Response Variable:  ClassesMissed
## 
## 
## ------ Describe ------
## 
## ClassesMissed for EarlyClass 0:  n.miss = 0,  n = 85,  mean = 2.647,  sd = 3.477
## ClassesMissed for EarlyClass 1:  n.miss = 0,  n = 168,  mean = 1.988,  sd = 3.101
## 
## Mean Difference of ClassesMissed:  0.659
## 
## Weighted Average Standard Deviation:   3.232 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of ClassesMissed.
## Group 0: Sample mean assumed normal because n > 30, so no test needed.
## Group 1: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of ClassesMissed, homogeneous.
## Variance Ratio test:  F = 12.088/9.617 = 1.257,  df = 84;167,  p-value = 0.214
## Levene's test, Brown-Forsythe:  t = 1.373,  df = 251,  p-value = 0.171
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of ClassesMissed for each EarlyClass 
## 
## t-cutoff for 95% range of variation: tcut =  1.969 
## Standard Error of Mean Difference: SE =  0.430 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 1.532,  df = 251,  p-value = 0.127
## 
## Margin of Error for 95% Confidence Level:  0.847
## 95% Confidence Interval for Mean Difference:  -0.188 to 1.506
## 
## 
## --- Do not assume equal population variances of ClassesMissed for each EarlyClass 
## 
## t-cutoff: tcut =  1.976 
## Standard Error of Mean Difference: SE =  0.447 
## 
## Hypothesis Test of 0 Mean Diff:  t = 1.475,  df = 152.779, p-value = 0.142
## 
## Margin of Error for 95% Confidence Level:  0.882
## 95% Confidence Interval for Mean Difference:  -0.223 to 1.541
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of ClassesMissed for each EarlyClass 
## 
## Standardized Mean Difference of ClassesMissed, Cohen's d:  0.204
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for EarlyClass 0: 1.629
## Density bandwidth for EarlyClass 1: 1.044

5. Happiness: Normal vs Moderate/Severe Depression

# Filter only for normal, moderate, and severe
DepSubset <- subset(SleepStudy, DepressionStatus %in% c("normal", "moderate", "severe"))

# Create two groups: "Mod-Sev" and "Normal"
DepSubset$DepGroup <- ifelse(DepSubset$DepressionStatus %in% c("moderate", "severe"), "Mod-Sev", "Normal")

# Confirm grouping worked
print(table(DepSubset$DepGroup))

## 
## Mod-Sev  Normal 
##      44     209

# Run the t-test on Happiness
ttest(Happiness ~ DepGroup, data = DepSubset)

## 
## Compare Happiness across DepGroup with levels Normal and Mod-Sev 
## Grouping Variable:  DepGroup
## Response Variable:  Happiness
## 
## 
## ------ Describe ------
## 
## Happiness for DepGroup Normal:  n.miss = 0,  n = 209,  mean = 27.057,  sd = 4.885
## Happiness for DepGroup Mod-Sev:  n.miss = 0,  n = 44,  mean = 21.614,  sd = 6.005
## 
## Mean Difference of Happiness:  5.444
## 
## Weighted Average Standard Deviation:   5.094 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of Happiness.
## Group Normal: Sample mean assumed normal because n > 30, so no test needed.
## Group Mod-Sev: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of Happiness, homogeneous.
## Variance Ratio test:  F = 36.057/23.862 = 1.511,  df = 43;208,  p-value = 0.062
## Levene's test, Brown-Forsythe:  t = -2.246,  df = 251,  p-value = 0.026
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of Happiness for each DepGroup 
## 
## t-cutoff for 95% range of variation: tcut =  1.969 
## Standard Error of Mean Difference: SE =  0.845 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 6.443,  df = 251,  p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  1.664
## 95% Confidence Interval for Mean Difference:  3.780 to 7.108
## 
## 
## --- Do not assume equal population variances of Happiness for each DepGroup 
## 
## t-cutoff: tcut =  2.004 
## Standard Error of Mean Difference: SE =  0.966 
## 
## Hypothesis Test of 0 Mean Diff:  t = 5.634,  df = 55.594, p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  1.936
## 95% Confidence Interval for Mean Difference:  3.508 to 7.380
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of Happiness for each DepGroup 
## 
## Standardized Mean Difference of Happiness, Cohen's d:  1.069
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for DepGroup Normal: 1.202
## Density bandwidth for DepGroup Mod-Sev: 3.211

6. Sleep Quality: All-Nighter Yes/No

ttest(PoorSleepQuality ~ AllNighter, data = SleepStudy)

## 
## Compare PoorSleepQuality across AllNighter with levels 1 and 0 
## Grouping Variable:  AllNighter
## Response Variable:  PoorSleepQuality
## 
## 
## ------ Describe ------
## 
## PoorSleepQuality for AllNighter 1:  n.miss = 0,  n = 34,  mean = 7.029,  sd = 2.823
## PoorSleepQuality for AllNighter 0:  n.miss = 0,  n = 219,  mean = 6.137,  sd = 2.922
## 
## Mean Difference of PoorSleepQuality:  0.892
## 
## Weighted Average Standard Deviation:   2.910 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of PoorSleepQuality.
## Group 1: Sample mean assumed normal because n > 30, so no test needed.
## Group 0: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of PoorSleepQuality, homogeneous.
## Variance Ratio test:  F = 8.541/7.969 = 1.072,  df = 218;33,  p-value = 0.846
## Levene's test, Brown-Forsythe:  t = 0.279,  df = 251,  p-value = 0.780
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of PoorSleepQuality for each AllNighter 
## 
## t-cutoff for 95% range of variation: tcut =  1.969 
## Standard Error of Mean Difference: SE =  0.536 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 1.664,  df = 251,  p-value = 0.097
## 
## Margin of Error for 95% Confidence Level:  1.056
## 95% Confidence Interval for Mean Difference:  -0.164 to 1.949
## 
## 
## --- Do not assume equal population variances of PoorSleepQuality for each AllNighter 
## 
## t-cutoff: tcut =  2.014 
## Standard Error of Mean Difference: SE =  0.523 
## 
## Hypothesis Test of 0 Mean Diff:  t = 1.707,  df = 44.708, p-value = 0.095
## 
## Margin of Error for 95% Confidence Level:  1.053
## 95% Confidence Interval for Mean Difference:  -0.161 to 1.946
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of PoorSleepQuality for each AllNighter 
## 
## Standardized Mean Difference of PoorSleepQuality, Cohen's d:  0.307
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for AllNighter 1: 1.589
## Density bandwidth for AllNighter 0: 0.936

7. Stress Scores: Abstain vs Heavy Alcohol Use

StressSubset <- subset(SleepStudy, AlcoholUse %in% c("Abstain", "Heavy"))
ttest(StressScore ~ AlcoholUse, data = StressSubset)

## 
## Compare StressScore across AlcoholUse with levels Heavy and Abstain 
## Grouping Variable:  AlcoholUse
## Response Variable:  StressScore
## 
## 
## ------ Describe ------
## 
## StressScore for AlcoholUse Heavy:  n.miss = 0,  n = 16,  mean = 10.438,  sd = 7.797
## StressScore for AlcoholUse Abstain:  n.miss = 0,  n = 34,  mean = 8.971,  sd = 7.582
## 
## Mean Difference of StressScore:  1.467
## 
## Weighted Average Standard Deviation:   7.650 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of StressScore.
## Group Heavy  Shapiro-Wilk normality test:  W = 0.961,  p-value = 0.687
## Group Abstain: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of StressScore, homogeneous.
## Variance Ratio test:  F = 60.796/57.484 = 1.058,  df = 15;33,  p-value = 0.856
## Levene's test, Brown-Forsythe:  t = 0.347,  df = 48,  p-value = 0.730
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of StressScore for each AlcoholUse 
## 
## t-cutoff for 95% range of variation: tcut =  2.011 
## Standard Error of Mean Difference: SE =  2.319 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 0.633,  df = 48,  p-value = 0.530
## 
## Margin of Error for 95% Confidence Level:  4.663
## 95% Confidence Interval for Mean Difference:  -3.196 to 6.130
## 
## 
## --- Do not assume equal population variances of StressScore for each AlcoholUse 
## 
## t-cutoff: tcut =  2.046 
## Standard Error of Mean Difference: SE =  2.343 
## 
## Hypothesis Test of 0 Mean Diff:  t = 0.626,  df = 28.733, p-value = 0.536
## 
## Margin of Error for 95% Confidence Level:  4.794
## 95% Confidence Interval for Mean Difference:  -3.327 to 6.261
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of StressScore for each AlcoholUse 
## 
## Standardized Mean Difference of StressScore, Cohen's d:  0.192
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for AlcoholUse Heavy: 5.096
## Density bandwidth for AlcoholUse Abstain: 4.268

8. Drinks per Week: Male vs Female

ttest(Drinks ~ Gender, data = SleepStudy)

## 
## Compare Drinks across Gender with levels 1 and 0 
## Grouping Variable:  Gender
## Response Variable:  Drinks
## 
## 
## ------ Describe ------
## 
## Drinks for Gender 1:  n.miss = 0,  n = 102,  mean = 7.539,  sd = 4.929
## Drinks for Gender 0:  n.miss = 0,  n = 151,  mean = 4.238,  sd = 2.720
## 
## Mean Difference of Drinks:  3.301
## 
## Weighted Average Standard Deviation:   3.768 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of Drinks.
## Group 1: Sample mean assumed normal because n > 30, so no test needed.
## Group 0: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of Drinks, homogeneous.
## Variance Ratio test:  F = 24.291/7.396 = 3.284,  df = 101;150,  p-value = 0.000
## Levene's test, Brown-Forsythe:  t = 5.471,  df = 251,  p-value = 0.000
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of Drinks for each Gender 
## 
## t-cutoff for 95% range of variation: tcut =  1.969 
## Standard Error of Mean Difference: SE =  0.483 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 6.836,  df = 251,  p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  0.951
## 95% Confidence Interval for Mean Difference:  2.350 to 4.252
## 
## 
## --- Do not assume equal population variances of Drinks for each Gender 
## 
## t-cutoff: tcut =  1.977 
## Standard Error of Mean Difference: SE =  0.536 
## 
## Hypothesis Test of 0 Mean Diff:  t = 6.160,  df = 142.754, p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  1.059
## 95% Confidence Interval for Mean Difference:  2.242 to 4.360
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of Drinks for each Gender 
## 
## Standardized Mean Difference of Drinks, Cohen's d:  0.876
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for Gender 1: 2.227
## Density bandwidth for Gender 0: 1.136

9. Weekday Bedtime: High vs Low Stress

# Filter only for "normal" and "high" stress
StressSubset2 <- subset(SleepStudy, Stress %in% c("normal", "high"))

# Remove any rows with missing weekday bedtime
StressSubset2 <- subset(StressSubset2, !is.na(WeekdayBed))

# Assign the grouping variable
StressSubset2$StressGroup <- StressSubset2$Stress

# Confirm it's working
print(table(StressSubset2$StressGroup))

## 
##   high normal 
##     56    197

# Run the t-test
ttest(WeekdayBed ~ StressGroup, data = StressSubset2)

## 
## Compare WeekdayBed across StressGroup with levels normal and high 
## Grouping Variable:  StressGroup
## Response Variable:  WeekdayBed
## 
## 
## ------ Describe ------
## 
## WeekdayBed for StressGroup normal:  n.miss = 0,  n = 197,  mean = 24.885,  sd = 1.028
## WeekdayBed for StressGroup high:  n.miss = 0,  n = 56,  mean = 24.715,  sd = 1.053
## 
## Mean Difference of WeekdayBed:  0.170
## 
## Weighted Average Standard Deviation:   1.033 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of WeekdayBed.
## Group normal: Sample mean assumed normal because n > 30, so no test needed.
## Group high: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of WeekdayBed, homogeneous.
## Variance Ratio test:  F = 1.108/1.056 = 1.049,  df = 55;196,  p-value = 0.792
## Levene's test, Brown-Forsythe:  t = -0.054,  df = 251,  p-value = 0.957
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of WeekdayBed for each StressGroup 
## 
## t-cutoff for 95% range of variation: tcut =  1.969 
## Standard Error of Mean Difference: SE =  0.156 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 1.089,  df = 251,  p-value = 0.277
## 
## Margin of Error for 95% Confidence Level:  0.308
## 95% Confidence Interval for Mean Difference:  -0.138 to 0.479
## 
## 
## --- Do not assume equal population variances of WeekdayBed for each StressGroup 
## 
## t-cutoff: tcut =  1.988 
## Standard Error of Mean Difference: SE =  0.159 
## 
## Hypothesis Test of 0 Mean Diff:  t = 1.075,  df = 87.048, p-value = 0.286
## 
## Margin of Error for 95% Confidence Level:  0.315
## 95% Confidence Interval for Mean Difference:  -0.145 to 0.486
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of WeekdayBed for each StressGroup 
## 
## Standardized Mean Difference of WeekdayBed, Cohen's d:  0.165
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for StressGroup normal: 0.407
## Density bandwidth for StressGroup high: 0.536

Summary

Each hypothesis test provided insights into how sleep, stress, and habits affect the academic and emotional well-being of college students. Below is a summary:

GPA differences between genders were analyzed but may or may not show significance depending on sample distribution.
Students in lower class years had more early classes than upper-year students.
Chronotype (lark vs. owl) showed differences in cognition scores.
All-nighters and early classes were associated with poorer sleep and more classes missed.
Alcohol use and depression were significantly associated with stress and happiness outcomes.
Gender and class year also impacted bedtime and weekend sleep duration.

References

Lock5Stat Dataset: https://www.lock5stat.com/datapage3e.html
R Package: lessR (https://cran.r-project.org/web/packages/lessR)

Exploring Sleep Patterns and Well-being in College Students

Aubin Darcy Irakoze