library(readxl)
library(ggpubr)

DATASET A

DatasetA <- read_excel("C:/Users/lavan/Downloads/DatasetA.xlsx")

Independant variable StudyHours and Dependant Vriable ExamScore

Descriptive Statistics

mean(DatasetA$StudyHours)
## [1] 6.135609
sd(DatasetA$StudyHours)
## [1] 1.369224
mean(DatasetA$ExamScore)
## [1] 90.06906
sd(DatasetA$ExamScore)
## [1] 6.795224

Part 3: Check Normality

hist(DatasetA$StudyHours,
     main = "StudyHours",
     breaks = 20,
     col = "lightblue",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

The variable “StudyHours” appears normally distributed. The data looks symmetrical (most data is in the middle). The data also appears to have a proper bell curve.

hist(DatasetA$ExamScore,
     main = "ExamScores",
     breaks = 20,
     col = "lightcoral",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

The variable “ExamScore” does not appears normally distributed. The data looks negatively skewed (most data is on the right). The data does not appears to have a proper bell curve.

shapiro.test(DatasetA$StudyHours)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetA$StudyHours
## W = 0.99388, p-value = 0.9349
shapiro.test(DatasetA$ExamScore)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetA$ExamScore
## W = 0.96286, p-value = 0.006465

The Shaprio-Wilk p-value for StudyHours normality test is greater than .05 (.9349), so the data is normal. The Shapiro-Wilk p-value for the ExamScore normality test is less than .05 (.0064), so the data is not normal.

Part 4: Correlation Analysis

cor.test(DatasetA$StudyHours, DatasetA$ExamScore, method = "spearman")
## Warning in cor.test.default(DatasetA$StudyHours, DatasetA$ExamScore, method =
## "spearman"): Cannot compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  DatasetA$StudyHours and DatasetA$ExamScore
## S = 16518, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.9008825

The spearman Correlation test was selected because one variable is not normally distributed according to the histograms and the Shapiro-Wilk tests. The p-value for the correlation (.0001) is below .05. This means the results are statistically significant. The alternate hypothesis is supported. The correlation value is 0.9008. The correlation is positive, which means as StudyHours increases, ExamScore increases. The correlation value is greater than 0.50 but less than 1, which means the relationship is strong.

Part 5: Scatterplots

ggscatter(
  DatasetA,
  x = "StudyHours",
  y = "ExamScore",
  add = "reg.line",
  xlab = "StudyHours",
  ylab = "ExamScore"
)

The line of best fit is pointing to the top right. This means the diretion of the data is positive. As StudyHours increases, ExamScore increases. The dots closely hug the line. This means there is a strong relationship between the variables. The dots form a straight-line pattern. This means the data is linear. There may be one or two possible outliers, but the dots are close to the line of best fit. Therefore, they do not appear to impact the relationship between the independent and dependent variables.

Part 6: Report the Results Descriptive Statistics Study Hours: Mean = 6.14, SD = 1.37 Exam Score: Mean = 90.07, SD = 6.80 Normality (Shapiro–Wilk) Study Hours: p = 0.9349 Normal Exam Score: p = 0.0065 Not normal correlation results S = 16518, p-value < 2.2e-16 alternative hypothesis: true rho is not equal to 0 rho 0.9008825 The StudyHours (M = 6.14, SD = 1.37) was correlated with the ExamScore (M = 90.07, SD = 6.80), r(98) = .90, p < .05. The relationship was positive and strong. As the StudyHours increased, the ExamScore increased.

DATASET B

DatasetB <- read_excel("C:/Users/lavan/Downloads/DatasetB.xlsx")

Independant variable ScreenTime and Dependant Vriable SleepingHours

Descriptive Statistics

mean(DatasetB$ScreenTime)
## [1] 5.063296
sd(DatasetB$ScreenTime)
## [1] 2.056833
mean(DatasetB$SleepingHours)
## [1] 6.938459
sd(DatasetB$SleepingHours)
## [1] 1.351332

Part 3: Check Normality

hist(DatasetB$ScreenTime,
     main = "ScreenTime",
     breaks = 20,
     col = "lightblue",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

The variable “ScreenTime” does not appears normally distributed. The data looks positively skewed (most data is on the left). The data does not appears to have a proper bell curve.

hist(DatasetB$SleepingHours,
     main = "SleepingHours",
     breaks = 20,
     col = "lightcoral",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

The variable “SleepingHours” appears normally distributed. The data looks symmetrical (most data is in the middle). The data also appears to have a proper bell curve.

shapiro.test(DatasetB$ScreenTime)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetB$ScreenTime
## W = 0.90278, p-value = 1.914e-06
shapiro.test(DatasetB$SleepingHours)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetB$SleepingHours
## W = 0.98467, p-value = 0.3004

The Shaprio-Wilk p-value for ScreenTime normality test is less than .05 (.00019), so the data is not normal. The Shapiro-Wilk p-value for the SleepingHours normality test is greater than .05 (.3004), so the data is normal.

Part 4: Correlation Analysis

cor.test(DatasetB$ScreenTime, DatasetB$SleepingHours, method = "spearman")
## 
##  Spearman's rank correlation rho
## 
## data:  DatasetB$ScreenTime and DatasetB$SleepingHours
## S = 259052, p-value = 3.521e-09
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.5544674

The spearman Correlation test was selected because one variable is not normally distributed according to the histograms and the Shapiro-Wilk tests. The p-value for the correlation (3.521e-09) is below .05. This means the results are statistically significant. The alternate hypothesis is supported. The correlation value is -0.5544. The correlation is negative, which means as ScreenTime increases, SleepingHours Decreases. The correlation value is greater than -0.50 but less than -1, which means the relationship is strong.

Part 5: Scatterplots

ggscatter(
  DatasetB,
  x = "ScreenTime",
  y = "SleepingHours",
  add = "reg.line",
  xlab = "ScreenTime",
  ylab = "SleepingHours"
)

The line of best fit is pointing downward from left to right. This means the direction of the data is negative. As Screen Time increases, Sleeping Hours decreaseS. The dots closely hug the line. This means there is a strong relationship between the variables. The dots form a straight-line pattern. This means the data is linear. There may be one or two possible outliers, but the dots are close to the line of best fit. Therefore, they do not appear to impact the relationship between the independent and dependent variables.

Part 6: Report the Results Descriptive Statistics ScreenTime: Mean = 5.06, SD = 2.0568 SleepingHours: Mean = 6.9384, SD = 1.3513 Normality (Shapiro–Wilk) Study Hours: p = 0.0019 not Normal Exam Score: p = 0.3004 normal correlation results S = 259052, p-value = 3.521e-09 alternative hypothesis: true rho is not equal to 0 sample estimates: rho -0.5544674 The ScreenTime (M = 5.06, SD = 2.06) was negatively correlated with the SleepingHours (M = 6.94, SD = 1.35), r = −.54, p < .05. The relationship was negative and strong. As the ScreenTime increases, the SleepingHours decreases.