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Introduction

• The Student Performance Data set, which is available on Kaggle, provides significant insights into students’ academic performance.
• This data set contains a diverse variety of features that provide a full picture of students’ accomplishments, behaviors, and characteristics.
• The data set contains data on students’ demographics, parental backgrounds, test results, and study habits.
• This data set can be used by researchers, educators, and data enthusiasts to investigate concerns regarding student achievement, find trends, and draw conclusions about the primary determinants of academic success.

Introduction Cont.

• In this study, we aim to investigate the relationship between gender and test preparation course.
• We will use statistical analysis to explore whether there is a significant difference in test preparation course of gender.

Problem Statement

• The primary question driving this investigation is whether gender has a significant impact on test.preparation.course.
• We want to determine male or female are associated to complete test preparation course.
• To answer this question, we will utilize statistical methods to analyze the data and draw conclusions.
• In this assignment, we have to check if there is any statistical significant difference or if there is any association between test.preparation.course and gender(male and female) by hypothesis testing of association.
• There are many variables in the data set. There are a total of 1001 individuals in which 483 are male and 519 are women.
• We have chosen the data set gender and test.preparation.course to check if there is any association between them.

Data

This data set contains a diverse variety of features that provide a full picture of students’ accomplishments, behaviors, and characteristics. Data consists of variables of different types characters as well as numeric.

• gender: Here the student’s gender is shown(female/male)
• race/ethnicity: Here the student’s race is shown under 5 group,(group A, group B, group C, group D, group E)
• parental.level.of.education: Here student’s parental highest level of education completed is shown.
• lunch: Here represent the lunch type as standard or free/reduced
• test.preparation.course: Here shown test preparation course was completed or not.
• math.score: Shows marks for the student’s mathematics exam.
• reading.score: Shows marks for the student’s reading exam.
• writing.score: Shows marks for the student’s writing exam.

For this analysis, we will use open data obtained from the https://www.https://www.kaggle.com/datasets/spscientist/students-performance-in-exams/data

Descriptive Statistics and Visualisation

• We will begin by summarizing the important variables in our investigation.
• This will involve calculating descriptive statistics such as mean, median, and standard deviation for income based on different education levels.
• Additionally, we will create visualizations, such as box plots and histograms, to explore the distribution of test preparation course for each gender category.

#check current directory
getwd() 

## [1] "E:/RMIT/APPLIED ANALYTICS/Assignments/final"

# set directory
setwd("E:/RMIT/APPLIED ANALYTICS/Assignments/final") 

# load student performance data
st_performance <- read.csv("E:/RMIT/APPLIED ANALYTICS/Assignments/final/StudentsPerformance.csv") 

# view the data set
View(st_performance) 

# produce the first 1-6 data in the data set
print.data.frame(head(st_performance)) 

##   gender race.ethnicity parental.level.of.education        lunch
## 1 female        group B           bachelor's degree     standard
## 2 female        group C                some college     standard
## 3 female        group B             master's degree     standard
## 4   male        group A          associate's degree free/reduced
## 5   male        group C                some college     standard
## 6 female        group B          associate's degree     standard
##   test.preparation.course math.score reading.score writing.score
## 1                    none         72            72            74
## 2               completed         69            90            88
## 3                    none         90            95            93
## 4                    none         47            57            44
## 5                    none         76            78            75
## 6                    none         71            83            78

# checking variable types
str(st_performance) 

## 'data.frame':    1000 obs. of  8 variables:
##  $ gender                     : chr  "female" "female" "female" "male" ...
##  $ race.ethnicity             : chr  "group B" "group C" "group B" "group A" ...
##  $ parental.level.of.education: chr  "bachelor's degree" "some college" "master's degree" "associate's degree" ...
##  $ lunch                      : chr  "standard" "standard" "standard" "free/reduced" ...
##  $ test.preparation.course    : chr  "none" "completed" "none" "none" ...
##  $ math.score                 : int  72 69 90 47 76 71 88 40 64 38 ...
##  $ reading.score              : int  72 90 95 57 78 83 95 43 64 60 ...
##  $ writing.score              : int  74 88 93 44 75 78 92 39 67 50 ...

# gender converted from character to factor using the as.factor() function and the levels() function
st_performance$gender <- as.factor(st_performance$gender)
levels(st_performance$gender) 

## [1] "female" "male"

# test preparation course converted from character to factor using the as.factor() function and the levels() function
st_performance$test.preparation.course <- as.factor(st_performance$test.preparation.course)
levels(st_performance$test.preparation.course) 

## [1] "completed" "none"

# check missing values
sum(is.na(st_performance)) 

## [1] 0

# print gender count
gender_count <- summary(st_performance$gender) 
gender_count

## female   male 
##    518    482

# print test preparation count on "completed" & "none"
test_preparation_count <- summary(st_performance$test.preparation.course)  
test_preparation_count

## completed      none 
##       358       642

Decsriptive Statistics Cont.

# Statistical summary of test preparation course with respect to male and female.

# Convert the 'test.preparation.course' variable to numeric 

st_performance$test.preparation.course <- as.numeric(st_performance$test.preparation.course)

#  perform the summarization

st_performance %>%
  group_by(gender) %>%
  summarise(Min = min(test.preparation.course, na.rm = TRUE),
            Q1 = quantile(test.preparation.course, probs = 0.25, na.rm = TRUE),
            Median = median(test.preparation.course, na.rm = TRUE),
            Q3 = quantile(test.preparation.course, probs = 0.75, na.rm = TRUE),
            Max = max(test.preparation.course, na.rm = TRUE),
            Mean = mean(test.preparation.course, na.rm = TRUE),
            SD = sd(test.preparation.course, na.rm = TRUE),
            n = n(),
            Missing = sum(is.na(test.preparation.course))) -> table1
knitr::kable(table1)

# visualize the relationship between gender and test preparation course

table <- 
  table(st_performance$test.preparation.course, st_performance$gender)%>% 
  prop.table(margin = 2)
knitr::kable(table)

# Descriptive visualization - Bar plot

barplot(table, ylab = "Preparation within group", ylim = c(0, .9), 
        legend = rownames(table), beside = TRUE, 
        args.legend = c(x = "top", horiz = TRUE, title = "Test Preparation Course"), 
        xlab = "Gender", col = c("yellow", "green"), border = "#69b3a2")

Hypothesis Testing

• The Null Hypothesis is as follows:

  H0:There is no association in the population between gender and completion of test preparation course.

• The Alternative Hypothesis is as follows:

  HA:There is an association in the population between gender and completion of test preparation course.

• The Chi-square Test of Association was chosen as the hypothesis test for this data set because we are interested in the link between gender and exam preparation course, both of which are categorical variables.

# calculate the chi-squared value using the chisq.test() function.

chi1 <- chisq.test(
  table(st_performance$gender, st_performance$test.preparation.course))
chi1

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  table(st_performance$gender, st_performance$test.preparation.course)
## X-squared = 0.015529, df = 1, p-value = 0.9008

# check the observed and expected values

chi1$observed

##         
##            1   2
##   female 184 334
##   male   174 308

chi1$expected

##         
##                1       2
##   female 185.444 332.556
##   male   172.556 309.444

# find the critical value

qchisq(p = .95, df = 1)

## [1] 3.841459

# find the p-value

pchisq(q = 0.015529, df = 1, lower.tail = FALSE)

## [1] 0.900828

Discussion

• The Chi-squared value (0.015529) was less than the critical value (3.841459). This means we failed to reject the Null Hypothesis.
• The p-value (0.900828) is greater than the significance level of 0.05. Therefore, the result is NOT statistically significant.

The experiment began with the question of whether females or males were more likely to complete a test preparation course. The Chi-square Test of Association was conducted to investigate if there was a relationship between gender and test preparation course. The findings failed to reject the Null Hypothesis since they demonstrated no correlation between the two variables and were not statistically significant. As a result, they are inconclusive. The investigation’s strength is its relatively high sample size (n = 1000). However, there are numerous limits to this analysis. Some examples include not knowing if the students are from the same school, not knowing the students’ ages, the students being only from the United States, and so on. Future research investigating the relationship between gender and test preparation course should include additional information such as age, school, and socioeconomic level to produce a clearer and more significant result. There was no correlation between gender and completion of a test preparation course in this study. The findings cannot be generalized to the whole population due to a lack of statistical significance.

References

• Data Source: https://www.https://www.kaggle.com/datasets/spscientist/students-performance-in-exams/data