#Overview: This document will discuss the differences in subject scores for high school students based on gender and race.

#Introduction: The dataset used for the document is the hsb2 dataset from the ‘openintro’ library in R. This dataset was performed by the National Center of Education Statistics, and was published by the UCLA institute for Digital Research & Education - Statistical Consulting.

#Exploring the data

#store the dataset
library(openintro)
## Loading required package: airports
## Loading required package: cherryblossom
## Loading required package: usdata
hsb2 <- hsb2

#summary
summary(hsb2)
##        id            gender              race               ses    
##  Min.   :  1.00   Length:200         Length:200         low   :47  
##  1st Qu.: 50.75   Class :character   Class :character   middle:95  
##  Median :100.50   Mode  :character   Mode  :character   high  :58  
##  Mean   :100.50                                                    
##  3rd Qu.:150.25                                                    
##  Max.   :200.00                                                    
##      schtyp            prog          read           write            math      
##  public :168   general   : 45   Min.   :28.00   Min.   :31.00   Min.   :33.00  
##  private: 32   academic  :105   1st Qu.:44.00   1st Qu.:45.75   1st Qu.:45.00  
##                vocational: 50   Median :50.00   Median :54.00   Median :52.00  
##                                 Mean   :52.23   Mean   :52.77   Mean   :52.65  
##                                 3rd Qu.:60.00   3rd Qu.:60.00   3rd Qu.:59.00  
##                                 Max.   :76.00   Max.   :67.00   Max.   :75.00  
##     science          socst      
##  Min.   :26.00   Min.   :26.00  
##  1st Qu.:44.00   1st Qu.:46.00  
##  Median :53.00   Median :52.00  
##  Mean   :51.85   Mean   :52.41  
##  3rd Qu.:58.00   3rd Qu.:61.00  
##  Max.   :74.00   Max.   :71.00
#head function
head(hsb2)
## # A tibble: 6 × 11
##      id gender race  ses    schtyp prog        read write  math science socst
##   <int> <chr>  <chr> <fct>  <fct>  <fct>      <int> <int> <int>   <int> <int>
## 1    70 male   white low    public general       57    52    41      47    57
## 2   121 female white middle public vocational    68    59    53      63    61
## 3    86 male   white high   public general       44    33    54      58    31
## 4   141 male   white high   public vocational    63    44    47      53    56
## 5   172 male   white middle public academic      47    52    57      53    61
## 6   113 male   white middle public academic      44    52    51      63    61

With 200 observations of 11 variables, ‘hsb2’ can be organized into two sections of variables. First are the variables about the backgrounds of the students (of which all are high school seniors). In this section, we see things like socioeconomic status, school type (whether it is public or private), and what program the students are involved in (whether it is general, academic, or vocational). although the only variables useful to us are gonna be those focusing on gender and race. The second section of variables are school subjects with their entries being scores on a standardized test relating to that subject. it is worth noting that the scores for these variables do not exceed 76 and in the case of writing do not exceed 67, so we can assume that this standardized test is not scored on a percentage system.

#Analysis part I

For the first segment of the analysis we will be focusing on the subject of gender. We will be attempting to disprove the null hypothesis that the male and female genders perform the same in each subject. The alternative hypothesis is that the male and female genders perform differently in those same subjects. All of this is given an alpha of 0.05.

#dividing the data
male <- subset(hsb2, gender == "male")
female <- subset(hsb2, gender == "female")

#two sided t-test on both genders based on all subjects
t.test(male$read, female$read)$p.value
## [1] 0.457161
t.test(male$write, female$write)$p.value
## [1] 0.0003408849
t.test(male$math, female$math)$p.value
## [1] 0.6815673
t.test(male$science, female$science)$p.value
## [1] 0.07602685
t.test(male$socst, female$socst)$p.value
## [1] 0.4656103

So the results from the gender section of the analysis reveal four p-values that go above the value of 0.05 with 3 of those values by a significant margin. The four p-values suggest that we fail to reject the null hypothesis. Therefore, there is not enough evidence to declare a difference in the subjects reading, math, science, and social studies. Writing shares a different story in which the p-value is under 0.05 by a significant margin, which means that we reject the null hypothesis, and that there is significant data to state that there is a difference in performance among writing scores.

#Analysis part II

This second segment focuses on race instead of gender, so we shall hold a similar hypothesis test in which the null hypothesis states that there is no difference and the alternative hypothesis is that there is at least one difference. Once again, the alpha value will still be 0.05.

#dividing the data
asian <- subset(hsb2, race == "asian")
afamerican <- subset(hsb2, race == "african american")
hispanic <- subset(hsb2, race == "hispanic")
white <- subset(hsb2, race == "white")

unlist(summary(aov(read ~ race, data = hsb2)))[9]
##      Pr(>F)1 
## 0.0006538515
format(unlist(summary(aov(write ~ race, data = hsb2)))[9],scientific = FALSE)
##         Pr(>F)1 
## "0.00005784516"
format(unlist(summary(aov(math ~ race, data = hsb2)))[9],scientific = FALSE)
##         Pr(>F)1 
## "0.00006840199"
format(unlist(summary(aov(science ~ race, data = hsb2)))[9],scientific = FALSE)
##            Pr(>F)1 
## "0.00000002561595"
format(unlist(summary(aov(socst ~ race, data = hsb2)))[9],scientific = FALSE)
##      Pr(>F)1 
## "0.04098048"

This time, the analysis did not wield any different results, all of the p-values ended up below the alpha of 0.05. Thus, we fail to reject the null hypothesis and state that there is not enough evidence to prove that race has an affect on the scores of students.

#Conclusions The ‘hsb2’ data set shows us that although race has no affect on the scores of a student, gender does manage to play a role in the scores of writing and not much else.

#Limitations The sample for ‘hsb2’ is quite small with only 200 entries, and although the sample does have students from a variety of backgrounds both economically and socially, the data may not be representative of the large number of students within the US.

This document was produced as a final project for MAT 143H - Introduction to Statistics (Honors) at North Shore Community College.
The course was led by Professor Billy Jackson.
Student Name: Matthew Blackman Semester: Spring 2024