Stats Assignment

1. This is the relationship between age and GPA1.

thesis %>% 
  drop_na(Age, GPA1) %>%                                  
  ggplot(aes(Age, GPA1)) +
  geom_point() +
  theme_minimal() +                                             
  geom_smooth(formula = y~x, method = lm, se = FALSE) +       
  labs(title = "Relationship between GPA(1) and Age",     
       x = "Age",
       y = "GPA")

cor.test(thesis$Age, thesis$GPA1)

    Pearson's product-moment correlation

data:  thesis$Age and thesis$GPA1
t = 0.25668, df = 39, p-value = 0.7988
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.2699939  0.3443673
sample estimates:
       cor 
0.04106779 

The correlation between Age and GPA was not statistically significant, r(39) = .04, ns.

2. Here is the difference between the GPA1 of students in the Business college and Arts & Sciences college.

thesis %>% 
  filter(College == "BU" | College == "AS") -> BUASCollege

t.test(BUASCollege$GPA1 ~ BUASCollege$College)

    Welch Two Sample t-test

data:  BUASCollege$GPA1 by BUASCollege$College
t = -1.2753, df = 38.772, p-value = 0.2098
alternative hypothesis: true difference in means between group AS and group BU is not equal to 0
95 percent confidence interval:
 -0.7143396  0.1619586
sample estimates:
mean in group AS mean in group BU 
         3.02381          3.30000 

The GPAs of those attending Business College (M = 3.02) and Arts & Sciences College (M = 3.30) were not statistically significantly different, t(38.78) = -1.28, ns

thesis %>% 
  drop_na(GPA1,College) %>%
  ggplot(aes(x = College, y = GPA1)) +
  geom_boxplot() +
  geom_jitter(width = .1) +
  theme_minimal() +
  labs(title = "GPA1 by College", x = "College", y = "GPA1")

3. Here is the difference between the GPA1 of students in Communications vs Accounting.
   

thesis %>% 
  filter(Major == "Account" | Major == "Comm") -> AccountCommMajor

t.test(AccountCommMajor$GPA1 ~ AccountCommMajor$Major)

    Welch Two Sample t-test

data:  AccountCommMajor$GPA1 by AccountCommMajor$Major
t = 0.95153, df = 5.297, p-value = 0.3827
alternative hypothesis: true difference in means between group Account and group Comm is not equal to 0
95 percent confidence interval:
 -0.7868789  1.7368789
sample estimates:
mean in group Account    mean in group Comm 
                3.675                 3.200 

The GPAs of Accounting Majors (M = 3.68) and Communications Majors (M = 3.20) were statistically significantly different, t(5.30) = .95, p > .05

thesis %>% 
  filter(Major == "Account" | Major == "Comm") %>% 
  ggplot(aes(x = Major, y = GPA1)) +
  geom_boxplot() +
  geom_jitter(width = .1) +
  theme_minimal() +
  labs(title = "GPA(1) in Acconting vs. Communications", x = "Major", y = "GPA")

4. This is the difference between Mood1 and Mood2 over time.
   

t.test(thesis$Mood1, thesis$Mood2, paired = T)

    Paired t-test

data:  thesis$Mood1 and thesis$Mood2
t = -2.1686, df = 40, p-value = 0.03611
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.80105415 -0.02821414
sample estimates:
mean of the differences 
             -0.4146341 

summary(thesis)

      Age            Sex              SelfEsteem        Mood1             Mood2            Major             College         
 Min.   :19.00   Length:43          Min.   :14.00   Min.   :-4.0000   Min.   :-4.0000   Length:43          Length:43         
 1st Qu.:20.25   Class :character   1st Qu.:23.50   1st Qu.:-1.0000   1st Qu.: 0.0000   Class :character   Class :character  
 Median :23.50   Mode  :character   Median :25.00   Median : 0.0000   Median : 0.0000   Mode  :character   Mode  :character  
 Mean   :24.07                      Mean   :24.44   Mean   :-0.2381   Mean   : 0.2381                                        
 3rd Qu.:26.00                      3rd Qu.:26.00   3rd Qu.: 1.0000   3rd Qu.: 1.0000                                        
 Max.   :41.00                      Max.   :29.00   Max.   : 3.0000   Max.   : 3.0000                                        
 NA's   :1                                          NA's   :1         NA's   :1                                              
      GPA1            GPA2          Home          
 Min.   :1.400   Min.   :2.20   Length:43         
 1st Qu.:2.725   1st Qu.:3.00   Class :character  
 Median :3.200   Median :3.45   Mode  :character  
 Mean   :3.117   Mean   :3.40                     
 3rd Qu.:3.675   3rd Qu.:4.00                     
 Max.   :4.000   Max.   :4.00                     
 NA's   :1       NA's   :1                        

Moods 1 and 2 were both highest around 0, (M = -.23) than at time 1 (M = .23), t(40) = -2.17, p < .05.

thesis %>% 
  pivot_longer(cols = c(Mood1, Mood2), names_to = "Time", values_to = "Mood") %>% 
  ggplot(aes(x = Time, y = Mood)) +
  geom_boxplot() +
  geom_jitter(width = .1) +
  theme_minimal() +
  labs(title = "Comparison of Mood1 and Mood2 over Time", x = "Mood1", y = "Mood2")

Warning: Removed 2 rows containing non-finite values (stat_boxplot).
Warning: Removed 2 rows containing missing values (geom_point).

5. This is the relationship between where students are from (Home) and what college they are in.
   

thesis %>%
  mutate(Home = as_factor(Home)) %>%
  mutate(College = as_factor(College)) %>%
  drop_na(Home, College) %>%                                
  ggplot(aes(x = Home,fill = College)) +
  geom_bar(position = "fill") +
  theme_minimal() +   
  coord_flip() +
  labs(title = "Relationship between Home and College",      
       x = "Home",
       y = "College")

table(thesis$College, thesis$Home)
chisq.test(thesis$College, thesis$Home)

There was no marginally statistically significant relationship between College and Home, chi-square(2) = .76, p = .68 ns.

6. This is the difference between the Self Esteem of students who came from different locations (Home).

thesis %>% 
  drop_na(Home, SelfEsteem) %>% 
  group_by(Home) %>% 
  summarize(Mean = mean(SelfEsteem), 
            "Std Dev" = sd(SelfEsteem),
            N = n())

NA

SelfEsteem_ANOVA <- aov(thesis$SelfEsteem~ thesis$Home)
summary(SelfEsteem_ANOVA)

            Df Sum Sq Mean Sq F value Pr(>F)
thesis$Home  2  15.76   7.879   1.043  0.362
Residuals   39 294.53   7.552               
1 observation deleted due to missingness

There were no statistically significant differences in Self Esteem by Home F(2, 39) = 1.043, ns.

thesis %>% 
  drop_na(Home,SelfEsteem) %>%
  ggplot(aes(x = Home, y = SelfEsteem)) +
  geom_boxplot() +
  geom_jitter(width = .1) +
  theme_minimal() +
  labs(title = "Difference in SelfEsteem", x = "Home", y = "SelfEsteem")