t-test

library(readxl)
mydata <- read_xlsx("./Midterm.xlsx")

mydata <- as.data.frame(mydata)

head(mydata, 3)

##   ID Points Group
## 1  1    9.0     1
## 2  2    9.0     1
## 3  3    7.5     1

Description:

• ID
• Points: Number of points achieved on Midterm exam
• Group: 1 (English course), 2 (Slovenian course)

mydata$GroupF <- factor(mydata$Group,
                      levels = c(1, 2),
                      labels = c("English", "Slovenian"))

head(mydata, 3)

##   ID Points Group  GroupF
## 1  1    9.0     1 English
## 2  2    9.0     1 English
## 3  3    7.5     1 English

library(ggplot2)

Eng <- ggplot(mydata[mydata$GroupF == "English",  ], aes(x = Points)) +
              theme_linedraw() + 
              geom_histogram(binwidth = 2, colour = "black", fill = "darkred") +
              ylab("Frequency") +
              ggtitle("English course") +
              scale_x_continuous(breaks = c(1:15), 
                                 limits = c(0, 16))

Slo <- ggplot(mydata[mydata$GroupF == "Slovenian",  ], aes(x = Points)) +
             theme_linedraw() + 
             geom_histogram(binwidth = 2, colour = "black", fill = "darkblue") +
             ylab("Frequency") +
             ggtitle("Slovenian course") +
             scale_x_continuous(breaks = c(1:15), 
                                limits = c(0, 16))

library(ggpubr)
ggarrange(Eng, Slo,
          ncol = 2, nrow = 1)

## Warning: Removed 2 rows containing missing values or values outside the scale
## range (`geom_bar()`).
## Removed 2 rows containing missing values or values outside the scale
## range (`geom_bar()`).

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:car':
## 
##     recode

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(rstatix)

## 
## Attaching package: 'rstatix'

## The following object is masked from 'package:stats':
## 
##     filter

mydata %>%
  group_by(GroupF) %>%
  shapiro_test(Points)

## # A tibble: 2 × 4
##   GroupF    variable statistic     p
##   <fct>     <chr>        <dbl> <dbl>
## 1 English   Points       0.972 0.416
## 2 Slovenian Points       0.962 0.101

library(psych)

## 
## Attaching package: 'psych'

## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha

## The following object is masked from 'package:car':
## 
##     logit

describeBy(mydata$Points, mydata$GroupF)

## 
##  Descriptive statistics by group 
## group: English
##    vars  n mean   sd median trimmed  mad min max range  skew kurtosis
## X1    1 40 8.93 2.92      9       9 2.22 1.5  15  13.5 -0.26     -0.1
##      se
## X1 0.46
## ---------------------------------------------------- 
## group: Slovenian
##    vars  n mean  sd median trimmed  mad min max range skew kurtosis
## X1    1 51 9.18 2.5      9    9.15 2.22   3  15    12  0.1     0.12
##      se
## X1 0.35

library(car)
leveneTest(mydata$Points, mydata$GroupF)

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  1  0.8523 0.3584
##       89

t.test(mydata$Points ~ mydata$GroupF,
       var.equal = TRUE,
       alternative = "two.sided")

## 
##  Two Sample t-test
## 
## data:  mydata$Points by mydata$GroupF
## t = -0.44187, df = 89, p-value = 0.6597
## alternative hypothesis: true difference in means between group English and group Slovenian is not equal to 0
## 95 percent confidence interval:
##  -1.3822629  0.8793217
## sample estimates:
##   mean in group English mean in group Slovenian 
##                8.925000                9.176471

library(effectsize)

## 
## Attaching package: 'effectsize'

## The following object is masked from 'package:psych':
## 
##     phi

## The following objects are masked from 'package:rstatix':
## 
##     cohens_d, eta_squared, omega_squared

effectsize::cohens_d(mydata$Points ~ mydata$GroupF,
                     pooled_sd = TRUE)

## Cohen's d |        95% CI
## -------------------------
## -0.09     | [-0.51, 0.32]
## 
## - Estimated using pooled SD.

library(effectsize)
interpret_cohens_d(0.09, rules = "sawilowsky2009")

## [1] "tiny"
## (Rules: sawilowsky2009)