Education

library(readxl)
mydata <- read_xlsx("./Skills.xlsx")
mydata <- as.data.frame(mydata)
head(mydata)

##   ID Time Course
## 1  1   59      A
## 2  2   50      A
## 3  3   45      A
## 4  4   55      A
## 5  5   35      A
## 6  6   28      A

Description:

• ID: ID of a person
• Time: Time spent solving a problem.
• Course: Type of course (A, B or C)

mydata$CourseF <- as.factor(mydata$Course)

library(dplyr)  # Loads the dplyr package for data manipulation

## 
## 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

mydata %>%      # Pipes the dataset to the next operation
  group_by(CourseF) %>%  # Groups observations by course
  summarise(
    n = n(),                    # Number of employees per course
    mean_time = mean(Time),     # Mean completion time
    sd_time = sd(Time),         # Standard deviation of completion time
    median_time = median(Time), # Median completion time
    min_time = min(Time),       # Minimum completion time
    max_time = max(Time)        # Maximum completion time
  )

## # A tibble: 3 × 7
##   CourseF     n mean_time sd_time median_time min_time max_time
##   <fct>   <int>     <dbl>   <dbl>       <dbl>    <dbl>    <dbl>
## 1 A          10      41.5   10.6         39.5       28       59
## 2 B          10      37     10.4         40.5       18       50
## 3 C          10      26.8    8.84        24         15       39

library(ggplot2)
ggplot(mydata, aes(x = Course, y = Time)) +
  geom_violin(fill = "grey90", alpha = 0.6, trim = FALSE) +
  geom_boxplot(width = 0.1, fill = "grey60", outlier.shape = 16) +
  labs(
    title = "Distribution of Problem-Solving Time Across Training Courses",
    x = "Training course",
    y = "Time required to solve the problem (minutes)"
  ) +
  theme_bw()

library(car)
leveneTest(mydata$Time, mydata$CourseF)

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  2  0.0643 0.9378
##       27

library(onewaytests)
welch.test(Time ~ CourseF, 
           data = mydata)

## 
##  Welch's Heteroscedastic F Test
## 
## data:  Time and CourseF
## F = 6.0276, num df = 2.000, denom df = 17.875, p-value =
## 0.009982

library(dplyr)
library(rstatix)

## 
## Attaching package: 'rstatix'

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

mydata %>%
  group_by(CourseF) %>%
  shapiro_test(Time)

## # A tibble: 3 × 4
##   CourseF variable statistic     p
##   <fct>   <chr>        <dbl> <dbl>
## 1 A       Time         0.946 0.618
## 2 B       Time         0.896 0.200
## 3 C       Time         0.889 0.166

results <- aov(Time ~ CourseF, 
               data = mydata)

summary(results)

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## CourseF      2   1135   567.3   5.724 0.00847 **
## Residuals   27   2676    99.1                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

library(effectsize)

## 
## Attaching package: 'effectsize'

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

eta_squared(results)

## For one-way between subjects designs, partial eta squared is
##   equivalent to eta squared. Returning eta squared.

## # Effect Size for ANOVA
## 
## Parameter | Eta2 |       95% CI
## -------------------------------
## CourseF   | 0.30 | [0.06, 1.00]
## 
## - One-sided CIs: upper bound fixed at [1.00].

interpret_eta_squared(0.30, rules = "cohen1992")

## [1] "large"
## (Rules: cohen1992)

pairwise.t.test(mydata$Time, g = mydata$CourseF,
                paired = FALSE,
                p.adj = "bonferroni")

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  mydata$Time and mydata$CourseF 
## 
##   A      B     
## B 0.9634 -     
## C 0.0081 0.0900
## 
## P value adjustment method: bonferroni