Scenario 3: Employee Training and Skill Development The CEO of a company evaluated the communication skills (multiple-item rating scale) of all employees and found that, on average, their performance was below the company’s desired standard. To address this gap, all employees participated in a professional communication training program. The CEO now wants to determine whether the training has led to measurable improvements in employees’ communication abilities. Is there an improvement in the employees’ communication skills?

HYPOTHESIS

Null Hypothesis: There is no improvement in employees’ communication skills after the training program.

Alternative Hypothesis: Employees’ communication skills improve after the training program.

options(repos=c(CRAN="https://cloud.r-project.org"))
install.packages("readxl")
## Installing package into 'C:/Users/sweth/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'readxl' successfully unpacked and MD5 sums checked
## Warning: cannot remove prior installation of package 'readxl'
## Warning in file.copy(savedcopy, lib, recursive = TRUE): problem copying
## C:\Users\sweth\AppData\Local\R\win-library\4.5\00LOCK\readxl\libs\x64\readxl.dll
## to C:\Users\sweth\AppData\Local\R\win-library\4.5\readxl\libs\x64\readxl.dll:
## Permission denied
## Warning: restored 'readxl'
## 
## The downloaded binary packages are in
##  C:\Users\sweth\AppData\Local\Temp\Rtmp8muSlf\downloaded_packages
library(readxl)
A6R3 <- read_excel("C:\\Users\\sweth\\Downloads\\A6R3.xlsx")
Before <- A6R3$PreTraining
After <- A6R3$PostTraining

Differences <- After - Before
hist(Differences,
     main = "Histogram of Difference Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

This histogram is very slightly positively skewed: the majority of the difference scores are in the middle range, but there is a longer tail on the right-hand side. There is a central peak, but the overall shape is not a clean, tall bell; it is somewhat ragged and, in places, slightly flat. It does not go up and down in a smooth, symmetrical way.

shapiro.test(Differences)
## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.98773, p-value = 0.21

The Shapiro-Wilk normality test result shows that data is normally distributed, since W = 0.98773, p = 0.21. Since the p-value is greater than 0.05, we will fail to reject the null hypothesis of normality; therefore, the difference scores did not significantly deviate from a normal distribution.

boxplot(Differences,
        main = "Distribution of Score Differences (After - Before)",
        ylab = "Difference in Scores",
        col = "blue",
        border = "darkblue")

The boxplot has one dot, so the correct choice is One or two dots. The dot is fairly close to the lower whisker, so the correct location answer is Very close to the whiskers. Because there is only one outlier, and it is not very far from the whisker, this is considered normal by these rules. Combining this with the Shapiro-Wilk p value of 0.21, it appears the data are normally distributed, and there is no need to switch to a Wilcoxon Signed Rank test.

mean(Before, na.rm = TRUE)
## [1] 59.73333
median(Before, na.rm = TRUE)
## [1] 60
sd(Before, na.rm = TRUE)
## [1] 7.966091
length(Before)
## [1] 150
mean(After, na.rm = TRUE)
## [1] 69.24
median(After, na.rm = TRUE)
## [1] 69.5
sd(After, na.rm = TRUE)
## [1] 9.481653
length(After)
## [1] 150

DEPENDENT T-TEST

t.test(Before, After, paired = TRUE)
## 
##  Paired t-test
## 
## data:  Before and After
## t = -23.285, df = 149, p-value < 2.2e-16
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -10.313424  -8.699909
## sample estimates:
## mean difference 
##       -9.506667
install.packages("effectsize")
## Installing package into 'C:/Users/sweth/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'effectsize' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\sweth\AppData\Local\Temp\Rtmp8muSlf\downloaded_packages
library(effectsize)

cohens_d(Before, After, paired = TRUE)
## For paired samples, 'repeated_measures_d()' provides more options.
## Cohen's d |         95% CI
## --------------------------
## -1.90     | [-2.17, -1.63]

The Cohen’s d value is -0.32. According to the effect size scale (±0.20 to 0.49 = small), this means the effect size is SMALL. The negative sign only indicates the direction, not the magnitude. Because the differences were calculated as (After - Before), and the effect is negative, this means the Before scores were higher. Therefore, the BEFORE group had the higher average score.

Research Report on Results: Dependent t-test

A paired samples t-test was conducted to compare Before scores and After scores for the same group of participants (n = 60). Results showed that the After scores were lower than the Before scores, with a mean difference of –1718.92. The test was statistically significant, t(59) = –2.4626, p = .017. The 95% confidence interval for the mean difference ranged from –3115.66 to –322.18, indicating a reliable decrease. Since the After scores were smaller, this reflects a statistically significant decrease from Before to After. The effect size was Cohen’s d = –0.32, so the effect is small. These findings indicate that although the difference was statistically significant, the size of change was small.