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?

Null Hypothesis (H₀): There is no difference in the mean scores between the Before and After conditions.

Alternative Hypothesis (H₁): There is a significant difference in the mean scores between the Before and After conditions.

DESCRIPTIVE STATISTICS AND NORMALITY CHECK 

library(readxl)
dataset <- read_excel("C:/Users/Poojitha Dibbamadugu/Downloads/A6R3.xlsx")

Before <- dataset$PreTraining
After <- dataset$PostTraining

Differences <- After-Before

hist(Differences,
     main = "Histogram of Difference Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "Purple",
     border = "black",
     breaks = 20)

# QUESTION 1: Is the histograms symmetrical, positively skewed, or negatively skewed?
# ANSWER: Symmetrical, not strongly skewed.

# QUESTION 2: Did the histogram look too flat, too tall, or did it have a proper bell curve?
# ANSWER: Too tall (sharp peak, high kurtosis).

shapiro.test(Differences)
## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.98773, p-value = 0.21
# QUESTION 1: Was the data normally distributed or abnormally distributed?
# If p > 0.05 (P-value is GREATER than .05) this means the data is NORMAL (continue with Dependent t-test).
# If p < 0.05 (P-value is LESS than .05) this means the data is NOT normal (switch to Wilcoxon Sign Rank).
# ANSWER: Normally distributed.-  p-value = 0.21 (> 0.05), so the differences follow a normal distribution.


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

# QUESTION 1: How many dots are in your boxplot?
# A) No dots.
# B) One or two dots. 
# C) Many dots.
# ANSWER: No dots.

# QUESTION 2: Where are the dots in your boxplot?
# A) There are no dots.
# B) Very close to the whiskers (lines of the boxplot).
# C) Far from the whiskers (lines of the boxplot).
#ANSWER: There are no dots.

# QUESTION 3: Based on the dots and there location, is the data normal?
#ANSWER: Data is normal (based on outlier check only).i.e Dependent t-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
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]
# QUESTION 1: What is the size of the effect?
# The effect means how big or small was the difference between the group averages.
# ± 0.00 to 0.19 = ignore
# ± 0.20 to 0.49 = small
# ± 0.50 to 0.79 = moderate
# ± 0.80 to 1.29 = large
# ± 1.30 to +   = very large
#ANSWER: A Cohen's D of 1.09 indicates the difference between the group averages was large. There was a meaningful and substantial effect 


 

# QUESTION 2: Which group had the higher average score?
# ANSWER: The After group had the higher average score (Mean = 69.24 vs. Mean = 59.73).
# Since After > Before, the training improved scores.

RESULT PARAGRAPH

A dependent t-test was conducted to compare scores before and after the intervention among 150 participants. Results showed that post-intervention scores (After) were significantly lower than pre-intervention scores (Before), t(149) = -23.29, p < .001. The mean difference was -9.51, with a 95% confidence interval ranging from -10.31 to -8.70. The effect size was Cohen’s d = -1.90, indicating a very large effect. These results suggest that the intervention led to a substantial decrease in scores from the Before to After condition.