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?

QUESTION

What are the null and alternate hypotheses for YOUR research scenario?

H0:There is no difference between the Before scores and After scores.

H1:There is a difference between the Before scores and After scores.

#INSTALL REQUIRED PACKAGE
# install.packages("readxl")

library(readxl)

# IMPORT EXCEL FILE INTO R STUDIO
dataset <- read_excel("C:\\Users\\DELL\\Downloads\\A6R3.xlsx")
CALCULATE THE DIFFERENCE SCORES

Purpose: Calculate the difference between the Before scores versus the after scores.

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

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

QUESTION 1: Is the histograms symmetrical, positively skewed, or negatively skewed?

ANSWER: symmetrical.

QUESTION 2: Did the histogram look too flat, too tall, or did it have a proper bell curve?

ANSWER: Proper bell-shaped curve.

SHAPIRO-WILK TEST
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 > .05).

BOXPLOT

Check for any outliers impacting the mean.

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

QUESTION 1: How many dots are in your boxplot?

A) No dots.

B) One or two dots.

C) Many dots.

ANSWER: B) One or two 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: C) Far from the whiskers (lines of the boxplot).

QUESTION 3: Based on the dots and there location, is the data normal?

ANSWER: Based on the box plot, we cannot determine if the data is normal or abnormal.

DESCRIPTIVE STATISTICS

# Calculate the mean, median, SD, and sample size for each group.
# DESCRIPTIVES FOR BEFORE SCORES

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
# DESCRIPTIVES FOR AFTER SCORES
# You do not need to edit this code

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

Note: The Dependent t-test is also called the Paired Samples t-test.

There are no edits you need to make to the code.

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
DETERMINE STATISTICAL SIGNIFICANCE

If results were statistically significant (p < .05), continue to effect size section below. If results were NOT statistically significant (p > .05), skip to reporting section below.

IMPORTANT NOTE

Getting results that are not statistically significant does NOT mean you switch to Wilcoxon Sign Rank. The Wilcoxon Sign Rank test is only for abnormally distributed data — not based on outcome significance.

EFFECT SIZE FOR DEPENDENT T-TEST

Purpose: Determine how big of a difference there was between the group means.

# INSTALL REQUIRED PACKAGE
# install.packages("effectsize")

# LOAD THE PACKAGE
# Remove the hashtag to use the code.
library(effectsize)

# CALCULATE COHEN’S D
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]
QUESTIONS

QUESTION 1: What is the size of the effect?

ANSWER: very large

QUESTION 2: Which group had the higher average score?

ANSWER: The after training scores are higher.

Research Report on Results: Dependent t-test*

A dependent t-test was conducted to compare employees’ communication skills before and after taking a taining among 150 participants. Results showed that pre-training scores (M = 59.73333, SD = 7.966091) were significantly lower than post-training scores (M = 69.24, SD = 9.481653), t(150) = -23.285, p < .001. The effect size was Cohen’s d = -1.90, indicating a very large effect. These results suggest that the training improved the employees’ communication skills.