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 between the Before scores and After scores.

ALTERNATE HYPOTHESIS (H1)

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

IMPORT EXCEL FILE

Import your Excel dataset into R to conduct analyses.

INSTALL REQUIRED PACKAGE

options(repos = c(CRAN = "https://cloud.r-project.org"))
install.packages("readxl")
## Installing package into 'C:/Users/N Geetha Shivani/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'readxl' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\N Geetha Shivani\AppData\Local\Temp\RtmpEj40w6\downloaded_packages

LOAD THE PACKAGE

library(readxl)

IMPORT EXCEL FILE INTO R STUDIO

dataset <- read_excel("C:\\Users\\N Geetha Shivani\\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 a histogram for difference scores to visually check skewness and kurtosis.

CREATE THE HISTOGRAMS

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

QUESTIONS

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

A)The histogram looks symmetrical.

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

A)The histogram has a proper bell-shaped curve.

SHAPIRO-WILK TEST

Check the normality for the difference between the groups.

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

QUESTIONS: .

QUESTION 1: Was the data normally distributed or abnormally distributed?

[NOTE: 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)].

A)The data is normally distributed because 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")

QUESTIONS:

QUESTION 1: How many dots are in your box plot?

A)One or two dots.

QUESTION 2: Where are the dots in your box plot?

A)Far away from the Whiskers(lines of the box plot).

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

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

[If there are no dots, the data is normal.

If there are one or two dots and they are CLOSE to the whiskers, the data is normal

If there are many dots (more than one or two) and they are FAR AWAY from the whiskers, this means data is NOT normal. Switch to a Wilcoxon Sign Rank.

Anything else could be normal or abnormal. Check if there is a big difference between the median and the mean. If there is a big difference, the data is not normal. If there is a small difference, the data is normal.]

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

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

After checking the difference between mean and median, there is a small difference, the data is normal. Hence, proceeding with dependent t-test.

DEPENDENT T-TEST

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

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.

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

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?

A)A Cohen’s D value of –1.90 represents a very large effect size, showing a substantial difference between the two group means.

QUESTION 2:Which group had the higher average score?

A)The after training scores are higher.

Research Report on Results:Dependent t-test

A dependent t-test was conducted to examine differences in communication skill scores before and after the training among 150 participants. The results showed that pre-training scores (M = 59.73, SD = 7.97) were significantly lower than post-training scores (M = 69.24, SD = 9.48), t(150) = –23.285, p < .001. The effect size was large (Cohen’s d = –1.90), indicating a substantial change between the two measurements. Overall, the findings demonstrate that communication skill scores increased following the training.