Scenario 3

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 AND LOAD REQUIRED PACKAGE

# install.packages("readxl")
library(readxl)
## Warning: package 'readxl' was built under R version 4.5.2

IMPORT EXCEL FILE INTO R STUDIO

dataset <- read_excel("C:/Users/Murari_Lakshman/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

You do not need to edit this code.

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

QUESTION

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 boxplot?
A) One or two dots.

QUESTION 2: Where are the dots in your boxplot?
A) Far away from the whiskers.

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 AND LOAD THE REQUIRED PACKAGE

# install.packages("effectsize")
library(effectsize)
## Warning: package 'effectsize' was built under R version 4.5.2

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 of -1.90 indicates the difference between the group averages was very large 

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 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.