Research 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?

Purpose:

Used to test if there is a difference between Before scores and After scores (comparing the means).

NULL HYPOTHESIS (H0)

There is no difference between employees’ communication skills before and after the training.

ALTERNATE HYPOTHESIS (H1)

There is a difference between employees’ communication skills before and after the training.

IMPORT EXCEL FILE

Import your Excel dataset into R to conduct analyses.

INSTALL AND LOAD REQUIRED PACKAGE

chooseCRANmirror(graphics = FALSE, ind = 1) 
#install.packages("readxl")
library(readxl)

IMPORT EXCEL FILE INTO R STUDIO

A6R3<- read_excel("C:\\Users\\manit\\OneDrive\\Desktop\\A6R3.xlsx")

CALCULATE THE DIFFERENCE SCORES

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

Before <- A6R3$PreTraining
After <- A6R3$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)

QUESTION 1: Is the histograms symmetrical, positively skewed, or negatively skewed?
ANSWER: The histogram looks symmetrical.

QUESTION 2: Did the histogram look too flat, too tall, or did it have a proper bell curve?
ANSWER: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 1: Was the data normally distributed or abnormally distributed?
ANSWER: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")

QUESTION 1: How many dots are in your boxplot?
Ans)One or two dots.

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

QUESTION 3: Based on the dots and there location, is the data normal?
Ans)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 abnormal. 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 abnormal. If there is a small difference, the data is normal.

DESCRIPTIVE STATISTICS

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 the 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 REQUIRED PACKAGE

install.packages("effectsize")
## Installing package into 'C:/Users/manit/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\manit\AppData\Local\Temp\RtmpUlFPJB\downloaded_packages
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

Answer the questions below as a comment within the R script:

QUESTION 1: What is the size of the effect?
Ans)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?
Ans)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 training 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.