HYPOTHESIS

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

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

Execution:

library(readxl)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
library(ggpubr)
library(rstatix)    
## 
## Attaching package: 'rstatix'
## The following object is masked from 'package:stats':
## 
##     filter
library(tidyr)
dataset <- read_excel("/Users/patel777/Desktop/Week6/A6R3.xlsx")
Before <- dataset$PreTraining
After <- dataset$PostTraining

Differences <- After - Before

HISTOGRAM

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

QUESTIONS

Q1: Is the histograms symmetrical, positively skewed, or negatively skewed?

A)The histogram looks symmetrical.

Q2: 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

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

QUESTION

Q1: 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

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

QUESTIONS

Q1:How many dots are in your boxplot?

A)One or two dots.

Q2:Where are the dots in your boxplot?

A)Far away from the whiskers.

Q3: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

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

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.

CALCULATE COHEN’S D

##install.packages("effectsize")   
packageVersion("effectsize")     
## [1] '1.0.1'
library(effectsize)
## 
## Attaching package: 'effectsize'
## The following objects are masked from 'package:rstatix':
## 
##     cohens_d, eta_squared
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

Q1: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

Q2: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 computed to compare the differences in the employees’ communication skills before and after taking a taining among 150 employees. Results indicated that the participants’ mean scores on the test before the training (M = 59.73333, SD = 7.966091) were significantly lower than the participants’ mean scores on the test after the training (M = 69.24, SD = 9.481653), t(150) = -23.285, p < .001. The effect size, Cohen’s d = -1.90, suggests a very large effect. Overall, the findings from this test suggest that the training was able to increase the employees’ communication skills.