DEPENDENT T-TEST

This analysis is for RESEARCH SCENARIO 3 from assignment 6. It tests to compare Communication Skills Score before and after taking a training.

Hypotheses

  • H0 (Null Hypothesis): There is no improvement in communication skills after the training
  • H1 (Alternate Hypothesis): There is a measurable improvement in communication skills

Result paragraph

A dependent t-test was conducted to compare Communication Skills Score before and after having a defensive driving course among 150 participants. Results showed that post-training Skills Scores (M = 69.24, SD = 9.48) were significantly higher than pre-course scores (M = 59.73, SD = 7.97), t(149) = -23.285, p < .001. The effect size was Cohen’s d = -1.90, indicating a large effect. These results suggest that the training significantly enhanced Communication Skills.

R code and Analysis

CHECK NORMAL DISTRIBUTION

IMPORT EXCEL FILE Import your Excel dataset into R to conduct analyses.

# INSTALL REQUIRED PACKAGE

# install.packages("readxl")

# LOAD THE PACKAGE

library(readxl)

# IMPORT EXCEL FILE INTO R STUDIO

dataset <- read_excel("//apporto.com/dfs/SLU/Users/minhoku_slu/Downloads/A6R3.xlsx")

CALCULATE THE DIFFERENCE SCORES Purpose: Calculate the difference between the Before scores versus the after scores.

# RENAME THE VARIABLES

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)

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

  • ANSWER: The histogram is negatively skewed.

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

  • ANSWER: The histogram have a proper bell 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 was normally distributed.

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?

      1. No dots.
      1. One or two dots.
      1. Many dots. # ANSWER:B

  • QUESTION 2: Where are the dots in your boxplot?

      1. There are no dots.
      1. Very close to the whiskers (lines of the boxplot).
      1. Far from the whiskers (lines of the boxplot).

  • ANSWER:B

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

  • ANSWER: 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

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 * p< 0.001

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?

  • YOUR ANSWER: 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?

  • YOUR ANSWER: After group has higher score.