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# Assignment 6 — Research Scenario 3
# Training: Pre vs Post Communication
# DEPENDENT T-TEST & NORMALITY CHECK
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# NULL HYPOTHESIS (H0)
# There is no difference between the PreTraining scores and PostTraining scores.
# ALTERNATE HYPOTHESIS (H1)
# There is a difference between the PreTraining scores and PostTraining scores.
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# IMPORT EXCEL FILE
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# Load required package
# If never installed, remove the hashtag before the install code.
# If previously installed, leave the hashtag in front of the code.
# install.packages("readxl")
library(readxl)
# Import your Excel dataset
dataset <- read_excel("A6R3.xlsx")
Before <- dataset$PreTraining
After <- dataset$PostTraining
# Difference scores: After minus Before
Differences <- After - Before
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# HISTOGRAM OF DIFFERENCE SCORES
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hist(Differences,
main = "Histogram of Difference Scores",
xlab = "After - Before",
ylab = "Frequency",
col = "blue",
border = "black",
breaks = 20)
# QUESTION 1: Is the histogram symmetrical, positively skewed, or negatively skewed?
# ANSWER: It look nearly symmetrical.
# QUESTION 2: Did the histogram look too flat, too tall, or did it have a proper bell curve?
# ANSWER: It resembled a proper bell curve, not too flat or too peaked.
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# SHAPIRO-WILK NORMALITY TEST
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shapiro.test(Differences)
##
## Shapiro-Wilk normality test
##
## data: Differences
## W = 0.98773, p-value = 0.21
## From the output:
## Shapiro-Wilk normality test
## W = 0.98773, p-value = 0.21
# QUESTION: Was the data normally distributed or abnormally distributed?
# If p > 0.05 this means the data is NORMAL (use Dependent t-test).
# If p < 0.05 this means the data is NOT normal (switch to Wilcoxon Sign Rank).
# ANSWER: The data were normally distributed (W = 0.988, p = 0.210 > .05),
# so it is appropriate to use a Dependent t-test.
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# BOXPLOT OF DIFFERENCE SCORES
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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?
# A) No dots.
# B) One or two dots.
# C) Many dots.
# ANSWER: B
# QUESTION 2: Where are the dots in your boxplot?
# A) There are no dots.
# B) Very close to the whiskers (lines of the boxplot).
# C) Far from the whiskers (lines of the boxplot).
# ANSWER: B
# QUESTION 3: Based on the dots and their location, is the data normal?
# - If there are no dots, or only one/two close to the whiskers, data is likely normal.
# - Many dots far from the whiskers = likely NOT normal.
# ANSWER: The boxplot did not show problematic/extreme outliers,
# which is consistent with the Shapiro-Wilk result indicating normal data.
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# DEPENDENT T-TEST (PAIRED SAMPLES T-TEST)
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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
## From the output:
## 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 p < .05 → statistically significant difference.
# If p > .05 → NOT statistically significant.
# Here, p-value < .001 (reported as < 2.2e-16), so:
# The difference between PreTraining and PostTraining scores IS statistically significant.
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# EFFECT SIZE FOR DEPENDENT T-TEST (COHEN'S D)
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# INSTALL REQUIRED PACKAGE (if not already installed)
# 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]
## From the Rq3 HTML output:
## Cohen's d | 95% CI
## --------------------------
## -1.90 | [-2.17, -1.63]
# QUESTION 1: What is the size of the effect?
# ± 0.00 to 0.19 = ignore
# ± 0.20 to 0.49 = small
# ± 0.50 to 0.79 = moderate
# ± 0.80 to 1.29 = large
# ± 1.30 and above = very large
# ANSWER:
# Cohen’s d was -1.90, which is a VERY LARGE effect size.
# This indicates a very large difference between the pre- and post-training scores.
# QUESTION 2: Which group had the higher average score?
# With the way we calculated differences (After minus Before):
# - If the mean difference is POSITIVE → After scores were higher.
# - If the mean difference is NEGATIVE → Before scores were higher.
# From the output: mean difference = -9.506667 (negative).
# ANSWER:
# The Before (PreTraining) scores were higher on average than the After (PostTraining) scores.
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# RESEARCH REPORT ON RESULTS: DEPENDENT T-TEST
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# A dependent t-test was conducted to compare communication scores before and after the
# training among 150 participants. Results showed that post-training scores were
# significantly different from pre-training scores, t(149) = -23.29, p < .001, with a
# mean difference of -9.51 points (After – Before). The 95% confidence interval for the
# mean difference ranged from -10.31 to -8.70. The effect size was very large,
# Cohen’s d = -1.90, indicating a substantial change in scores across time.