DEPENDENT T-TEST & WILCOXON SIGN RANK

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

NULL HYPOTHESIS (H0)

There is no difference between the Pre training and Post training

ALTERNATE HYPOTHESIS (H1)

There is a difference between the Pre training and Post training

#install.packages("readxl")

library(readxl)

dataset <- read_excel("C:\\Users\\navya\\Downloads\\A6R3.xlsx")

CALCULATE THE DIFFERENCE SCORES

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)

# DIRECTIONS: Answer the questions below directly in your code.

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

# QUESTION 2: Did the histogram look too flat, too tall, or did it have a proper bell curve?
# ANSWER: The histogram appears irregular and flattened which does not form a perfect bell curve

SHAPIRO-WILK TEST

shapiro.test(Differences)

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

# DIRECTIONS: Answer the questions below directly in your code.

# QUESTION 1: Was the data normally distributed or abnormally distributed?
# 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).
# ANSWER:
# Since p value is 0.21 where p>0.05 it is normally distributed so we can continue with dependent t-test.

BOXPLOT

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

# DIRECTIONS: Answer the questions below directly in your code.

# 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 there location, is the data normal?
# 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.
# ANSWER: The dot is closed to the Whisker. In Shapiro Wilk test as p=0.21 which is >0.05 where it is normal. So, we can continue with dependent t-test.

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

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

EFFECT SIZE FOR DEPENDENT T-TEST

Purpose: Determine how big of a difference there was between the group means.

#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? Since Cohen’s d value is 1.90 >1.30, effect size is very large.

QUESTION 2: Which group had the higher average score? YOUR ANSWER: Since the effect size was negative,before scores were higher than after scores.

Research Report on Results: Dependent t-test

Goal: Write a paragraph summarizing your findings

#A dependent t-test was conducted to compare pre-training and post-training scores among the 150 participants. The results showed that post-training scores (69.24,SD=9.48) were significantly higher than pre-training scores(M=59.73,SD=7.97),indicating improvement after training. The analysis revealed a statistically significant difference between the two points, t(149)=-23.29, p<0.001, with an average increase of 9.51 points from before to after training. The effect size was Cohen’s d=1.90, indicating a very large effect, meaning that the training produced a strong and meaningful improvement in participant scores.

WILCOXON SIGN RANK TEST

wilcox.test(Before, After, paired = TRUE)

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  Before and After
## V = 43, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0

DETERMINE STATISTICAL SIGNIFICANCE

EFFECT SIZE FOR WILCOXON SIGN RANK TEST

INSTALL REQUIRED PACKAGE

#install.packages("rstatix")
#install.packages('coin')

LOAD THE PACKAGE

library(rstatix)

## 
## Attaching package: 'rstatix'

## The following objects are masked from 'package:effectsize':
## 
##     cohens_d, eta_squared

## The following object is masked from 'package:stats':
## 
##     filter

CALCULATE RANK BISERIAL CORRELATION (EFFECT SIZE)

df_long <- data.frame(
  id = rep(1:length(Before), 2),
  time = rep(c("Before", "After"), each = length(Before)),
  score = c(Before, After)
 )

wilcox_effsize(df_long, score ~ time, paired = TRUE)

## # A tibble: 1 × 7
##   .y.   group1 group2 effsize    n1    n2 magnitude
## * <chr> <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 score After  Before   0.861   150   150 large

QUESTION

Q1) What is the size of the effect? Answer: The Rank biserial correlation was 0.861 so it is between ± 0.50 to 1.00 = very large
Q2) Which group had the higher average score? The effect size was positive which is 0.861, which indicates that the After scores were higher than the Before scores.So, After group had the higher average scores.

SUMMARY OF RESULTS

Goal: Write a paragraph summarizing your findings

A Wilcoxon signed rank test was conducted to compare before and after scores intervention between 150 participants. Mean scores were Md_before=60 and Md_after=69.5. The test revealed a statistically significant difference between two time points, V=43,p<0.001. These results indicate that there was a significant increase in scores from before to after. The effect size was a rank bivariate correlation of 0.861, indicating a very large effect.

DESCRIPTIVE STATISTICS

NAVYA SRI MULUKUNTLA

2025-11-19

DEPENDENT T-TEST & WILCOXON SIGN RANK

NULL HYPOTHESIS (H0)

ALTERNATE HYPOTHESIS (H1)

CALCULATE THE DIFFERENCE SCORES

HISTOGRAM

SHAPIRO-WILK TEST

BOXPLOT

DESCRIPTIVE STATISTICS

DESCRIPTIVES FOR BEFORE SCORES

DESCRIPTIVES FOR AFTER SCORES

DEPENDENT T-TEST

DETERMINE STATISTICAL SIGNIFICANCE

EFFECT SIZE FOR DEPENDENT T-TEST

LOAD THE PACKAGE

CALCULATE COHEN’S D

QUESTIONS

Research Report on Results: Dependent t-test

Goal: Write a paragraph summarizing your findings

WILCOXON SIGN RANK TEST

DETERMINE STATISTICAL SIGNIFICANCE

EFFECT SIZE FOR WILCOXON SIGN RANK TEST

INSTALL REQUIRED PACKAGE

LOAD THE PACKAGE

CALCULATE RANK BISERIAL CORRELATION (EFFECT SIZE)

QUESTION

SUMMARY OF RESULTS

Goal: Write a paragraph summarizing your findings