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# DifferenceLogic.r
# Statypus Academy: Two Sample Population Means
# Course Resources: r.statypus.org
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# --- SECTION 1: THE INDEPENDENT CASE (Two Separate Hills) ---

# 1. Prepare the data from the built-in Iris set
seto <- iris$Sepal.Length[iris$Species == "setosa"]
vers <- iris$Sepal.Length[iris$Species == "versicolor"]

# 2. Plot the "Two Hills"
# This plot shows two distinct populations with an observable gap.
plot(density(seto), xlim=c(4, 8), ylim=c(0, 1.2),
     main="Scenario A: Independent (The Two-Hill Logic)",
     xlab="Sepal Length (cm)", lwd=2)

lines(density(vers), col="blue", lwd=2)

# 3. Marking the Centers (The peaks of the hills)
abline(v=mean(seto), lty=2)
abline(v=mean(vers), col="blue", lty=2)

# STOP: Use this plot to complete Task 1 on your handout.


# --- SECTION 2: THE PAIRED CASE (The Hill of Change) ---

# 1. We simulate a "PM measurement" for the same Setosa plants.
# We assume each flower grew a small amount (mean = 0.3cm).
set.seed(45)
pm_measure <- seto + rnorm(50, mean=0.3, sd=0.1)

# 2. THE PAIRED MAPPING: Subtract FIRST to find individual change
change <- pm_measure - seto

# 3. Plot the "One Hill of Change"
# We are plotting the story of growth, not the flowers themselves.
plot(density(change), xlim=c(-0.2, 0.8),
     main="Scenario B: Paired (The Single-Hill Logic)",
     xlab="Individual Growth (cm)", lwd=2, col="darkgreen")

# 4. The Null Marker (Zero Change)
# If the Day was uneventful, the hill would be centered here.
abline(v=0, lty=3, col="red", lwd=2)

# STOP: Use this plot to complete Task 2 on your handout.